Statistical inference of joint competing risks models from comparative bathtub shape distributions with hybrid censoring

In reliability engineering studies, the class of lifetime distributions with bathtub-shaped failure rate functions is particularly important since the lifetimes of electro-mechanical, electronic, and mechanical goods are frequently modelled with this characteristic. Comparative competing risk data are obtained in a variety of applications, including engineering, biological, medical, and other related fields. In this study, we adopted the statistical inference of joint distributions with a bathtub shape or increasing failure rate function (Chen distributions). The problem of determining the relative merits of products according to their lifetime duration is discussed under the hybrid type-I censoring scheme. Also, under consideration of independent causes of failure, a survival analysis and the assessment of one risk in the presence of other risks are discussed. The maximum likelihood (ML) method and the Bayes approach relative to the symmetric loss function are used to estimate the model parameters. Additionally, we build the classical confidence intervals (CIs) (asymptotic CI and bootstrap CI) to compare with the Bayes credible intervals. Moreover, theoretical results are evaluated and contrasted using a Monte Carlo simulation study. Finally, for illustration purposes, a real data set obtained from a laboratory experiment is evaluated using the suggested model with some brief comments.