Browsing by Author "Ashkamini"

Now showing 1 - 3 of 3

Bayes analysis of one-shot device testing data with correlated failure modes using copula models
(Taylor and Francis Ltd., 2023) Ashkamini; Reema Sharma; Satyanshu K. Upadhyay
Copula models are capable of modeling the dependence structure among the random variables, a phenomenon that is often required in the statistical analysis. Such models are the flexible substitutes of multivariate distributions because they model both the marginal distributions and the joint dependence structure distinctly. Because of such important features, the models are recognized as popular tools in a variety of situations including reliability engineering and survival analysis. The present paper studies a Bayesian approach using three Archimedean copulas, namely, the Gumbel Hougaard copula, the Frank copula and the Joe copula for analyzing one-shot device testing data with two correlated failure modes collected from a constant stress accelerated life test. One-shot devices are units that can be used only once and destroyed immediately after the use. Obviously, one obtains either left or right censored data on the failure times instead of actual failure times of the devices. Finally, all the considered copula models are compared using the Bayesian model selection tools. A real dataset is analyzed as an illustration of the proposed Bayesian methodology. © 2023 Taylor & Francis Group, LLC.
Bayes analysis of one-shot device testing data with correlated failure modes using copula models
(Taylor and Francis Ltd., 2025) Ashkamini; Reema Sharma; Satyanshu Kumar Upadhyay
Copula models are capable of modeling the dependence structure among the random variables, a phenomenon that is often required in the statistical analysis. Such models are the flexible substitutes of multivariate distributions because they model both the marginal distributions and the joint dependence structure distinctly. Because of such important features, the models are recognized as popular tools in a variety of situations including reliability engineering and survival analysis. The present paper studies a Bayesian approach using three Archimedean copulas, namely, the Gumbel Hougaard copula, the Frank copula and the Joe copula for analyzing one-shot device testing data with two correlated failure modes collected from a constant stress accelerated life test. One-shot devices are units that can be used only once and destroyed immediately after the use. Obviously, one obtains either left or right censored data on the failure times instead of actual failure times of the devices. Finally, all the considered copula models are compared using the Bayesian model selection tools. A real dataset is analyzed as an illustration of the proposed Bayesian methodology. © 2023 Taylor & Francis Group, LLC.
Metropolis Algorithm Based Bayesian Analysis of a Competing Risk Data Using Copula-Frailty Model
(Pleiades Publishing, 2024) Ashkamini; Reema Sharma; Satyanshu K. Upadhyay
Abstract: Competing risks can play a significant role in the design and analysis of critical intelligent systems which experience several risks of failure but actually fail due to a single cause that occurs first. The failure time of various components of these systems may be correlated as one failure may lead to another. In order to model such a dependence structure, copula models and frailty models have been developed for such competing risk data. The frailty term is used to describe the underlying heterogeneity among the units and the copula function is utilized to represent the dependence between the failure times. A Bayesian analysis using the Weibull distribution as the underlying failure time distribution to describe the competing risk data is carried out. The paper also considers some other models and compares them using a few standard Bayesian model comparison tools. Lastly, a real data set is studied to illustrate the proposed Bayesian approach. © Allerton Press, Inc. 2024.