Search Results (3)

This paper presents a comprehensive reliability analysis framework for the Chris–Jerry (CJ) lifetime distribution under an improved adaptive progressive Type-II censoring plan. The CJ model, recently introduced to capture skewed lifetime behaviors, is studied under a modified censoring structure designed to provide greater flexibility in terminating life-testing experiments. We derive maximum likelihood estimators for the CJ parameters and key reliability measures, including the reliability and hazard rate functions, and construct approximate confidence intervals using the observed Fisher information matrix and the delta method. To address the intractability of the likelihood function, Bayesian estimators are obtained under independent gamma priors and a squared-error loss function. Because the posterior distributions are not available in closed form, we apply the Metropolis–Hastings algorithm to generate Bayesian estimates and two types of credible intervals. A comprehensive simulation study evaluates the performance of the proposed estimation techniques under various censoring scenarios. The framework is further validated through two real-world datasets: one involving rainfall measurements and another concerning mechanical failure times. In both cases, the CJ model combined with the proposed censoring strategy demonstrates superior fit and reliability inference compared to competing models. These findings highlight the value of the CJ distribution, together with advanced censoring methods, for modeling lifetime data in physics and engineering applications. Full article

This study introduces a novel approach to accelerated life test experiments by examining competing risk factors using the Tampered Random Variable (TRV) model. This approach remains extensively unexplored in current research. The methodology is implemented for a simple step-stress life test (SSLT) model and accounts for various causes of failure. The Power Chris–Jerry (PCJ) distribution is utilized to model the lifetimes of units under different stress levels, incorporating unique shape parameters while maintaining a fixed-scale parameter. This study employs the TRV model to integrate constant tampering coefficients for each failure cause within step-stress data analysis. Maximum-likelihood estimates for model parameters and tampering coefficients are derived from SSLT data, and some confidence intervals are presented based on the Type-II censoring scheme. Furthermore, Bayesian estimation is applied to the parameters, supported by appropriate prior distributions. The robustness of the proposed method is validated through comprehensive simulations and real-world applications in different scientific domains. Full article

This article is an extension of the Chris-Jerry distribution (C-JD) in that a two-parameter Chris-Jerry distribution (TPCJD) is suggested and its characteristics are studied. Based on the determined domain of attraction and other major statistical properties, the proposed TPCJD seems to fit into the Gumbel domain. Additionally, it has been confirmed that the stress strength is reliable. The tail study suggests that the TPCJD’s substantial tail makes it suited for a range of applications. The study took into account the single acceptance sampling approach using both simulation and real-life situations. The parameters of the TPCJD were estimated by some classical and Bayesian approaches. The mean squared errors (MSE), linear-exponential, and generalized entropy loss functions were deployed to obtain the Bayesian estimators aided by the Markov chain Monte Carlo (MCMC) simulation. An analysis of lifetime data on two events justified the use of the proposed distribution after comparing the results with some standard lifetime models. Full article