Statistical Inference of Some Life Testing Models under Various Censoring Schemes

Abstract

In this dissertation, statistical inferences for the unknown model parameters for various lifetime distributions have been investigated along with different scenarios, including accelerated life testing and competing risks model. Some well-known lifetime models are considered in this purpose. Due to limitations of time, cost, and resources in life-testing experiments, failure times of all experimental units can not be recorded. Thus, different censoring schemes have been suggested as potential responses to such scenarios. In this study, Type I progressive hybrid censoring, adaptive Type II progressive censoring, improved adaptive Type II progressive censoring, unified hybrid censoring, and unified progressive hybrid censoring schemes are considered. In life-testing experiments, a product may fail due to various causes, competing with each other. Such models are dubbed as the competing risks models. It is not always feasible to determine the underlying causes of failure for each experimental unit. In such circumstances, the causes accountable for the failure can only be partially noticed. Further, it is also possible that no failure occurs during the testing of extremely reliable products under ordinary stress circumstances. As a result, many products like this undergo extensive testing at high stress levels in order to see the necessary number of failures in a short period of time. In this study, statistical inferences for unknown model parameters have been obtained under different censoring schemes. Point estimates have been inferred under both classical and Bayesian frameworks. In case of classical estimation, maximum likelihood and maximum product spacing estimation procedures are employed. To compute these estimates some numerical techniques such as Newton’s method, expected maximization, and stochastic expected maximization methods have been adapted. Existence and uniqueness of the maximum likelihood estimates have been studied. The Bayes estimates are derived under symmetric and asymmetric loss functions based on informative and non-informative priors. To obtain the Bayes estimates, Lindley’s approximation method and Markov chain Monte Carlo method have been employed. These samples have been generated by using Gibb’s sampling technique, Metropolis-Hastings algorithm, and importance sampling method. By using the asymptotic normality property of the maximum likelihood estimates, approximate confidence intervals of the unknown model parameters have been constructed from the observed Fisher information matrix. Further bootstrap confidence intervals and highest posterior density credible intervals for the model parameters are derived in the context of comparing interval estimates. An extensive Monte Carlo simulation study has been carried out to compare the performance of proposed estimates. Finally, some real data sets have been analyzed to illustrate the operability and applicability of the proposed methods. Finally, some concluding remarks and future research directions are presented.