Reliability Inference for Multicomponent Systems Based on the Inverted Exponentiated Pareto Distribution and Progressive First Failure Censoring

Multicomponent stress-strength (MC-SS) reliability evaluation is essential for risk management and decision-making across many industries. By evaluating the relationship between the strength of components and the stresses they experience, this analysis assists in identifying potential failure points and guiding proactive measures to enhance system reliability. The primary objective of this study is to investigate the reliability inference for the MC-SS model under progressive first-failure censoring. We assume that the stress and strengths random variables follow the inverted exponentiated Pareto distribution (IEPD) with a shared second shape parameter. The Bayesian and non-Bayesian procedures are employed to obtain the parameter estimates and MC-SS reliability estimate. Moreover, the highest posterior density credible intervals and asymptotic confidence intervals are created. Using the Markov Chain Monte Carlo approach, the Bayesian estimates of the MC-SS reliability are yielded under different loss functions. The proposed methodology was rigorously tested using simulation experiments to evaluate its performance under various conditions. To evaluate the suitability of the IEPD for analyzing two datasets, we compare its performance to other models using goodness-of-fit measures and graphical representation. We estimate unknown parameters using maximum likelihood and Bayesian methods and assess the MC-SS reliability of all competing models. The investigation shows that the IEPD outperforms the other models and consistently produces the most reliable estimates. This implies that the IEPD is a better option for applications that need reliable and precise predictions.