Reliability Analysis For Multicomponent System Stress-strength Model

In the reliability theory and applied research,the stress-strength model(SSM)is widely used and extremely important.In particular,the statistical analysis of system SSM has become an important topic in the field of reliability engineering.However,the existing researches of SSM are mainly for component or simple systems.There are few studies on the reliability analysis of multi-component complex system SSM.In this thesis,classical statistical and Bayes statistical methods are used to make inference for reliability of complex cold standby redundancy system,complex coherent system,multi-state system SSM and dynamic SSM of coherent system.(1)Based on the assumption that strength and stress follow generalized half-logistic distributions,the N-M-cold-standby redundancy system SSM is statistically analyzed.First,exact expression of system stress-strength reliability(SSR)is derived.The maximum likelihood estimation(MLE),uniformly minimum variance unbiased estimation(UMVUE)and Bayes estimation of SSR based on progressive Type-II censored samples are obtained.Then,the asymptotic confidence interval(ACI)and approximate highest posterior density credible interval are calculated based on the asymptotic normality of MLE and Monte Carlo sampling method,respectively.Finally,the performance of different estimation methods are compared by numerical simulation.A real data analysis is presented for an illustration of the effectiveness of these estimation methods.(2)The statistical analysis of the SSM of coherent system with multiple types of components is studied by using survival signature.It is supposed that strengths and stresses follow Gompertz distributions,the expressions of SSR with common scale parameter and different scale parameters are derived.According to Newton-Raphson iteration method and Kullback-Leibler divergence,MLEs,maximum spacing estimations of system SSR are obtained.Then,the generalized confidence intervals(GCI)and two point estimations of system SSR are calculated based on generalized pivot quantity(GPQ).By performing Fisher Z transformation on the GPQ,the modified GCIs of system SSR are also proposed.At the same time,we get the Bootstrap confidence intervals(BCI)of system SSR.Finally,the performance of different estimation methods are compared by numerical simulation.A real data analysis is provided to illustrate the proposed procedures.(3)The definitions of generalized survival signature(GSS)for continuous and discrete multi-state systems are proposed.In the light of the GSS,the statistical analysis of continuous multi-state system SSM is studied.It is assumed that the state of multi-state system is defined by using the ratio between strength and stress random variables.The exact expression of SSR is derived under Weibull distributions.Then,MLE,UMVUE and Bayes estimation are calculated.The performance of different estimation methods for SSR of system in different states is given by numerical simulation.Additionally,the model is analyzed and verified by using two real data sets.(4)Based on the assumption that strength and stress follow exponential distributions,the statistical analysis of discrete multi-state system SSM is studied by using GSS.Suppose that the state of multi-state system is defined by the relationship between strengths and stresses,and the dependence structure between different strengths is depicted by Gumbel copula.On the basis of above assumptions,the expressions for SSR of system in different states are derived.Then,method-of-moment estimation and maximum pseudo-likelihood estimation of dependence parameter are given.In the light of these two semiparametric estimations of dependence parameter,MLEs,ACIs,BCIs and transformation-based confidence intervals for SSR of system in different states are obtained.Finally,the performance of different estimation methods are compared by numerical simulation.A real data analysis is provided to illustrate the proposed procedures.(5)The system dynamic SSM is studied based on survival signature.The strength of component degenerates under the influence of stress with random cycle.Under the assumption that the strength and stress follow exponential distributions and the cycle of stress satisfies the Poisson process,the exact expression of system dynamic SSR is derived.The best linear unbiased estimaton(BLUE)of parameter is calculated under Type-II censored sample.Then,the best linear unbiased predictions(BLUP)for unobserved system failure times are obtained.Based on different censored schemes,the performance of BLUEs for parameters and BLUPs for unobserved failure times of different coherent systems are compared by numerical simulation.