可靠性增长试验中一类结构可靠度的统计分析

The Statistical Analysis for Some Structure Reliability in the Reliability Growth Tests

摘要: 设X_i1,X_i2……,X_in,是X_i的随机样本（i=1,2,…,m）,且这些样本间是相互独立的,又设X_i～N（θ_i,δ_i²）(θ_i与δ_i未知),且对某一常数c有P（X₁>c）≤P（X₂>c）≤…≤P(X_m>c）基于上述样本,文中给出P（X_m>c）的点估计和在某种意义下最优的置信下限。

Abstract: Let X_i1,X_i2……,X_in, be a sample for random variable X_i, （i=1,2,…,m） and X_ij, 1≤ i≤m, 1≤j≤n_i be independent. Suppose that X_i is distributed as N（θ_i,δ_i²）(θ_iandδ_i are unknown） and the condition P（X₁>c）≤P（X₂>c）≤…≤P(X_m>c）,for some tixed number c holds.
In this paper, we have given the point estimate and the lower confidence limit forP（X_m＞c） based on all data X_ij, 1≤ i≤m, 1≤j≤n_i, which has important value in the reliability engineering.