Stress-strength reliability estimation of time-dependent consecutive k / n :F systems for inverse Weibull distribution

In reliability theory and engineering applications, the stress-strength model has become a widely used and critically important model. This article studies the reliability modeling and statistical inference of time-dependent consecutive k/n:F systems based on the inverse Weibull distribution. By introducing the strength degradation value of components and the difference between the initial strength and stress of components at time t, time-dependent failure modeling and assessment of the system reliability are performed. Based on the asymptotic likelihood theory and Bayesian statistical methods, the maximum likelihood estimation (MLE), Bayesian estimation, asymptotic confidence interval (ACI), and highest posterior density (HPD) credible interval of the system reliability are obtained. The mean square error (MSE) of the estimations and the coverage probabilities (CP) of the two interval estimation methods are analyzed. The reliability estimates of the system with different values of time-dependent shape parameters are simulated numerically. The average coverage width (AW) of the two interval estimation methods and the coverage probabilities under the Monte Carlo simulation algorithm are compared, and the trend of system reliability with the time parameter t is analyzed. An empirical dataset is analyzed to demonstrate the developed model and the methodology employed.