Stress-strength reliability, defined as $\mathcal{R}=P(Y<X)$, plays a vital role in evaluating a system's ability to withstand stress, especially in complex engineering scenarios. This study investigated $\mathcal{R}$ when both the stress $Y$ and strength $X$ followed independent Weibull distributions with a common shape parameter and distinct scale parameters. The analysis was conducted under an improved adaptive progressive Type-Ⅱ censoring scheme. We employed both classical and Bayesian estimation techniques. Classical inference was performed using maximum likelihood estimation and the maximum product of spacings methods, providing point and interval estimates based on their statistical properties. For Bayesian analysis, we proposed two approaches, one based on the likelihood function and the other on the spacings function, using independent gamma priors. Posterior estimates were obtained via Markov Chain Monte Carlo under a squared error loss, along with corresponding credible intervals. A comprehensive simulation study evaluated and compared the performance of the four estimators, two classical and two Bayesian, across varying censoring scenarios. The proposed methods were further validated using real-world data from organic white light-emitting diode devices, illustrating their practical utility.

The use of competing risk frameworks for the analysis of reliability/survival data has gained popularity in recent years, primarily because traditional techniques are inadequate for effectively analyzing such data. In this study, we examined the independent competing risks model with lifetimes of units distributed according to the Nadarajah–Haghighi distribution. Our focus was on estimating the unknown parameters, as well as the reliability and failure rate functions, using both frequentist and Bayesian estimation methods under an improved adaptive progressive Type-Ⅱ censoring mechanism. The frequentist estimation involved deriving point estimators and approximate confidence intervals using the asymptotic properties of classical estimators. Bayes estimators were obtained through symmetric squared loss and the Metropolis-Hastings algorithm, which generated samples from the joint posterior distribution. Additionally, the highest posterior density credible intervals were calculated. Given the complex nature of the acquired estimators, we conducted a comprehensive simulation study to numerically compare the performance of the proposed estimates across various experimental scenarios. To empirically validate the proposed inferential framework, we analyzed two real-world competing risk datasets, highlighting the effectiveness of the applied techniques in reliability data analysis.

Reliability evaluation holds significant importance in multiple fields, especially in engineering. Given the fast-paced advancement of modern products, researchers face the challenge of gathering a suitable amount of observed data on products that exhibit high reliability. An adaptive progressively Type-II hybrid censoring strategy is a commonly used form of censorship that helps to improve the accuracy of statistical tests by ending the experiment after getting a predetermined number of observed data. In this paper, we use this technique when the parent distribution of the population under consideration is the exponentiated Teissier distribution. We use the likelihood method to calculate point and interval estimates for model parameters and reliability indices. To determine the required interval ranges for various parameters, we use both the normal approximation of likelihood estimates and the normal approximation of their logarithm. Additionally, the Bayesian estimation method is employed to obtain point estimates and two types of credible intervals by sampling from the full conditional distributions. A simulation experiment is carried out to compare different approaches through varied experimental plans, effective number of failures, and priors. Two engineering applications are considered by analyzing the failure times of electronic components and aircraft windshields.

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.