Stress-strength reliability analysis of system with multiple types of components using survival signature

In this paper, we study the estimation for stress-strength reliability of the system with multiple types of components based on survival signature. In the situation that different types of components are subjected to different types of random stresses, the maximum likelihood estimator, maximum spacing estimator, bootstrap-p confidence interval, two point estimators and generalized confidence interval using generalized pivotal quantity for system stress-strength reliability are derived under the assumption that the stresses and strengths variables follow the Gompertz distributions with common or unequal scale parameters. Additionally, when the stresses and strengths variables follow the Gompertz distributions with unequal scale parameters, a modified generalized confidence interval for the system stress-strength reliability based on the Fisher Z transformation is also proposed. In the situation that the system is subjected to the common stress, the above point estimators and confidence intervals for the system stress-strength reliability are also developed. Monte Carlo simulations are performed to compare the performance of these point estimators and confidence intervals. A real data analysis is presented for an illustration of the findings.