浴盆形失效率函数剩余寿命的性质及其应用

The Residual Life Time of Bathtub-alike Failure Rate Function: Properties and Applications

在对许多系统产品的寿命数据的统计分析的基础上 ,研究了当系统失效率函数具有浴盆形时 ,不可修系统在 τ时刻的剩余寿命 F( x+τ)F( x) 和可修系统在 [0 ,τ]间的平均失效次数 E( Nx( τ) ) ,结果表明 ,它们作为参数 x的函数 ,当 τ≤t2 - t1时 ,分别在 [t1,t2 - τ]间取得最大值、最小值 ;当 τ>t2 -t1时 ,分别在 [0 ,t1,]间取得最大值、最小值。由此构造出一个具有该种特点的混合分布 ,并用一个例子来加以验证。

In respect to statistic description of the residual life time of many system products, a thorough study is made into the residual life time F(x+τ)/F(x) of the irreparable system and the average failure times E(N x(τ)) of the reparable system, which are both functions of parameter x, when the system's failure rate function is bathtub alike. Results show that when τ≤t 2-t 1 , both parameters can reach the maximum and minimum at the range of [t 1, t 2-τ] , and when τ>t 2-t 1 , at the range of [0, t 1]. In this case, a mixed distribution pattern is obtained with an example provided for demonstration and application.