A Copula Based Stress-Strength Reliability Estimation with Lindley Marginals

  • A. James Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry – 605 014, India
  • N. Chandra Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry – 605 014, India
  • M. Pandey Department of Zoology and DST Centre for Mathematical Sciences, Institute of Sciences, Banaras Hindu University, Varanasi 221 005, India
Keywords: Stress-strength reliability, Lindley distribution, Fralie-Gumble-Morgenstern, maximum likelihood estimation, inference function margins, semi-parametric method, Monte-Carlo simulation


The stress-strength model is a basic tool used in evaluating the reliability (R). It shows that a component or system with stress (Y) and strength (X) will fail if the stress exceeds the strength, and its counterpart allows it to function. Usually, the statistical independence between X and Y are assumed and reliability models are extensively developed in the literature. However, in real life, there are many situations in which the dependence stress-strength is taken into account. So it is important to consider and model the association between them. In this paper, we estimated R when the stress and strength parameters are linked by a Fralie-Gumble-Morgenstern copula with Lindley marginals. The estimates of reliability and dependence parameter are obtained by using maximum likelihood estimation (MLE), inference function margins (IFM), and semi parametric (SP) methods. In addition, the length of the asymptotic confidence interval and the coverage probability of the dependence parameter are also computed. A simulation study is performed to evaluate the effectiveness of the various estimates, and a real data set is also used for illustrative purposes.


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Author Biographies

A. James, Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry – 605 014, India

A. James has received M.Sc. (Statistics) in 2017 from St. Thomas College, Thrissur and pursuing for Ph.D. (Statistics) degree in the Department of Statistics, Ramanujan School of Mathematical Sciences at Pondicherry University, India. Her research interest is Copula based stress-strength modelling in reliability theory.

N. Chandra, Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry – 605 014, India

N. Chandra is an active senior faculty and researcher in the Department of Statistics, Ramanujan School of Mathematical Sciences at Pondicherry University, India. He has received Ph.D. (Statistics) degree in 2002 from Banaras Hindu University, India. Dr. Chandra is a recipient of Senior Research Fellow. He is presently working on competing risk hazards analysis and dependence stress-strength reliability modelling. His research interests include Classical and Bayesian inference, life testing and reliability modelling and Cox’s PH modelling in survival analysis, Accelerated life testing and Augmenting strength reliability.

M. Pandey, Department of Zoology and DST Centre for Mathematical Sciences, Institute of Sciences, Banaras Hindu University, Varanasi 221 005, India

M. Pandey received her Ph.D. degree in Statistics in 1977 from Banaras Hindu University, Varanasi, India. Her major field of study is Preliminary Test Statistical Inference, Reliability Theory, Bayesian reliability, Stress-strength model in reliability and Biostatistics. She is retired Professor of Biostatistics and presently associated with Department of Science and Technology Centre for Interdisciplinary Mathematical Sciences, Government of India at Institute of Science, Banaras Hindu University, Varanasi, India. Her current research interest are Estimation in Accelerated Life Testing, Bayesian Estimation of Family of Bivariate Exponential Models under Stress – strength setup, Environmental Pollution and Application of Multivariate Techniques.


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