系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2015年
1期
260~266
,共null页
n中取k系统 可靠 It Phase—type分布
n中取k繫統 可靠 It Phase—type分佈
n중취k계통 가고 It Phase—type분포
k-out-of-n system; reliability; Phase-type distribution
本文以n中取k系统为研究对象，采用Phase—type（PH）分布代替指数分布等典型分布，假设部件在工作状态、储备状态和维修状态停留时间均为连续时间PH分布；建立了一种描述能力更强的系统可靠性解析模型，利用矩阵解析方法获得了系统稳态概率，推导出系统稳态可用度、工作时间、平均故障间隔时间和维修台故障件到达率的解析表达式；并通过算例验证了模型的正确性和适用性，演示了给定n值后，k值变化对系统可靠性规律的影响．
本文以n中取k繫統為研究對象，採用Phase—type（PH）分佈代替指數分佈等典型分佈，假設部件在工作狀態、儲備狀態和維脩狀態停留時間均為連續時間PH分佈；建立瞭一種描述能力更彊的繫統可靠性解析模型，利用矩陣解析方法穫得瞭繫統穩態概率，推導齣繫統穩態可用度、工作時間、平均故障間隔時間和維脩檯故障件到達率的解析錶達式；併通過算例驗證瞭模型的正確性和適用性，縯示瞭給定n值後，k值變化對繫統可靠性規律的影響．
본문이n중취k계통위연구대상，채용Phase—type（PH）분포대체지수분포등전형분포，가설부건재공작상태、저비상태화유수상태정류시간균위련속시간PH분포；건립료일충묘술능력경강적계통가고성해석모형，이용구진해석방법획득료계통은태개솔，추도출계통은태가용도、공작시간、평균고장간격시간화유수태고장건도체솔적해석표체식；병통과산례험증료모형적정학성화괄용성，연시료급정n치후，k치변화대계통가고성규률적영향．
This research investigates a k-out-of-n system in which the operational, standby and repair time of units follow continuous Phase-type distribution, instead of exponential distribution or other typical distributions. The proposed model provides an analytic reliability model that is more suitable to charac- terize the real situation. The stationary distribution is built by using matrix analytic methods; and several performance measures of interest, such as the system stationary availability, operational time, mean time between failures （MTBF） and failure arrival rate, are obtained. Finally, the validity and applicability of the model are implemented by numerical applications; and the influences of k on the system reliability laws are demonstrated when the value of n is fixed.
