Reliability Analysis of the General Class of Inverted Exponentiated Family Using Tampered Random Variable Model

ABSTRACT In this paper, we have investigated the problem of parameter estimation for a General Class of Inverted Exponentiated (GCIE) family based on the Tampered Random Variable (TRV) model under simple step‐stress life testing (SSLT) using Type‐II censoring. We employ maximum likelihood estimation (MLE) to estimate the unknown model parameters. We also propose the maximum product of spacings (MPS) method as an alternative to the MLE approach, addressing situations where the MLE method may not be feasible. We derive asymptotic confidence intervals (ACI) based on the asymptotic normality of MLE. Additionally, we use bootstrapping methods to generate boot‐ and boot‐ confidence intervals for the unknown parameters. The Bayesian estimation is also performed using Markov Chain Monte Carlo (MCMC) methods under the squared error loss (SEL) function and Linex loss (LL) function; also, the highest posterior density (HPD) intervals of the unknown model parameters are constructed. We then perform a simulation study to examine the finite sample properties of the proposed estimators. Our results show that the proposed methods perform well under different simulation scenarios. Additionally, we compare the performance of the MLE and MPS methods through the simulation study. To determine the optimal censoring plan, we have considered three different optimality criteria. For illustration purposes, we have considered step‐stress Type‐II censored data from two real data sets: the first data set is solar lighting device data, which contains failure times (in hours) of 35 solar lighting devices. Whereas, the second data set contains relief times (measured in minutes) of 20 patients who received an analgesic. We have fitted these two data sets into a member of the GCIE family under a step‐stress scenario using the TRV model. Our analysis demonstrates a good fit of these data sets to our proposed distribution. We also provide comparisons of the existing models, namely the cumulative exposure model and tampered failure rate model, with the TRV model based on both the data set.