Xiaolin Shi*, Pu Lu and Yimin Shirgardoun Pages 1 - 13 ( 13 )
Background: Reliability analysis for the systems with masked data have been studied by many scholars. However, most researches focused on a system that is either series or parallel only, and the component in the system is mainly exponential or Weibull. In engineering practice, it is often seen that the structure of a system is a combination of series and parallel a system, and other types of components are also used in the system. So it is important to study the reliability analysis of hybrid systems with modified Weibull components.
Objective: For the hybrid system with masked data, the constant stress partial accelerated life test is performed under type-II progressive hybrid censoring. These data from life test are used to estimate unknown parameters and reliability index of system. The research results will not only provide theoretical basis and reference for system reliability assessment but also favor the patents on partial accelerated life test.
Methods: Maximum likelihood estimates of unknown parameters are investigated with the numerical method. The approximate conﬁdence intervals, and bootstrap confidence intervals for parameters are constructed by the asymptotic theory and the bootstrap method, respectively.
Results: Maximum likelihood estimations of unknown parameters and reliability index of system are derived, the approximate conﬁdence intervals and bootstrap conﬁdence intervals for unknown parameters are proposed. The performance of estimation of unknown parameters and reliability index are evaluated numerically through Monte Carlo method.
Conclusion: The performance on maximum likelihood estimation method is effective and satisfying. For the conﬁdence intervals of parameters, bootstrap method outperforms the approximate method.
Hybrid system, modified Weibull distribution, masked data, constant-partially accelerated life tests, progressively hybrid censoring, reliability estimation, maximum likelihood estimation, asymptotic confidence interval, Bootstrap confidence interval
School of Electronics Engineering, Xi`an University of Posts and Telecommunications, WeiGuo Road, Xi`an, 710121, Department of Applied Mathematics, Northwestern Polytechnical University, YouYi, Road, Xi`an, 710072, Department of Applied Mathematics, Northwestern Polytechnical University, YouYi, Road, Xi`an, 710072