SRC Forum - Message Replies
Forum: Reliability & Maintainability Questions and Answers
Topic: Reliability & Maintainability Questions and Answers
Topic Posted by: Reliability & Maintainability Forum
Organization: System Reliability Center
Date Posted: Mon Aug 31 12:47:36 US/Eastern 1998
Posted by: Min Hee
Date posted: Wed Feb 25 10:25:11 US/Eastern 2004
My question is similar point with previous question.
On reliability demonstration, I will demonstrate 0 failure at one equipment during test time.
I have to determine confidence interval and I want to know what value and criteria are applied in usual case. Thanks.
Subject: R Demo Zero Failures
Reply Posted by: Jorge Romeu
Date Posted: Wed Mar 3 9:36:07 US/Eastern 2004
A query on Reliability Demonstration with Zero Failures (r=0) and its related statistical confidence (1-alpha) in a life study was submitted to the Forum. This is a very interesting topic that has been addressed in more detail in the RAC Book, Practical Statistical Tools for the Reliability Engineer, by Mr. Tony Coppola.(see the RAC web site for products)
The question is, how to determine the confidence to demonstrate, at zero failures, in the test time allotted, the required reliability. The answer is, it depends on the sample size n. And usually, one pre-establishes the confidence first and determines the sample size that will provide such a confidence, as a consequence.
First of all, we need to clearly establish who is the interested party. For, there are two hypotheses here: the null (H0) that the product is good (Reliability is acceptable) and its alternative (H1) that the product is bad (Reliability is too low). And there are two risks: the producer's risk (alpha) of rejecting a good product or the consumer's risk (beta) of accepting a bad product. In a reliability demonstration test, the customer is usually the interested party. Therefore, he pre-establishes the consumer's risk beta of accepting a low reliability.
Assume we place "n" items on a life test, for a pre-specified duration (T). Each item has only two outcomes: either fail or pass the test of length T. The sample must be of random and independent elements. Hence, each item on test represents an independent Bernoulli trial. Then, the number of observed failures (r) our of "n" trials constitutes a Binomial experiment. And one can, using Binomial tables with the minimum acceptable reliability (probability "p" for each independent item, to survive the test of length T), calculate the sample size "n" that will provide the "confidence" (1-alpha) required.
We are providing below some references available in the RAC Web page as well as the Reliability Engineering RAC book information.
1. Practical Statistical Tools for the Reliability Engineer. Coppola, A. RAC 1999. Section 7.2, pages 60 and 61.
2. Statistical Confidence Romeu, J. RAC START Sheet. http://rac.alionscience.com/pdf/STAT_CO.pdf
3. Statistical Assumptions of an Exponential Distribution Romeu, J. RAC START Sheet. http://rac.alionscience.com/pdf/E_ASSUME.pdf