Abstract
Complex systems are usually composed of simple hybrid systems. In this paper, we consider statistical inference for two fundamental hybrid systems: series-parallel and parallel-series systems based on masked data. Assuming dependent lifetimes of components modelled by Marshall and Olkin’s bivariate exponential distribution in the system, we present maximum likelihood and interval estimation of parameters of interest. Intensive simulation studies are performed to demonstrate the efficiency of the methods.
Highlights
In a system consisting of several components, the reliability analyses are usually made by analyzing lifetime data
We have studied statistical inference for threecomponent hybrid systems based on masked data, for which the lifetimes of units are nonindependent and nonidentical distributed
The results have demonstrated that the procedure can achieve good estimation performances under small and moderate sample sizes, and the estimates are more accurate if more failures are observed, indicating the efficiency of the estimation method
Summary
In a system consisting of several components, the reliability analyses are usually made by analyzing lifetime data. In the series system with constant, linear and polynomial failure components in the presence of masked data, the maximum likelihood (ML) and other estimation methods were studied among many researchers (e.g., [2,3,4,5,6]). Bayes methods with various priors were used for the estimation of parameters in series and parallel systems (see, e.g., Sarhan [8,9,10], Jiang and Zhang [11]). Most researches of masked data focused on a system with either series or parallel only and assumed independent and identical component lifetime in the system.
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