IAPQR Transactions - A UGC-CARE Listed Journal

Abstract
Gravitational Wave (GW) signals of astrophysical origin are typically weak. This is because gravity is a weak force, weakest among the four forces we know of. In order to detect GW signals, one must make differential measurements of effective lengths less than thousand-th of the size of a proton. In spite of the detectors achieving extraordinary sensitivity, the detector noise typically overwhelms the signal, so that GW signals are deeply buried in the data. The challenge to the data analyst is of extracting the GW signal from the noise, that is, first deciding whether a signal is present or not then if present, measuring its parameters. However, in the search for Coalescing Compact Binary (CBC) signals, shortduration non-Gaussian noise transients (glitches) in the detector data significantly affect the search sensitivity. χ² discriminators are therefore employed to mitigate their effect. We show that the underlying mathematical structure of any χ²  is a vector bundle over the signal manifold P, that is, the discriminator and the full vector bundle comprising the subspaces S and the base manifold P constitute the χ² discriminator. We show that this structure paves the way for constructing effective χ² discriminators against different morphologies of glitches. Here we specifically demonstrate our method on blip glitches, which can be modelled as sine-Gaussians, which then generates an optimal χ² statistic for blip glitches. manifold traced out by the signal waveforms in the Hilbert space of data segments D. The χ² is then defined as the square of the L_² norm of the data vector projected onto a finite-dimensional subspace S (fibre) of D chosen orthogonal to the triggered template waveform. Any such fibre leads to a χ² discriminator and the full vector bundle comprising the subspaces S and the base manifold P constitute the χ² discriminator. We show that this structure paves the way for constructing effective χ² discriminators against different morphologies of glitches. Here we specifically demonstrate our method on blip glitches, which can be modelled as sine-Gaussians, which then generates an optimal χ² statistic for blip glitches.

Author
Sanjeev Dhurandhar: Inter University Centre for Astronomy and Astrophysics, Pune, India.
 

Abstract
Star formation scenario in galaxies of various morphological types is significant in the sense that it characterises the structure formation in the universe. Star
formation Rate (SFR) is an important index to study the above phenomenon. But direct measurement of SFR is im- possible as one has to accurately count stars formed per year in a galaxy. In this paper, we investigate the star formation by first forming homogeneous clusters of the galaxies using Gaussian Mixture Model Based Clustering technique (GMMBC) applied on a large data set of galaxies in the Local Volume (LV) and then predicting the star formation rate (SFR) within each cluster using Bayesian LASSO and Bayesian Linear-Regression Analysis techniques. Our investigation reveals five homogeneous clusters of galaxies having different star formation scenaria. Two of them are massive, disc-dominated, highly rotating, forming stars with highest rates and free from the influence of environment while other two have lower SFR, probably turbulence resisting the process of star formation. The remaining one is a cluster of dwarf galaxies where star formation is affected by high density environment. Our cluster specific predictive model uses a number of relevant auxiliary predictor variables in order to improve on the power in predicting SFR for newly discovered galaxies. We cross validate the SFRs in the various coherent clusters and compare with other (physical) model-based SFR values ( 𝑆𝐹𝑅 , say) assumed to be reasonable representative of true SFRs derived and discussed by various authors.

Authors
Soumojit Das: Institute for Social Research, University of Michigan, Ann Arbor, MI, USA
Tanuka Chattopadhyay: University of Calcutta, Kolkata, India
Asis K. Chattopadhyay: University of Calcutta, Kolkata, India
Partha Lahiri: University of Maryland, College Park, USA
 

Abstract:
In this article, ‘Improved Warning Limits control chart to monitor the number of defectives in a sample’ (IWL-d) chart is proposed. It is numerically verified that, IWL-d chart significantly reduces the out of control ‘Average Time to Signal’ (ATS) as compared to the d chart, ‘Modified Control Chart with Warning Limits to monitor the number of defectives in a sample’ (MCCWL-d) proposed by Rattihalli et al. (2021-2022) and ‘Improved Control Chart’ (ICC-d) proposed by Gadre and Rattihalli (2022).

Author
M. P. Garde  Retd. Professor, Savitribai Phule Pune University, Pune, India
 

Abstract:
This paper proposes an innovative framework to deliver Artificial Intelligence (AI) education in Bengali, aligning with two key directives of India’s National Education Policy (NEP) 2020: (a) promoting education in regional languages, and (b) expanding AI literacy for all students. Despite growing interest, AI-related resources in Bengali remain scarce, and existing language models demonstrate limited translation accuracy for technical content. To address this gap, we present a dual-LLM solution—one fine-tuned for AI domain knowledge and the other for high-quality English–Bengali machine translation. The framework proposes to employ Retrieval Augmented Generation (RAG) to maintain an up-to-date knowledge base and improve response quality. We also explore architectural choices and design considerations to ensure robustness, accuracy, and educational relevance. Our approach aims to democratize AI education by making it accessible and engaging for Bengali-speaking learners, fostering inclusion and equal opportunity in technology education. The paper also has a case study where performance of LLMs has been evaluated using in context learning. The context has been provided in the form of textbooks available in Bengali.

Authors
Susita Koner Department of Computer Science, Bangabasi Morning College, University of Calcutta, Kolkata,  
Saptarsi Goswami Department of Computer Science, Bangabasi Morning College, University of Calcutta, Kolkata,
Amlan Chakrabarti A.K. Choudhury School of IT, University of Calcutta. Kolkata, India
 

Abstract:
Statistical process control (SPC) is essential for preserving quality and reducing variation in production and service operations. SPC relies on control charts, which graphically show process performance over time. However, interpreting these charts can be challenging, particularly when trends are overlooked. Then, pattern recognition (PR) enhances and automates SPC analysis by identifying non-random patterns that indicate specific problems or different control chart patterns (CCPs) seen in the process behavior. Multivariate statistical process control (MSPC) is an advanced extension of traditional SPC that monitors multiple correlated variables simultaneously, providing a comprehensive view of process stability. This paper presents a multivariate control chart pattern recognition model using support vector machine (MCCPR-SVM) to recognise control chart patterns (CCPs) in multivariate process. Support vector machine (SVM) was chosen for its effectiveness in handling high-dimensional data and distinguishing CCPs in multivariate process. Synthetic data was generated by taking three variables for normal (NR), increasing trend (IT), decreasing trend (DT), systematic (SY) and cyclic (CY) patterns. The model was evaluated using confusion matrices and it has been observed that the model exhibits high performance and overall accuracy of the model is 97.2%.

Authors
KHIMYA TINANI  Department of Statistics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, 
SARAH PATHAN  Department of Statistics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, 
MEGHA SIKAWAT Department of Statistics, Sardar Patel University, Vallabh Vidyanagar, Gujarat,
 

Abstract
This is a story of Y2 K (yr 2000) in Indian industry. An engine manufacturing company faced the problem of low Lubrication Oil Pressure (LOP) of a six-cylinder diesel engine. The engine under study was used for power generation application. In this paper, we describe how planned Design of Experiment (DOE) was used successfully to resolve the issue of low LOP. Planning or designing an experiment is a well-known technique in statistical literature. What is new is a successful application in resolving the low LOP issue. Hence, we thought of reporting the study in the paper. The paper is written in a tutorial format and would be useful in other studies.

Authors :
Avinash Dharmadhikari and Prakash Ganesh Mandke : Pune, Maharashtra, India
 

Abstract
It is well known that the amount of information contained in a ranked set sample is larger than that contained in a simple random sample of same size. In this paper, varentropy properties of the ranked set sample are considered. The expression for varentropy of different modifications of ranked set sampling such as median ranked set sampling and moving extreme ranked set sampling are derived. The stochastic comparison of varentropy based on different modifications of ranked set samples are made. The upper bound and recurrence relation for varentropy are also presented. A dispersion index based on Kullback-Leibler divergence using ranked set sample is also discussed.

Authors :
Manoj Chacko : Department of Statistics, University of Kerala, Trivandrum, India 
Varghese George : St. Stephen's College, Pathanapuram, Kerala, India
 

Abstract
Prediction of the optimum time for software release has been an exploring research area in recent times. In this article, we propose a new formulation of the software testing problem in discrete set-up using the sizebiased concept and incorporate the Bayesian technique for finding out the optimum testing time through a trade-off between the total cost of testing the software and the attained bug size. We also show how this cost is related with reliability of the software, the reliability so computed being also determined in an easy way of just finding whether a bug is present or not.The model so developed has been tested on a simulated example, as well as verified with an actual commercial software. It is expected that our modeling will work on any software where data have been collected using a discrete framework. We conclude with possible extensions to our work in future.

Authors :
Ashis Kumar Chakraborty : Statistical Quality Control & Operations Research, Indian Statistical Institute, India
Anisha Das : Department of Statistics, Florida State University, USA
 

Abstract
Astronomical Data specifically those from Globular Clusters and Young Massive Clusters are usually contaminated with outliers and missing data, detection of which might be very tedious in case the data size is considerably large. Moreover, for skewed multivariate data, Principal Component Analysis (PCA) is not an appropriate approach for dimension reduction. The Robust Principal Component Analysis along with the Missing Value Imputation Technique using the MissForest algorithm is applied to a data from the Harris catalogue {Harris 2010} of globular clusters and the results are demonstrated with some striking features of the clusters.
 

Author :
Abisa Sinha Adhikary : Amity University, Kolkata, India
 

Abstract
In this article, we have proposed runs rule-based control charts,namely, Improved Synthetic Control Chart’ (ISCC-x̄) and ‘Improved Group Runs Control Chart’(𝐼𝐺𝑅𝐶𝐶 −X̄) to detect shift in the process mean of a univariate production process. In zero state and also in steady state, it is numerically illustrated that 𝐼𝑆𝐶𝐶 −X̄ and 𝐼𝐺𝑅𝐶𝐶 −X̄ perform significantly better as compared to the related charts.

Authors :
M.P. Gadre : Shriram Institute of Information Technology, Paniv
S. S. Venegurkar : Prof. Ramkrishna More Arts Commerce Science College, Akurdi, Dist. Pune
R.V. Latpate : Department of Statistics, SPPU, Pune
 

Abstract
Nonlinear equations are solved in a wide range of domains, including applied mathematics, computer science, and engineering. Iterative solutions are the only way to solve non-trivial situations of these equations.Thus, the creation of an effective and efficient iterative technique is crucial and can have a good effect on the process of determining the numerical solution of numerous real-world issues. The goal of this study is to create a novel, and effective iterative approach to solving nonlinear equations. The recently designed iterative approach is based on the classical Secant method for resolving nonlinear equations, which are investigated in various scientific and engineering domains. The nonlinear equation root finding approach that has been developed has an order of convergence of 1.84 and requires three beginning points instead of just two. By the use of multiple benchmark problems with varying iterations, the newly created method's convergence was demonstrated and its performance was compared with the traditional Secant method. According to the results, the newly designed method outperformed the conventional Secant method in terms of iterations and order of convergence. This provides support for the recently discovered method's credibility and offers hope for future study that will further perfect it.

Authors :
Inderjeet and Rashmi Bhardwaj : University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Dwarka, Delhi , India
 

Abstract
An automatic procedure to perform sub-clustering on large samples is presented. At each iteration, the most diverse cluster is sub-clustered, and the global diversity of the new classification is compared to the previous one. The process stops if no improvement is found. The key to our procedure is the use of a quantitative measure of diversity, called the Leinster-Cobbold index, that takes into account the similarity between clusters. While this procedure has been successfully applied on a large sample of spectra of galaxies, we illustrate its efficiency with two examples in this paper.

Authors:
Hugo Chambon , Didier Fraix-Burnet : Univ. Grenoble-Alpes, CNRS, IPAG, Grenoble, France.
 

Abstract
Accelerated life testing procedure has become more prominent among researchers for the inspection of product reliability as it shortens testing time and reduces cost through harsher-than usual testing conditions. In this paper, we propose a two-stage accelerated life test sampling plan when lifetimes of a product follow Weibull distribution. The truncation time is divided into three parts, to perform a life test under usual, first level, and second level acceleration conditions. It is assumed that the product failure mechanism remains the same during accelerated inspection as that in usual testing conditions. The resultant plans specified by four parameters– single sample size and three acceptance numbers, are not only available in two to three options, but they also safeguard consumer as well as producer in comparison to the constant accelerated life test sampling plan for Weibull distribution. To assure certain quantile life while giving two predetermined levels of accelerations, the probability of acceptance of lot in each stage is a conditional probability of failure. We construct tables of optional optimal life test sampling plan design parameters for 25th and 50th quantile using R codes. R codes are provided for user-tailored construction of plans. The usage of plan is demonstrated using a real-life example.

Authors:
D.P. Raykundaliya and Jyoti Divecha : Department of Statistics, Sardar Patel University, Vallabh Vidyangar, Gujarat-India
Sanjay Christian : Department of Management, JG University, Ahmedabad, Gujarat-India
 

Abstract
This paper presents a systematic procedure for the construction and selection of Mixed Sampling Plans (MSP) using the Intervened Random Effect Poisson Distribution (IRPD) as the baseline model. The sampling plans are formulated using the Quick Switching System (QSS-1) as the attribute-based plan, incorporating parameters such as the Acceptable Quality Level (AQL) and the Maximum Allowable Percent Defective (MAPD). Decision-making tables are developed to facilitate the easy selection of appropriate sampling plans under different quality conditions. In the current framework, a Gamma prior distribution is assumed for the IRPD model. However, this assumption can be relaxed in future studies by considering alternative prior distributions such as the Inverse Gaussian, Beta-Binomial, and others to enhance model flexibility. Additionally, the Graphical Evaluation and Review Technique (GERT) can be used to analyse and visualise the flow and structure of the developed sampling plans. Beyond acceptance sampling, the IRPD model shows promise for broader applications, including queuing theory, stochastic modelling, and other areas involving random intervention effects.

Authors:
R. Vijaya Kumar , T. Venkatesan : Department of Statistics, St. Joseph’s College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India.
 

Absract
Reliability engineering methods can be used to figure out how reliable different systems are and how outside and inside factors affect system reliability. The study aims to develop a healthcare system for diagnosing diseases in healthcare, figuring out the factors influencing a patient's state, and so on, which should be set up per reliability engineering’s rules and principles. First, a mathematical model of the system or item being studied is made based on what the reliability analysis says needs to be done. In a study of a system's dependability, the structural function is a common way to show how it works. Unfortunately, this mathematical representation requires beginning data with comprehensive specifications. Medical error analysis’s initial healthcare data is ambiguous and insufficiently stated. In this study, a unique approach was used for system development’s mathematical modelling on the basis of ambiguous and insufficiently specified inputs from COVID-19 patients. Structural function helps compute different reliability indices and metrics employed in reliability engineering.

Authors:
Naresh Kumar : Goswami Ganesh Dutt Sanatan Dharam College, Palwal (Haryana), India
Amrita Agrawal : Saraswati Mahila Mahavidyalaya, Palwal (Haryana), India 

Absract
This article examines the linkage between productivity and employment closely, both in global and Indian contexts. The goal is to illuminate the dilemma confronting policymakers in contemporary times regarding this relationship.

Author:
Partha Pratim Mitra : Former Principal Labour & Employment Adviser Ministry of Labour, Government of India
 

Abstract
Water-supply network systems are an indispensable social infrastructure in modern society. Therefore, water supply utilities require high system robustness towards both accidents and natural disasters. In this study, we define a work performance indicator (WPI) to quantitatively measure the robustness of water supply utilities (WSU) in Japan. The WPI was defined from three perspectives: reliability, safety, and sustainability. Based on actual data expressing the work performance of Japanese WSU from 1980 to 2018, we illustrate the numerical results of WPIs to determine their regional characteristics. We applied statistical data analysis techniques such as multivariate regression analysis, cluster analysis, and principal component analysis to calculate the WPIs and investigate the historical and regional characteristics and trends of WSU in Japan during the investigated period. These approaches can be applied to the design and improvement of natural disaster mitigation policies, such as those focused on earthquakes in Japan.

Authors:
M.L.U.K. Piyasena And T. Oyama
National Graduate Institute for Policy Studies (GRIPS), 7-22-1 Roppongi, Minato-ku, Tokyo, Japan
 

Abstract
The objective of our study is to discern the aberrant functional and structural brain connectivity in mental disorder patients, ultimately to develop quality therapeutic strategies. We developed a bivariate mixed-effects model to ascertain the differences in brain connectivity between healthy individuals and affected patients. The model accounts for subject-specific variability and heteroscedastic errors, enabling it to handle correlations within and across different connectivity measures. Such comprehensive accounting allowed us to identify notable connectivity differences between groups. To validate the performance of our model, we conducted a simulation study. Then, we applied our method to neuroimaging data for late-life depression patients, assessing biomarker identification compared to univariate mixed-effects models.

Authors:
Pei-Shan Yen : Division of Epidemiology and Biostatistics, University of Illinois at Chicago, USA
Weihan Zhao : Division of Epidemiology and Biostatistics, University of Illinois at Chicago, USA
Dulal K. Bhaumik : Division of Epidemiology and Biostatistics and Department of Psychiatry, University of Illinois at Chicago, USA
 

Abstract
The current note discusses the analysis of data on a response variable collected at different time points, when the same experimental design is used at each time point. The mean response depends on a number of factors as well as on the time point at which it is measured. The parameters of the model are estimated using the generalized least squares method. A simulation study is conducted and the estimate of the variance-covariance matrix of the parameter estimators is obtained using the Jackknife technique.

Authors :
S.P. Mukherjee : Retd. Centenary Professor, Department of Statistics, University of Calcutta, India
Manisha Pal : Department of Statistics, St. Xavier’s University, Kolkata, India
 

Abstract
The reliability measure in reversed time such as reversed hazard rate and mean waiting time are recently employed for modeling and analysis of lifetime data. In the present paper, we introduce these reliability functions in terms of copulas and study their properties. Further, these copula based reliability measures are employed to study the dependence between random variable.

Authors :
P. G. Sankaran And N. Unnikrishnan Nair
Department of Statistics, Cochin University of Science and Technology, Kerala, India
 

Abstract
In this article, we considered the problem of survival analysis with competing causes of failure. For analysing competing risks survival data, we used parametric cause specific hazard regression model by assuming Rayleigh distribution as baseline model. The estimates of unknown parameters and cumulative cause specific hazard function are obtained through maximum likelihood as well as Bayesian methods of estimation. The Bayes estimates are obtained based on non-informative prior under two types of loss functions such as squared error loss function and LINEX loss function. For the comprehensive comparison of methods of estimation, we conduct a Monte Carlo simulation study. For the validation of proposed model, a bone marrow transplant real data is considered.

Authors :
Habbiburr Rehman : Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry, India
Navin Chandra : Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry, India
Aquil Ahmed : Department of Statistics & Operations Research, Aligarh Muslim University, India
Anupam Kumar : Department of Statistics, PUC, Mizoram University, Aizawl, India
 

Abstract
The total number of failures and the failure rate are the parameters to be estimated for assessing the performance of the Software. The Binomial type and exponential class software reliability growth model is considered and the Bayes estimators of the parameters are derived in this research paper. A non-informative prior for the total number of failures and gamma prior for Failure rate are assumed to obtain the Bayes estimator for the parameters. Using the Monte Carlo simulation technique, the performance of the derived Bayes estimators is studied by comparing with the corresponding maximum likelihood estimators. The proposed Bayes estimators are recommended for use with appropriate selection of prior constants.

Authors :
Rajesh Singh : Department of Statistics, Sant Gadge Baba Amravati University, Amravati
Kailash R. Kale : Department of Statistics, Ghulam Nabi Azad Arts, Commerce, and Science College, Barshitakli, Dist-Akola
Pritee Singh : Department of Statistics, Institute of Science, Nagpur
 

Abstract
The present article reflects on a few issues regarding the on-going trend in theory and applications of Statistics. The aspect of applications and the problems with sample surveys in several domains have been emphasized.

Author :
S. P. Mukherjee
Mentor, Indian Association for Productivity, Quality and Reliability.
 

Abstract
In this article we have derived the best linear unbiased estimator (BLUE) of the parameters ?2 and ?2 involved in the Morgenstern type bivariate exponential distribution by ranked set sampling (RSS). Also we have evaluated the BLUE's of ?2 and ?2 involved in the Morgenstern type bivariate exponential distribution by concomitants of ranked set sampling for some specific values of the sample size n. The efficiency comparison of the proposed estimators with that of the estimators using concomitants of order statistics and modified ranked set sampling is also made.

Authors : 
N.K. Sajeev Kumar : Department of Statistics, University College, Trivandrum, Kerala, India.
Sumi A.R. : Department of Statistics, University College, Trivandrum, Kerala, India.
 

Abstract
In this article, modification of the ‘Alternated Charting Statistic’ (ACS) scheme with the traditional Hotelling c 2 chart to control the mean vector of a bivariate normal process is proposed. With the bivariate ACS scheme in use, the two quality characteristics (X, Y) are controlled in an alternating fashion. The proposed control chart is called as ‘Weighed Alternated Charting Statistic’ (WACS) control chart to monitor the mean vector by using variable inspection. In WACS chart, which one of the two quality characteristic is to be inspected, is explained in detail. While defining the rule of the status of the process, the weights of each of the two quality characteristics are considered. It is numerically illustrated that the WACS chart performs better as compared to the c 2chart and ACS chart.

Author :
M.P. Gadre
Shriram Institute of Information Technology, Solapur, India.
 

Abstract
Raw Material Charging Station (RMCS) is one of the most important infrastructures in steel industry and is used to load and carry crushed iron ore to furnace. Breakdown behaviour of the RMCS was observed for a certain period, and its future behaviour was predicted using a reliability model. For improvement of availability however, a Six sigma approach was used. Initial focus was to reduce the repair time per month in order to make RMCS more available for use and save the financial loss due to unavailability of the furnaces to produce steel. This study discovers a way to simultaneously improve reliability, reduce repair time and thereby improve availability of the RMCS. The study also generalises an approach for improving reliability and availability for any mechanised repairable system using six sigma methodologies.

Authors :
Subrata Rath : SQC & OR Unit, Indian Statistical Institute, Pune, India.
Ashis Kumar Chakraborty : SQC & OR Unit, Indian Statistical Institute, Kolkata, India.
Subhashis Chatterjee : Mathematics Department, IIT(ISM) Dhanbad, India.
 

Abstract
In this paper, the problem of estimation of parameters and prediction of order statistics from a future sample based on upper k-record values arising from a two parameter Weibull distribution is considered. The maximum likelihood estimators and the Bayes estimators are obtained based on observed upper k-record values. Bayesian point predictors of the order statistics from a future sample and its two-sided equi-tailed prediction intervals are also derived. Finally, a numerical illustration is considered for exemplifying the proposed inferential procedures developed in this paper.

Authors :
Laji Muraleedharan and Manoj Chacko
Department of Statistics, University of Kerala, Trivandrum, India.
 

Abstract
Peritoneal Dialysis (PD) is a process of replacing kidney function that cleans waste product from the blood and removes extra fluid from the body. In most cases, PD process is slowed down by a peritoneal membrane infection called peritonitis, which is the leading cause of morbidity and dialysis failure among PD patients in developing countries. Early prevention of this infection is very crucial for the success of PD in resource-poor countries. Using a prospective study from Pietersburg provincial hospital in South Africa, we have investigated potential social, demographic, and biological risk factors that contribute to the first episode of peritonitis. Both semiparametric Cox proportional hazards and two parametric Accelerated Failure Time (AFT) survival models were fitted to the data and compared for their performance. Weibull AFT model fits better to the peritonitis longitudinal dataset followed by exponential AFT and Cox PH models. Among PD cohort of patients, 60.38% of peritonitis infections were recorded over the follow-up period with the majority of peritonitis infections are recorded among females (65.4%) and rural dwellers (65.7%) with (62.6%) of black Africans which shows a higher risk of developing peritonitis. Patients with no running water and electricity in the house who are living in rural areas with a low level of hemoglobin and shorter duration on PD are associated with a higher risk (hazard) of developing the first episode of peritonitis infections in the study area.

Authors :
Yehenew G Kifle
Department of Mathematics and Statistics, University of Maryland Baltimore County, USA

Tshepo F. Maja
Department of Statistics and Operations Research, University of Limpopo, South Africa

Ramon A. Tamayo
Pietersburg Limpopo Provincial Hospital, South Africa
 

Abstract
The first author was involved in a study with the goal of enhancing the quality and productivity of pregnancy/birth of children under “Suprajanan Scheme”, developed and initiated by Manashakti Research Centre (MRC) at Lonavla, near Mumbai, India in 2010. After implementation of the said scheme and collection of relevant data, the author had access to the data and accordingly, he analysed the same for statistical analysis. In order to derive and apply exact inference theory for meaningful elaborate analysis and valid conclusions, he collaborated with the second author and together, they developed the necessary results. It amounted to the formulation of inference problems involving four parameters p, a, b, c; 0 < p < 1 involved in four independent Bernoulli/Binomial experiments having P(H) = (p, ap, bp, cp); 0 < p, ap, bp, cp < 1 respectively. The applications and conclusions are explained with reference to the contexts.

Authors :
Avinash Dharmadhikari
Pune. India.
 

Bikas K Sinha
Koltata, India

Abstract
The present paper discusses the modelling and analysis of recurrent event data with competing risks in the presence of covariates. We propose an extension of the proportional cause-specific hazards model based on averaged counting process and averaged at-risk set process of recurrent events. The regression parameters are estimated using a partial likelihood approach. Asymptotic properties of the proposed estimators are established. Simulation procedures are carried out to assess the finite sample properties of the proposed estimators. The proposed method is applied to reallife data.

Authors :
P. G. Sankaran
Department of Statistics, Cochin University of Science and Technology Kerala

Sisuma M.S.
Department of Statistics, Cochin University of Science and Technology Kerala
 

Abstract:
In this article, for univariate processes, we propose improved control charts useful to detect shift in the process mean and to identify increases in the fraction nonconforming. These modified control charts are intended to reduce the out-of-control ‘Average Time to Signal’ (ATS). When the charting statistic is inside the control limits, but close to control limits (between the warning and the control limits), the process may not be operating properly. In such situations, to have substantial/additional information about quality of the process, in this article, we propose ‘Modified Control Chart with Warning Limits’ (MCCWL) to detect shifts in the process mean, increases in fraction nonconforming and to monitor shifts in the mean vector. It is modified in the sense that a rule is defined to stop the sampling and to declare the process as out of control. The corresponding expression for Average Run Length (ARL) is obtained. The design parameters are obtained under ‘Average Time to Signal’ (ATS) criterion. The proposed charts namely, ????? ? ??, ????? ? ??,????? ? ??? are shown to perform better than their competitors considered. Abstract: In this article, for univariate processes, we propose improved control charts useful to detect shift in the process mean and to identify increases in the fraction nonconforming. These modified control charts are intended to reduce the out-of-control ‘Average Time to Signal’ (ATS). When the charting statistic is inside the control limits, but close to control limits (between the warning and the control limits), the process may not be operating properly. In such situations, to have substantial/additional information about quality of the process, in this article, we propose ‘Modified Control Chart with Warning Limits’ (MCCWL) to detect shifts in the process mean, increases in fraction nonconforming and to monitor shifts in the mean vector. It is modified in the sense that a rule is defined to stop the sampling and to declare the process as out of control. The corresponding expression for Average Run Length (ARL) is obtained. The design parameters are obtained under ‘Average Time to Signal’ (ATS) criterion. The proposed charts namely, ????? ? ??, ????? ? ??,????? ? ??? are shown to perform better than their competitors considered.

Authors :
R. N. Rattihalli
Retd. Professor, Shivaji University, Kolhapur

M. P. Gadre
Shriram Institute of Information Technology, Paniv, District Solapur

R. A. Patel
Karnatak University, Dharwad
 

Abstract
In the process of preventing possible cyber-crimes through social media, a new research paradigm named Proactive Forensics has evolved. As a part of such research effort, this paper attempts to match profiles of two members in a social network as a measure of compatibility between two persons. Profile matching efforts made so far include; matching job profile with candidate profile to choose “right man for the right job”, matching profiles of same person from two different social nets like Facebook and LinkedIn and to ascertain that they belong to the same person and even matching of two different Genome profiles. However, this paper tries to identify whether a friendship request on a social net can be accepted on the basis of a matching value generated by comparing the features of two profiles. For the purpose of matching, this paper provides two measures of closeness between two profiles; first a measure of the degree of exact match of feature values and secondly a composite distance measure of different feature wise distances. This composite measure has been termed as a static measure of friendship. A modified Jacardian similarity and standard Cosine similarity have been used for final measure of closeness between two profiles. In addition, it has been found that many features, used for matching, give rise to different types of hierarchies. New distance measures have been developed for matching such hierarchic structures. It has also been proved that such new measures are valid distance measures.

Authors :
Puspendu Biswas
Software Development Department, IGT Solutions Pvt. Ltd., Gurgaon

Aditya Bagchi
Computer Science Department, Ramakrishna Mission Vivekananda Educational & Research Institute, Belur Math, Howrah
 

Abstract
In the class of two-level non-regular designs, Plackett-Burman ([14], 1946) designs have a special place. These designs have been widely used as screening designs because of their relative simplicity of use. Wang and Wu ([16],1995) observed that these designs possess certain hidden projection properties which are bestowed by the complexity of their partial aliasing relationships. They attributed the  success of Hamada and Wu’s ([9],1992) strategy for entertaining and estimating twofactor interactions from Plackett-Burman (PB) type designs to the hidden projection property.
In this paper, we have used the hidden projection property of the 24-run PB design to propose an alternative to the design suggested by Mclean and Anderson ([13],1984). The proposed design performs better in terms of increased degrees of freedom efficiency and reduced run size. We have also drawn non-isomorphic interaction graphs making D and Ds efficiency as the underlying criterion.

Authors :
Renu Kaul
Department of Statistics, Lady Shri Ram College for Women (University of Delhi), New Delhi

Sanjoy Roy Chowdhury
Department of Statistics, Lady Shri Ram College for Women (University of Delhi), New Delhi
 

Abstract
In this paper by using fraction conforming probabilities p1 and p2, we introduce Multivariate Process Capability Indices (MPCIs) ( 1) ( 2 ) and p p pk p MC MC which measures potential capability and actual capability respectively for multivariate non-normal processes. Computing aspects of p( p1) MC and  pk ( p2 ) MC are discussed in detail considering hyper rectangular specification region. Two cases of multivariate non-normal processes are considered. While constructing MPCIs, in the first case it is assumed that process variables are independent and in the second case it is assumed that process variables are linearly related. In the second case Principal Component Analysis is used to compute point estimate and interval estimate of proposed MPCIs. Real life problems are given for illustration of proposed MPCIs with their interpretations.

Authors :
Kailas Govinda Khadse
School of Mathematical Sciences, M. J. College (Autonomous), Jalgaon

Ramkrishna Lahu Shinde
School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon

Abstract
Taguchi’s ([8], 1987) robust parameter design, is a very useful technique for reducing variation and improving product’s quality. However, in some applications, his approach leads to unnecessary expensive experiments. Alternatively, one can use combined arrays by modelling the response itself rather than the expected loss for Orthogonal Fractional Factorial Designs.
In this paper, we have exploited the non-orthogonal column structure of the 12 run Plackett-Burman (PB) design to generate non-orthogonal combined arrays.

Authors :
Renu Kaul
Department of Statistics, Lady Shri Ram College for Women (University of Delhi), New Delhi

Sanjoy Roy Chowdhury
Department of Statistics, Lady Shri Ram College for Women (University of Delhi), New Delhi
 

Abstract
Timber components are very popular due to its flexibility in use and therefore, widely used in bridges and building constructions, rail tracks and supply electricity throughout the world and in Australia. The main reason of this choice is for their high strength per unit weight, low cost and excellent durability. Reliability of these components is extremely important because a failure of these components may cause loss of money, loss of properties, injuries or even loss of lives. Reliability depends on various factors such as species of the timber, structural dimensions in design, environmental condition, human factors in installation, operations and maintenance. In general, the timber structure failures are due to the loss of load bearing capacity from the decrease in peripheral dimensions at or below ground level and loss of strength of timber fibre affecting bending resistance. Soil factors and related decays reduce the diameter and the strength of timber component affecting the safety in operation and service. Rotting of fibre can be from centre to outward or outward to centre by accelerating fungal and insect (termite) attack affecting reliability, availability, maintainability and safety of infrastructure assets. This paper is on investigating soil factors for modelling in ground decay and estimating parameters for failure distribution of timber poles. Real life data from electricity supply company in Australia have been used for modelling and validation. Results from this investigation can be used in optimal decision in maintenance and replacements for reducing the life cycle costs and risks of in-service failure of timber poles and infrastructure assets in similar environment.

Authors :
Anisur Rahman
Griffith University, Gold Coast campus, Southport, Australia

Gopinath Chattapadhyay
Federation University, Victoria, Australia
 

Abstract
We contemplate an experimental situation which deals with a 2-factor quadratic response involving, in its model expectation, the mean term, both the linear  effects parameters, and both the quadratic effects parameters as well as the product term parameter. We assume the errors to be homoscedastic and uncorrelated. Our intention is to conduct a saturated design [SD] - using a subset of six distinct but suitably chosen design points in an appropriately defined factor space. Further to this, we wish to achieve maximum precision in joint estimation of the last three [quadratic effects] parameters. It is known beforehand that these three effect(s)/interaction(s) are likely to be non-negligible. We examine the flexibility to the extent that an experimenter can make a choice of an SD, retaining information on the three remaining effects/interactions as well. We use the D-optimality criterion and deal with a continuous design set-up. At the end, we also discuss about A-optimality criterion.

Authors :
Bikas K Sinha
Indian Statistical Institute, Kolkata.

Sobita Sapam
Manipur University, Canchipur [Imphal], Manipur.

Nripes Kumar Mandal
Calcutta University, Kolkata.

Abstract
The growth of the tertiary sector helped India to move on a higher growth pedestal. The present paper tries to explore the regional variation in female employment in the tertiary sector post liberalization. For the sake of the analysis, the states were classified under six zones. The percentage of female main and female marginal workers in the tertiary sector across the states were first analyzed to understand the level of interregional and intraregional variation in female employment in the tertiary sector across the states. The Modified Lilien Index was then used to understand the pace of change in female employment post liberalization across the zones. Lastly a multivariate regression was run to identify the factors behind such regional variation in female employment in the tertiary sector. The paper  concluded that the regional variation in female employment could not be captured properly through some macroeconomic aggregates. Introduction of vocational training for women along with a change in state policies are required for the reduction of such regional variation.

Author :
Dyuti Chatterjee
The Bhawanipur Education Society College, Kolkata
 

Abstract
Scheffé ([12],1958) introduced models of different degrees to represent the response function in a mixture experiment. He also introduced designs for the estimation of the model parameters. Later, several authors discussed the problem of finding optimum designs, especially for quadratic and cubic models. In this paper, we consider the problem of designing an optimal experiment for the purpose of performing one or more hypothesis tests in a quadratic mixture model with three components. We use the Bayesian decision theoretic approach for the purpose.

Authors :
N. K. Mandal
Former Professor, Department of Statistics, University of Calcutta

Manisha Pal
Department of Statistics, University of Calcutta
 

Abstract
Six Sigma was born with a disciplined problem-solving approach called D M A I C (Define, Measure, Analyse, Improve and Control) way back in 1979. The approach is data-intensive requiring statistical orientation and is used for defect reduction. Effect of such defect reduction is visible in the increased profit margin. This approach was a little silent on the waste accumulation in as-is complicated processes. Accumulated waste has direct impact on the cash flow of an organization and usually lean approach is adopted to optimise process flow to reduce, if not eliminate waste in any process. Hence, a new approach was initiated to adapt lean methodology to create better flow in the processes while continuing delivering Six Sigma results. Such approach is known as Lean Six Sigma (LSS). LSS is process flow intensive, requiring more of Industrial Engineering, Operations Research and lean orientation. Results derived from Six Sigma and Lean Six Sigma are well appreciated worldwide across the type and scale of the organizations. However, question started brewing on why the defects and waste are available in any organization in the first instance. This question designated both the Six Sigma and Lean Six Sigma approaches as reactive problem solving initiatives and gave birth of another very important initiative, named Design for Six Sigma (DFSS), to prevent defects and waste in any product and process, in its launch itself. This process is more domain discipline intensive, requiring discovery, invention and innovation. All these approaches together make more sense in business and unfortunately literature is little silent where these approaches are synchronised to leverage the business results for an organization. This paper is an attempt to create a model to integrate all these three approaches with adequate flexibility of interconnectivity within the approach elements for the overall sustainable, predictable and desirable business results. A case is also used to demonstrate the implementation of the mode.

Authors :
Subrata Pal
Shriram Institute for Industrial Research, 19, University Road, Delhi-110007, India

Ashis Kumar Chakraborty
Statistical Quality Control and Operations Research unit, Indian Statistical Institute

Subhashis Chatterjee
Department of Mathematics and Computing, IIT (ISM), Dhanbad
 

Abstract
The problem studied here involves choice of optimum designs for estimation of a full set of treatment effects contrasts in a block design (BD) setup, when positional effects may also be present, besides treatment and block effects. The experimenter is not sure about which of the two models, viz. a block design model or a row-column design model is appropriate. Using weights on the optimality criteria in the two set-ups based on prior knowledge, robust designs are investigated.

Author :
Madhura Mandal
Vivekananda Mahavidyalaya, Burdwan, West Bengal
 

Abstract
This article analyzes the level of precision of estimates of gross value added as per Annual Survey of Industries by examining the relative standard errors associated with the estimates. Annual trend in the estimates of gross value added at the level of state and industrial category is also studied to see if there exist any apparent fluctuations. Further, the article cross-validates the annual growth rates of production of manufacturing sector as assessed by the Index of Industrial Production by comparing the same with the growth rates based on Annual Survey of Industries.

Author :
G. C. Manna
Former Director General Central Statistics Office and National Sample Survey Office, Government of India Currently, Professor, Institute for Human Development & Senior Adviser, NCAER.

Abstract
Harris Extended Log-Kumaraswamy Distribution and its specialized form namely, the Marshall-Olkin Log-Kumaraswamy Distribution (MOLKw) is introduced and studied in this paper. We have given explicit form for the probability density function and the hazard rate function is derived and its shape properties are studied. Expressions for cumulative distribution function, quantiles and survival function are obtained. Method of maximum likelihood estimation is used for estimation of unknown parameters of the new distribution. The new model is applied on two real data sets on survival times of cancer patients and another data set on carbon fibre strength in the context of reliability studies. The stress strength analysis is carried out with respect to the new model and a simulation study is conducted to estimate the average bias, mean square error, coverage probability etc. for different parameter values.

Authors :
K. K. Jose
Department of Statistics, St.Thomas College, Palai, Arunapuram.

Jisha Varghese
Mahatma Gandhi University, Kottayam, Kerala, India.

Abstract
In some production processes, observations related to the quality characteristics of the process are independent. Under this set up, we propose the ‘Multivariate Unit and Group Runs control chart for mean vector’ (MV-UGR-M). It is verified that, the MV-UGR-M gives a significant reduction in the out-of-control ‘Average Time to Signal’ (ATS) in the zero state, as well in the steady state as compared to the ‘Multivariate Synthetic control chart for Mean vector’ (MV-Syn-M) chart, the ‘Multivariate Group Runs control chart for Mean vector’ (MV-GR-M) and the ‘Multivariate Modified Group Runs control chart for Mean vector’ (MV-MGR-M) charts.

Authors :
M.P. Gadre
Department of Statistics, Savitribai Phule Pune University, Pune.

V.C. Kakade
Department of Statistics, Tuljaram Chaturchand College, Baramati.

Abstract
In this paper we use firms’ data to study the effects of financial development on total factor productivity of India’s manufacturing sector between 1990 and 2018. We find evidence that financial development has significantly enhanced firm-level TFP in the sector. The evidence is stronger when micro indicators of financial development are used. The firms in Indian private sector need better access to the banking system, while the firms in the government sector and the foreign sector reveal the need for accessing the capital market. We find a significant relationship between financial development and industry-level TFP growth when controlling for time, and industry-time fixed effects. Our results are both statistically and economically significant. Our results are robust to different samples and specifications. Our results suggest that policies favoring financial development in India should be pursued further in order for the largest democracy in the world to advance its economic growth.

Author :
Manoj Kumar
SP Jain School of Global Management, Singapore.

Abstract
 The objective of this review paper is to summarize some of the well-known methods used in various stages of a pattern recognition system. Pattern recognition has become more and more popular and important to us and it induces attractive attention coming from wider areas. The general processing steps of pattern recognition are discussed, starting with the pre-processing, then the feature extraction, and classification. In this paper we have reviewed methods used in pattern recognition. This review paper introduces the basic concepts of pattern recognition, different methods used for pattern recognition like statistical and structural techniques, template matching, neural network and provides the understanding of various methods and related algorithms for classification.

Authors :
Khimys S. Tinani
Department of Statistics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, India.

Deepa H. Kandpal
Department of Statistics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, India.

Abstract
Asset Management is focused on realisation of value from assets through managing risk and opportunity. ISO standard for asset management ISO55000, 2014 stipulates effective control and governance of assets for desired balancing act of cost, performance and risk. This paper aims to study the maintenance and capital expenditure problems. It proposes how to balance cost, performance and risk for asset management. Decisions need to be based on performance and risk in addition to costs based on whole of life are supported by international standards for asset management. Option analysis and informed decision-making are proposed considering life cycle costs. Recent trend with industries is to align with latest international standards for asset management. Asset management in heavy haul rail network focuses on this by realisation of value from assets through managing risk and opportunity. Model for total cost of maintenance was developed covering risk costs associated with undetected surface/ subsurface cracks causing rail breaks and derailments and wear loss due to gauge face lubrication problems and intervention costs in inspections and interventions using progressive rail grinding and solar powered electric lubricators with remote performance monitoring. Illustrative examples are used to show how actions in inspection and subsequent rail grinding for controlling rolling contact fatigue (RCF) along with gauge face lubrication for controlling wear can be achieved in heavy haul railway. This maintenance and capital investment policy and decisions based on life cycle cost models can be used as reference for capital expenditure (capex) and operational expenditure (opex) balancing in any industry in general and heavy haul in particular.

Author :
Gopinath Chattopadhyay
School of Science Engineering and Information Technology, Federation University Northways Road, Churchill, PO Box 3191, Gippsland Mail Centre, Vic 3841.

Abstract
In reliability studies, the failure of individuals or items may be due to more than one causes or factors. These risk factors in some sense compete for the failure of the experimental units. Analysis of data in these circumstances is called competing risks analysis. In this paper, we consider the analysis of competing risk data under progressive type-II censoring by assuming the number of units removed at each stage is being random and follows a binomial distribution. Bayes estimators are obtained by assuming the population under consideration follows an exponential distribution. A simulation study is carried out to study the performance of different estimators derived in this paper. A real data set is also used for illustration.

Authors :
Manoj Chacko
Department of Statistics, University of Kerala Trivandrum 695 581, India.

Rakhi Mohan
Department of Statistics, University of Kerala Trivandrum 695 581, India.

Abstract
In this article, an acceptance sampling inspection plan for variable is discussed when the quality characteristic follows some non-normal distributions, viz., the exponential, Lindley, xgamma or Akash distribution. In this plan, the lot quality is to be measured by the lot mean (
). The plan parameters have been obtained by the two point approaches: the acceptable quality level (AQL) and the limiting quality level (LQL) or the rejectable quality level (RQL). For the given producer’s risk () and consumer’s risk (), the plan parameters: sample size () and acceptance number () are determined for different choices of AQL and LQL. A comparison study has been made in terms of the sample size () and an example is provided to illustrate the performance of the proposed plan

Authors :
Harsh Tripathi
Department of Statistics, Central University of Rajasthan, Rajasthan, India.

Sudhansu S. Maiti
Department of Statistics, Visva-Bharati University, Santiniketan, India.

Shovan Biswas
Department of Statistics, Visva-Bharati University, Santiniketan, India.

Mahendra Saha
Department of Statistics, Central University of Rajasthan, Rajasthan, India.

Abstract
This paper introduces a new generalization of the exponentiated rectangular distribution namely, Marshall-Olkin exponentiated rectangular distribution and studied its various properties. Also we illustrated empirically the potentiality of the new family by applying to real data sets. Applications in autoregressive time series modeling and stress-strength analysis are also considered. A simulation study is carried out to study the behaviour of estimates. Sample path properties of the newly developed time series models are also discussed.

Author :
E.S. Sindhu
Department of Statistics, Kuriakose Elias College, Mannanam, Kerala, India.

Sophia P. Thomas
Department of Statistics, St,Thomas College, Pala, Kerala, India.

Jiju Gillariose
Department of Statistics, St,Thomas College, Pala, Kerala, India.

Abstract
In this paper we introduce a new family of distributions namely Marshall Olkin Exponential Power (MOEP) distribution and its extensions. The advantage of studying this new family of distributions is the wide use of the model with respect to various data sets obtained from different areas. Some statistical and reliability properties of the new family of distributions are discussed. The method of maximum likelihood estimation is used to estimate the unknown parameters. The obtained results are validated using some real data set and it is shown that the new family provides a better fit than its base distributions. The stress strength reliability analysis is also carried out. Average mean square error, average confidence length, coverage probability etc. are computed using simulated data. Using the proposed model we develop autoregressive process with minification structure. We further extend the new distribution to obtain the Harris generalized exponential power distribution and some of its properties are studied.

In this paper we introduce a new family of distributions namely Marshall Olkin Exponential Power (MOEP) distribution and its extensions. The advantage of studying this new family of distributions is the wide use of the model with respect to various data sets obtained from different areas. Some statistical and reliability properties of the new family of distributions are discussed. The method of maximum likelihood estimation is used to estimate the unknown parameters. The obtained results are validated using some real data set and it is shown that the new family provides a better fit than its base distributions. The stress strength reliability analysis is also carried out. Average mean square error, average confidence length, coverage probability etc. are computed using simulated data. Using the proposed model we develop autoregressive process with minification structure. We further extend the new distribution to obtain the Harris generalized exponential power distribution and some of its properties are studied.

Authors :
K.K. Jose
Department of Statistics and Biostatistics, St. Thomas College Pala, Arunapuram.

Albin Paul
Mahatma Gandhi University, Kottayam, Kerala, India.

Abstract
The Mukherjee-Islam model is commonly used as a simple life time distribution to assess system reliability. We have introduced a location parameter ? (i.e. a time before which failure can’t occur) which makes it a more useful failure distribution than the existing ones. It has been shown to represent appropriate lower tail of the distribution of random variables having fixed lower bound. This study presents reliability computations and probability weighted moment estimation for this model. A comparative analysis is carried out between three-parameter finite range model and some existing bathtub shaped curve fitting models. Maximum likelihood estimation method has also been applied. Key words and Phrases: Reliability, Location parameter, Finite range failure model, Probability weighted moment, Comparative analysis.

Authors :
Showkat Ahmad Lone
Department of Statistics & Operations Research, Aligarh Muslim University, India. 

A. Islam
Department of Statistics & Operations Research, Aligarh Muslim University, India.

Ahmdur Hrahman
Department of Statistics & Operations Research, Aligarh Muslim University, India.

Abstract
Statistical analysis of standby systems with more than two units has received little attention because of mathematical intricacies involved in analyzing them. Also, such systems have been studied assuming the lifetime and repair time of the units to be independent. The present article is an attempt to study certain inferential aspects of a three unit hot standby system with dependent structure, assuming quadrivariate exponential distribution for the lifetimes of online unit, standby units and the repair time of a failed unit.

Authors :
V.S. Vaidyanathan
 Department of Statistics, Pondicherry University, India.

P. Chandrasekhar
Department of Statistics, Loyola College, Chennai, India.

Abstract
In manufacturing process, quality of an end product or component is often assessed by multiple critical output characteristics (or responses). These responses are often correlated or interacting. Change in process setting condition, with an intension to improve a particular response characteristic, may adversely affect another response. In this context, researchers had proposed various parametric and nonparametric Multivariate Statistical Process Control (MSPC) charts for monitoring of correlated responses and detecting out-of-control signal. However, there is little evidence of nonparametric MSPC research to identify influential response(s) for any out-of-control situation in a manufacturing process. In this paper, Mahalanobis-Taguchi System (MTS), based on Mahalanobis Distance (MD) scale and Taguchi’s Orthogonal Array (OA) design, is explored for detecting out-ofcontrol state and identify influential response(s) for an out-of-control state. Suitability of the approach is verified using a manufacturing process case study.

Authors :
Sagar Sikder
SQC & OR Unit, Indian Statistical Institute, Mumbai, India.

Iindrajit Mukerjee
Shailesh J. Mehta School of Management, IIT Bombay, India.

Subhash Chandra Panja
Department of Mechanical Engineering, Jadavpur University, Kolkata, India.

Abstract
Opposed to the general theory of infinite upper limit for lifetime distributions, Mukherjee and Islam ([4], 1983) proposed and studied a finite range distribution considering the fact that designed lifetime of equipment is actually finite. It is quite rational to consider interdependency of multi-component systems in analyzing reliability characteristics. In this article, we consider two-component coherent dependent systems by developing bivariate finite range distribution following the method of Farlie-Gumbel-Morgenstern copula. We investigate and study different reliability characteristics, such as mean time to system failure, system reliability and failure rate functions for finite range coherent dependent systems. We also compare the dependent finite range systems with independent finite range systems for mentioned reliability characteristics.

Authors :
Subhradev Sen
Alliance School of Business, Alliance University, Bangalore, India.

Ahmed Z. Afify
Department of Statistics, Mathematics and Insurance, Benha University, Egypt.

Abstract
Sampling plans in which items are put to test, to collect the life of the items in order to decide upon accepting or rejecting a submitted lot, are called reliability test plans. The basic probability model of the life of the product is specified as exponentiated Rayleigh distribution. For a given producer’s risk sample size, termination number, the waiting time to terminate the test plan and the operating characteristics are presented. The preference of the test plan over similar plans existing in the literature is established with respect to cost and time of the experiment.

Authors :
B. Sriram
Acharya Nagarjuna University Nagarjuna Nagar, India.

R.R.L. Kantam
Acharya Nagarjuna University Nagarjuna Nagar, India.

Abstract
An antihyperlipidemic drug like Atorvastatin calcium (ATC) suffers from poor oral bioavailability due to low solubility and first-pass metabolism by the liver. Combination of cholesterol synthesis inhibitor (ATC) and cholesterol absorption inhibitor (Ezetimibe) lowers the cholesterol level more than ATC alone. The combined drug can also reduce the risk of Type II diabetes mellitus due to use of a lower dose of atorvastatin calcium, particularly for geriatric patients. The objective of this work is to screen critical factors for developing a novel combined antihyperlipidemic drug delivery system in nanostructured lipid carrier (NLC) considering percent drug loading, and particle size(nm), as responses. Taguchi’s L8 orthogonal array design with replicates was used to screen factors. TEM study and zeta potential study of the optimal formulation was done which shows formulation within nanometric size range with high stability. Results indicate all four factors are critical to determining optimal formulation.

Authors :
Nabanita Mukherjee
Principal K M Kundnani College of Pharmacy, Mumba.

Rita Lala
Principal K M Kundnani College of Pharmacy, Mumba.

Indrajit Mukherjee
Shailesh J. Mehta School of Management, IIT Bombay.

Abstract
Low reliability problem due to high temperature direct chlorination (HTDC) vent gas compressor on Vinyl Chloride Monomer (VCM) plant of a petrochemical industry was solved. The study uses the conventional Six Sigma:Define, Measure, Analysis, Improvement and Control (DMAIC) phases to improve reliability of the HTDC compressor in terms of mean time between failure (MTBF). In many cases the Total Preventive Maintenance method or the classical reliability improvement method are adopted to solve such reliability problems. However, Authors found that the DMAIC approach of Six Sigma could solve this problem.

Authors :
Subrata Rath
Statistical Quality Control and Operations Research unit, Indian Statistical Institute, Pune.

Ashis Kumar Chakraborty
Statistical Quality Control and Operations Research unit, Indian Statistical Institute, Kolkata.

Abstract
A new class of distributions, called Odds xgamma-G family of distributions is proposed for modelling lifetime data. An account of the structural and reliability properties of the new class is presented. Maximum likelihood estimation of parameters of the class of distributions has been described. Two data sets have been analyzed to illustrate its applicability.

Authors :
Sudhansu S. Maiti
Department of Statistics, Visva-Bharati University, Santiniketan, India.

Sukanta Pramanik
Department of Statistics, Siliguri College, North Bengal University, Siliguri, India.

Abstract
The paper deals with the two non-identical unit cold standby system with two phase repair (Phase-1 and Phase-2) of a failed unit. Unit-1 gets priority in operation over the unit-2. A failed unit first attended by the skilled repairman in phase-1 to inspect and identify the faults and then attended by an ordinary repairman in phase-2 who completes the process of repair. After phase-2 repair the unit becomes as good as new. The failure time distributions of both the units and repair time distributions of Phase-1 for both the units are taken as exponential with different parameters, whereas the repair time distributions of phase-2 for both the units are taken as general. The various measures of system effectiveness are obtained by using regenerative point technique.

Authors :
Rakesh Gupta
Department of Statistics Ch. Charan Singh University, Meerut, India.

Vaishali
Department of Statistics Ch. Charan Singh University, Meerut, India.

Abstract
A new methodology is developed for estimating the variance function in a heteroscedastic regression set up with a focus on small sample regression based estimation. The three main features of the proposed methodology are as follows: (i) Signal-to-noise ratio is used as the response for the purpose of regression instead of a function of only the residuals of the fitted mean function, (ii) Before fitting the variance function, the data are trimmed following an optimal trimming procedure and (iii) The estimates of the parameters of the variance function obtained from the trimmed data are adjusted to minimize the mean square error of the estimates of variances. The effectiveness of the proposed methods of trimming and adjustments are demonstrated through extensive simulation. It is shown that the variances can be estimated more accurately as above compared to those obtained directly from an estimate of the corresponding variance function. Four sets of real life data are also analyzed for the purpose of illustration.

Authors :
Soham Chakraborty
SQC & OR Unit, Indian Statistical Institute, Kolkata.

Pathik Mandal
SQC & OR Unit, Indian Statistical Institute, Kolkata.

Abstract
Various methods are available in the literature for analysis of multi-level longitudinal service utilization and expenditure data. We discuss implementation of several methods to analyze service utilization and cost data. Hierarchical longitudinal service utilization data was analyzed using a log-gamma model. Mixed-effects models with random intercept and trend are the most appropriate method for analyzing data from hierarchical longitudinal studies and they provide the best fitting models. But these models also suffer from non-convergence problem, especially in the presence of random-effects at multiple levels. Researchers generally perform log transformation and use normal-based method to analyze service utilization data due to ease of use. Even though they are difficult to implement, generalized linear models is a more appropriate choice for analyzing service utilization data.

Authors :
Dulal K. Bhaumik
Department of Psychiatry, University of Illinois at Chicago, USA.

Subhash Aryal
Department of Biostatistics and Epidemiology UNT Health Science Center Fort Worth, TX, USA.

Scott Hur
Department of Psychiatry, University of Illinois at Chicago, USA.