Reliability analysis of J-out-of-N system with Nadarajah-Haghighi component under generalised progressive hybrid censoring

In reliability analysis of the J-out-of-N system, people usually assume that the lifetime of components in the system follows the exponential, Weibull or gamma distribution. However, this assumption has some limitations in fitting real-life data. Nadarajah–Haghighi distribution has more advantages than exponential, Weibull and gamma distributions in reliability modelling of real data. This paper investigates the reliability analysis of a J-out-of-N system in which the lifetimes of components follow Nadarajah–Haghighi distribution. Based on the generalised progressive hybrid censoring (GPHC) sample, the maximum likelihood estimates (MLEs), and the asymptotic confidence intervals of unknown parameters and the reliability function of the system are obtained by using the numerical procedure and asymptotic normality theory of MLEs, respectively. The Bayesian estimates under squared error loss are derived using the Tierney–Kadane’s (T–K) method. Furthermore, the Bayesian credible intervals are constructed based on Metropolis–Hastings method. Monte Carlo simulations are carried out to evaluate the performance of the proposed estimation methods. Finally, two real data sets are analysed for illustrative purposes.