具有多层试验数据的成败型元件之串并联系统及并串联系统可靠性置信下限的近似解

设系统A由K个独立的子系统B_1,B_2,…,B_K并(串)联而成,设第i个子系统B_i又由m_i个相互独立的成败型元件C_(i1),C_(i2),…C_(imi)串(并)联而成,设有多层试验数据: 元件C_(ij)试验N_(ij)次,成功S_(ij)次,失败F_(ij)次(i=1,2,…,K,j=1,2,…,m_i) 子系统B_i有成败型试验数据:试验N_i次,成功S_i次,失败F_i次(i=1,2,…,K) 系统A有成败型试验数据:试验N次,成功S次,失败F次。 本文给出利用此多层成败型试验数据,求系统A的可靠性置信下限的近似解的方法,本文利用一、二阶矩拟合的原则将上述数据折合为原系统A的伪成败型数据:伪试验数N~*,伪成功数S~*,然后从N~*,S~*出发利用单个成败型元件之可靠性的经典精确方法求出原系统A的可靠性置信下限的近似值。本文推导了伪试验数N~*,伪成功数S~*的计算公式,并给出了计算实例。

THE APPROXIMATE LOWER CONFIDENCE BOUND FOR SERIES-PARALLEL AND PARALLEL-SERIES SYSTEM RELIABILITY WITH HIER ARCHICAL PASS-FAIL TEST DATA

Let a system (A) be composed of K-independent subsystems B1, B2, B3,..., Bk in parallel (or, in series), and the i-th subsystem be composed of m1-independent pass-fail components Cf1, Cf2,..., Cfm in series (or, in parallel). There exist hierarchical test data as follow: For component Cij, the number of tests, successes, and failures is Nij, Sij andFij respectively (i=l,2,..., K, j = 1,2,..., mi) for subsystem Bi, similarly, Ni, Si, and Fi, respectively (i=l,2,..., K) for system (A), similarly, N, S, F.In this paper, a method for calculating the approximate lower confidence bound for system reliability of (A) is presented. The psuedo pass-fail data(psuedo number of tests N, psuedo number of successes S) are obtained from the hierarchical data by the 1-st and 2-nd order moment fitting method. Then, the approximate bound of (A) is obtained from N and S by the exact classical method for individual pass-fail component. The formulae for N and S with computation example are presented.