﻿ 一种经济的计数型截尾序贯检验
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1. 贵阳医学院 生物与工程学院, 贵阳 550025;
2. 南方汇通股份有限公司 建设装备部, 贵阳 550017

An economic truncated sequential test for a propotion
HU Si-gui1, ZHOU Xiao-jing2
1. School of Biology and Engineering, Guiyang Medical University, Guiyang 550025, China;
2. Construction and Equipment Department, South Huitong Co., Ltd., Guiyang 550017, China
Abstract:For the "high-cost, destructive" sample test of a proportion, such as the acceptance test of missiles hit ratio, the fuze reliability and so on, how to reduce the cost is the focus of management and researching. In the optimal truncated sequential tests on the average number of sample, we found that the average number of sample has decreasing trend with the increasing of truncated sample size. Through the decomposition of the test cost into test preparation cost and experimental test cost based on practical application, for the different ratios of test preparation costs and experimental test costs, the optimal truncated sample size and an economical truncated sequential test programme have been presented in this paper. Finally, the test plans in the International Electrotechnical Commission (IEC) standard IEC1123 have been used to validate the programme in this article.
Key words: sequential analysis     truncated sequential test     success/failure test     sample space ordering method

0 引言

 $$H_0: P = P_0 {\rm vs} H_1: P = P_1 (P_0>P_1) eqno$$ (1)

 $$\left\{ \begin{array}{ll} 0\leq L_{i+1}-L_i \leq 1,\ 0\leq U_{i+1}-U_i \leq 1 ,i=1,2,\cdots,N_t-1& \\ L_i+2\leq U_i,i=1,2,\cdots,N_t-1&\\ L_{N_t}+1=U_{N_t}& \end{array}\right.$$ (2)

 $$\left\{ \begin{array}{ll} E(M|P_0,T)= \sum_{n=1}^{N_t} n(Pr\{D_n|P_0,T \}+ Pr\{\tilde{D}_n|P_0,T\}) & \\ E(M|P_1,T)= \sum_{n=1}^{N_t} n(Pr\{D_n|P_1,T \}+ Pr\{\tilde{D}_n|P_1,T\}) &\\ \end{array}\right.$$ (5)

 $$\left \{ \begin{array}{ll} E(M|P_0,T^{A}(N_t))\leq E(M|P_0,T(N_t))& \\ E(M|P_1,T^{A}(N_t))\leq E(M|P_1,T(N_t))&\\ \end{array}\right .$$ (6)

 $$H_0: P_0=0.9,H_1: P_1=0.8$$ (7)

 图 1 $E(M|P_0,T^A(N_t))$,$E(M|P_1,T^A(N_t))$ 随 $N_t$ 的变化趋势图

 图 2 $E(M|P_0,T^A(N_t))$,$E(M|P_1,T^A(N_t))$ 随 $N_t$ 的变化趋势图

 $$C(N_t)=B_0\times N_t + B_1\times M$$ (8)

 $$E(C(N_t))=B_0\times N_t + B_1\times E(M|P,T^A(N_t))$$ (9)

 $$\widehat{E(M|P,T^A(N_t))}= \frac{E(M|P_0,T^A(N_t))+E(M|P_1,T^A(N_t))}{2}$$ (10)

 $$\widehat{{E(C(N_t))}}=B_0\times N_t + B_1\times {\widehat{E(M|T^A(N_t))}}$$ (11)
3.2 最佳样本量截尾值及其序贯检验方案

 $$\widehat{{E(C(N_t^*))}}= \mathop{\rm inf}\limits_{N_t}\{\widehat{{E(C(N_t))}} \}$$ (12)

 $$\Delta E(C_m)=mB_0 + B_1(\widehat{E(M|T^A(N_t+m))}-\widehat{E(M|T^A(N_t))})$$ (13)

 $$\frac{\widehat{E(M|T^A(N_t))}-\widehat{E(M|T^A(N_t+m))}}{m}= \frac{\mbox{试验准备费}(B_0)}{\mbox{试验测试费}(B_1)}$$ (14)

 图 3 $\widehat{E(M|T^A(N_t))}$ 随 $N_t$ 变化的趋势图

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文章信息

HU Si-gui, ZHOU Xiao-jing

An economic truncated sequential test for a propotion

Systems Engineering - Theory & practice, 2015, 35(2): 406-412.