Statistical inference for constant‐stress accelerated life tests with dependent competing risks from Marshall‐Olkin bivariate exponential distribution

Abstract

This paper considers a constant‐stress accelerated dependent competing risks model under Type‐II censoring. The dependent structure between competing risks is modeled by a Marshall‐Olkin bivariate exponential distribution, and the accelerated model is described by the power rule model. The point and interval estimation of the model parameters and the reliability function under the normal usage condition at mission time are obtained by using the maximum likelihood estimation method and the bootstrap sampling technique. Moreover, the pivotal quantities based estimation are adopted to estimate the model parameters and the generalized confidence intervals. As a comparison, we also consider the Bayes estimation and the highest posterior density credible intervals for the model parameters based on conjugate priors and importance sampling method, respectively. To illustrate the proposed methodology, a Monte Carlo simulation is used to study the performances of different estimation methods. Finally, a dataset is analyzed for illustrative purpose and a comparison with the original results is also given.

Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals

“…In such case, the system fails if any one component fails, it is indeed an example of dependent competing risk set up. In the literature, we find the study on dependent competing risk in Bai et al [2], Cai et al [13], Feizjavdian and Hashemi [23], Kundu [26], Kundu and Mondal [25], Shen and Xu [34], Lyu et al [29] and references therein.…”

“…The Bias of MLEs and DPDEs are given in the Table (2) for the pure data and contaminated data scheme. It is observed that MLEs are highly affected by contamination as biases of MLEs are increased in contaminated data setting compared to pure data setting.…”

The Inverse Epsilon Distribution as an Alternative to Inverse Exponential Distribution with a Survival Times Data Example

“…The exponential distribution and its generalizations play an important role in many areas of science, including physics, chemistry, medical sciences and reliability engineering (see e.g. [1,2,16,19]). Dombi et al [6] introduced the epsilon distribution, which may be treated as an alternative to the exponential distribution.…”