Under Type-II progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations (MLEs) of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover, two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria. Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.

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Background: Reliability analysis for the systems with masked data had 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 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.

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