基于巴斯卡数据成败型元件串联系统可靠性经典精确置信限

THE CLASSICAL EXACT OPTIMAL CONFIDENCE LIMIT OF RELIABILITY FOR THE SERIES SYSTEM OF THE PASS-FAIL COMPONENTS BASED ON THE PASKA DATA

设Ａ为由Ｋ个相互独立的成败型元件组成的串联系统，第ｉ个元件的可靠性ｐｉ，ｐｉ未知，ｉ＝１，２，…，Ｋ．设对第ｉ个元件，对于给定的ｍｉ，有ｎｉ个巴斯卡试验数据：Ｘｉ１，Ｘｉ２，…，Ｘｉｎｉ，其中Ｘｉｊ表示对第ｉ个元件进行试验，试验进行到ｍｉ次成功时所需要的试验次数ｊ＝１，２，…，ｎｉ，ｉ＝１，２，…，Ｋ．记Ｔｉ＝Ｘｉ１＋Ｘｉ２＋…＋Ｘｉｎｉ，ｉ＝１，２，…，ｋ．本文研究基于统计量（Ｔ１，Ｔ２，…，Ｔｋ）求串联系统Ａ的可靠性经典精确最优置信下限．

Suppose A is a series system of independent pass-fail components B1,B2,…,Bk,The reliability of Bi is pi, and the pi is unknow,i=1, 2, …,K.Suppose Xi is a Packa random variable with parameters mi , pi, and the mi is know. Suppose Xi1, Xi2, …,Xini is a random sample of Xi, i=1, 2,…,K. LetTi=Xi1+Xi2+…+Xini, i=1, 2,…,K.In this paper, we discuss the classical exact optimal confidence limit of reliability for the series system A based on the statistics (T1,T2,…,Tk )