Statistical analysis of stress–strength in a newly inverted Chen model from adaptive progressive type-Ⅱ censoring and modelling on light-emitting diodes and pump motors

A system's reliability is defined as the likelihood that its strength surpasses its stress, referred to as the stress–strength index. In this work, we introduce a new stress–strength model based on the inverted Chen distribution. By analyzing the failure times of organic white light-emitting diodes and pump motors, we focus on the inferences of the stress–strength index $\mathfrak{R}=P(Y<X)$, where: (1) the strength $(X)$ and stress $(Y)$ are independent random variables following inverted Chen distributions, and (2) the data are acquired using the adaptive progressive type-Ⅱ censoring plan. The inferences are based on two estimation approaches: maximum likelihood and Bayesian. The Bayes estimates are obtained with the Markov Chain Monte Carlo sampling process leveraging the squared error and LINEX loss functions. Furthermore, two approximate confidence intervals and two credible intervals are developed. A simulation study is done to examine the various estimations presented in this work. To assess the effectiveness of different point and interval estimates, some precision metrics are applied, especially root mean square error, interval length, and coverage probability. Finally, two practical problems are examined to demonstrate the significance and applicability of the given estimation approaches. The analysis demonstrates the suitability of the proposed model for examining engineering data and highlights the superiority of the Bayesian estimation approach in estimating the unknown parameters.