Reliability Estimation of Stress–Strength Model for Multi-Component System Based on Lomax Distribution Using the Survival Signature

In this paper, the stress–strength reliability of complex systems with diverse component types is investigated based on the theoretical framework of survival signatures. Assuming that both the strength and stress of components of the same type follow the Lomax distribution, the maximum likelihood estimation (MLE), maximum spacing estimation (MSPE), and Bayesian estimation for the stress–strength model are derived under the condition that components of the same type have common scale parameters. Subsequently, the 95% Bootstrap-p and Highest Posterior Density confidence intervals for the stress–strength reliability were derived using Monte Carlo simulation. Additionally, since stress cycles are represented by a Poisson process, a dynamic stress–strength model for the system subjected to periodic stresses over the interval (0,t] was developed, together with an approximate computational algorithm for this model. Finally, a simulation experiment was conducted using a system consisting of a total of nine components of three different types to analyze these estimation methods. The findings reveal that MLE exhibits the lowest estimation error, registering merely 0.001 in the case of small-sized samples. Compared with the previous two methods, Bayesian estimation has a relatively larger error. However, in the case of large samples, the error is 0.0112. In addition, the performance and accuracy of the dynamic model were verified through the proposed algorithm. The results indicate that compared with the static model at t=0, the error of the algorithm is 0.0464. Overall, the model evaluation results are satisfactory.