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Analysis of system reliability with dependent repair modes

机译：依赖维修模式的系统可靠性分析

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This paper proposes an imperfect-repair model for repairablensystems where two repair modes, perfect and minimal, occur in accordancenwith a Markov chain. It investigates the characteristics of the modelnand presents a statistical procedure for estimating the lifetimendistribution of the system, based on consecutive inter-failure times.nUnder the Brown-Proschan imperfect repair model, the system is repairednto: good-as-new under perfect-repair, its “condition just prior tonfailure” under minimal-repair. This imperfect-repair modelngeneralizes the Brown-Proschan imperfect-repair model, by allowingnfirst-order dependency between two consecutive repair modes. The modelnassumes that, at failure, the system undergoes either perfect repairn(restore to like new) or minimal repair (restore to like “justnbefore failure”), and the repair modes are subject to a Markovnprocess. The estimation procedure is developed in a parametric frameworknfor incomplete data where some repair modes are not recorded. Thens-expectation-maximization principle is used to address thenincomplete-data problem. Under the assumptions that the lifetimendistribution belongs to a parametric family having aging property andnexplicit form of the survival function, an algorithm is developed fornfinding the MLE (maximum likelihood estimates) of the reliabilitynparameters; the transition probabilities of the repair modes, as well asnthe distribution parameters. A Monte Carlo study shows the consistency,neffect of aging rate, effect of transition types, and effect of missingndata, for the estimates
机译：本文提出了一种可修复系统的不完善修复模型，其中根据马尔可夫链出现了两种修复模式，即完美修复和最小修复。它研究了该模型的特性，并基于连续的故障间隔时间，提出了一种统计程序来估计系统的寿命分布。n在Brown-Proschan不完善的修复模型下，将系统修复为：完美修复后的新产品，其在最小限度修复下的“先于失败的条件”。通过允许两个连续的修复模式之间具有一阶依赖关系，该不完善的修复模型可以概括化Brown-Proschan的不完善的修复模型。该模型假定，发生故障时，系统将经历完美的修复（恢复为新状态）或最小程度的修复（恢复为“在发生故障之前”），并且修复模式受Markovn过程影响。估计程序是在不记录某些修复模式的不完整数据的参数框架中开发的。然后采用期望最大化原则来解决数据不完整的问题。在假设寿命分布属于具有老化性质和生存函数的显式形式的参数族的前提下，开发了一种算法来确定可靠性参数的MLE（最大似然估计）。修复模式的转移概率以及分布参数。蒙特卡洛研究显示了估计的一致性，衰老率的影响，过渡类型的影响以及数据缺失的影响

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