The inspection paradox with random time

被引：7
|
作者：
Herff, W [1 ]
Jochems, B [1 ]
Kamps, U [1 ]
机构：
[1] RHEIN WESTFAL TH AACHEN,INST STAT,D-52056 AACHEN,GERMANY
来源：
STATISTICAL PAPERS | 1997年 / 38卷 / 01期
关键词：
delayed renewal process; renewal function; inspection paradox;
D O I：
10.1007/BF02925217
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
When considering a delayed renewal process one may be interested in both, the renewal function and the expected length of the interarrival time that contains some fixed time t. In general, it is difficult to obtain explicit expressions for specific underlying distributions. Replacing t by a random variable T and using prior information about T, that is, assuming that T has some continuous NBU (NWU) distribution function G, bounds of the quantities are derived as well as representations, if T is exponentially distributed. As an implication an equation of Wald type is shown. The results can be applied to the analysis of control charts in quality control. Moreover, related bounds of a sample mean based on a random sample size are given and an elementary renewal reward theorem is stated.
引用
收藏
页码：103 / 110
页数：8
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