Efficiency of ranked set sampling designs in power Lindley system reliability estimation with uncensored and right-censored data.

Accurate system reliability estimation facilitates engineers and statisticians in optimizing resource allocation within industrial and technological applications. In the field of statistical modeling for system reliability metrics, ranked set sampling (RSS) designs have been confirmed as effective alternatives to simple random sampling (SRS). In this study, we mainly focus on investigating the performance of different sampling designs, including SRS, RSS and extreme ranked set sampling (ERSS), on estimating stress-strength reliability when stress and strength are two independent random variables following power Lindley (PL) distributions under both uncensored and right-censored data. To obtain the parameter estimates of the PL distributions, the maximum likelihood (ML) method is used. Monte Carlo simulations considering perfect and imperfect ranking with uncensored data and perfect ranking with right-censored data show that RSS and ERSS provide more precise ML estimates of system reliability, R, compared to SRS under different sample sizes and parameter settings. Finally, applications to two datasets also illustrate the advantage of our proposed methodologies, which are conducive to enhanced precision in critical systems, cost-efficient resource allocation, adaptability to real-world data challenges.