Statistical inference of reliability for a K-out-of-N: G system with switching failure under Poisson shocks

Based on the stochastic uncertainty of the system's operating environment, this research presents statistical inferences on the mean time to failure (MTTF) of a K-out-of-N: G non-repairable system model with switching failure under Poisson shocks. The standby component is switched to the operating component when an operating component fails, with a switching failure probability of p. The MTTF of the system is derived by using the Markov process theory and the Laplace transform for two cases where the shock threshold is a constant value or a random variable. The maximum likelihood estimator (MLE) of the MTTF is obtained, and based on this estimator, asymptotic confidence interval estimation and hypothesis testing are performed. Based on the setting of the basic parameter values, the MTTF under two different cases of the shock threshold is compared. The effect of each parameter on the MTTF is analyzed in numerical simulation. The effectiveness of the above statistical inference methods is also verified by numerical simulation.