Bayesian analysis of multi-component stress-strength reliability using improved record values

Abstract

This research investigates statistical methods for estimating the reliability in a complex system composed of non-identical components with varying strengths in the presence of upper record ranked set samples. To model the behavior of these components, a specialized distribution in the shape of a bathtub is assumed. This distribution offers flexibility with adjustable levels of asymmetry, enabling its adaptation to different reliability scenarios. The study focuses on estimating the reliability of the system’s bathtub-shaped distribution by employing two different approaches: classical and Bayesian. In the classical approach, the system’s reliability is estimated using a maximum likelihood technique, and a simulation study is conducted to evaluate the accuracy of the estimates. The Bayesian approach, on the other hand, considers the use of the standard linear exponential (LINEX) loss function as an asymmetric loss function, as well as the squared error loss function as a symmetric loss function. Bayesian estimates of the system’s reliability are obtained by utilizing two independent gamma prior distributions. Due to the complexity of these estimates, the Markov chain Monte Carlo method is employed since closed-form solutions cannot be obtained. Extensive simulations reveal that as the number of records increases, the measurement accuracy decreases. In most cases, the Bayesian estimates obtained using the LINEX loss function yield the lowest values. The theoretical findings are illustrated through examples drawn from real-world datasets, specifically focusing on a dataset concerning the timing of consecutive failures in aircraft air conditioning systems to demonstrate the proposed methodologies.