Reliability Analysis of Modified Kies– Rayleigh Distribution with Optimal Progressive First-Failure Sampling Plans with Application to Turbocharged Diesel Engines

Abstract

This study investigates the utility of the newly modified Kies–Rayleigh distribution for analyzing progressively first-failure censored samples. We develop both classical and Bayesian estimators for the distribution’s parameters and derived reliability measures, including the reliability function and hazard rate. Interval estimation is addressed via approximate confidence intervals and Bayesian credible intervals. Classical estimates are obtained numerically by solving the likelihood equations, whereas Bayesian inference is conducted through Markov chain Monte Carlo sampling from the posterior distribution. To assess and compare the performance of the classical and Bayesian procedures, we carry out a comprehensive simulation study under multiple experimental scenarios. We also consider the design problem of choosing an optimal progressive sampling plan and evaluate competing plans using four standard optimality criteria. We analyze a dataset comprising time-to-failure observations for turbocharged engines from a single model of diesel engine. The results highlight the flexibility of the modified Kies–Rayleigh model and provide guidance on estimation and design choices for progressively censored reliability data.OPEN ACCESS Received: 21/09/2025 Accepted: 07/11/2025 Published: 21/07/2026

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