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Forum: Reliability & Maintainability Questions and Answers

Topic: Reliability & Maintainability Questions and Answers

Topic Posted by: Reliability & Maintainability Forum (src_forum@alionscience.com )
Organization: System Reliability Center
Date Posted: Mon Aug 31 12:47:36 US/Eastern 1998

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Original Message:

Posted by: Rel Engr
Date posted: Fri Feb 20 15:16:51 US/Eastern 2004
Subject: Question on Confidence
Message:
I am planning on conducting a reliability study using time censored data assuming a Chi-Square distribution. Assuming 0 failures, I have been estimating the appropriate length for the study to maintain a desired reliability and confidence. As I am limited on study length, I am considering lowering either confidence or reliability. Although I am reluctant to reduce confidence, it seams to be the option preferred by management to maintain a high minimum reliability. I am unclear on the effect of lowering confidence and was hoping someone could go into detail on the effect.


Reply:

Subject: Confidence Levels
Reply Posted by: Jorge Romeu (jromeu@alionscience.com )
Organization: RAC
Date Posted: Wed Mar 3 9:27:03 US/Eastern 2004
Message:
A query on the effect of lowering the statistical confidence (1-alpha) in a life study and its comparison to lowering the reliability expectations was submitted to the Forum. This is a very interesting topic that has been addressed in more detail in the RAC START sheet: Statistical Confidence http://rac.alionscience.com/pdf/STAT_CO.pdf The trade-off between the estimated reliability and its statistical confidence can be, in a nutshell, characterized as follows (via a numerical example). Let's assume that we state that the reliability of a device is 0.9 with 99% confidence (a statement that has been obtained from a randomized sample that has been tested for reliability). This means that 99% of the times that we conduct such a life test, the device reliability is 0.9 or more and only 1% of the times it is less than 0.9 (maybe much less). On the other hand, we may state that the reliability is 0.95 with 90% confidence. This means that 90% of the times we conduct such a life test, the device reliability is 0.95 or more and at most 10% of the times it is something else (below 0.95). This allows the real possibility that, once every ten times we conduct such an experiment, we erroneously state the device reliability to be 0.95 when in fact it may be much lower (e.g. 0.6). This may only happen 1% of the times, in the example given in the previous paragraph. It all depends on our needs. In general, the highest the confidence (1-alpha) the wider (H) the confidence interval (or bound). This is the price we must pay for having high confidence if we are unable to increase the size (n) of the sample (the device life variance alpha squared is a constant). Another source is the RAC START sheet: Statistical Assumptions of an Exponential Distribution http://rac.alionscience.com/pdf/E_ASSUME.pdf


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