Statistical inference for multi stress–strength reliability based on progressive first failure with lifetime inverse Lomax distribution and analysis of transformer insulation data

Abstract

Abstract This research aims to develop a multireliability inference method for stress–strength variables based on progressive first failure and an inverse Lomax distribution. This research examines the difficulties associated with estimating the stress–strength reliability function, R , when X , Y , and Z are drawn from three different Inverse Lomax distributions. On the basis of progressive first‐failure censored samples, reliability estimators for multi‐stress–strength Inverse Lomax distributions are estimated using the maximum likelihood, maximum product of spacing, and Bayesian estimation methods. The Bayes estimate of R is obtained using the MCMC method for a symmetric loss function. Monte Carlo simulations and real‐data applications are used to assess and compare the performance of the various suggested estimators.