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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

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Original Message:

Posted by: Andrew Rowland ( )
Date posted: Mon Nov 4 11:20:38 US/Eastern 2002
Subject: Weibull Analysis Results
I am analyzing field failure data of an electronic system. When performing a Weibull analysis, I find a beta of 0.952 with 19 samples. The source of information is only accurate to the day (i.e., I only know what date a failure occurred, not exact time), so I expected some error from this. Given the age of the equipment being analyzed, it would be expected to be operating within it's useful life. How far from 1.00 does the beta need to be before I would be wrong in using an exponential distribution? How much error can I expect due to the time reporting limitations of my data source?


Subject: Weibull Analysis
Reply Posted by: Jorge Romeu ( )
Organization: RAC
Date Posted: Tue Nov 5 15:39:54 US/Eastern 2002
To answer this two-part query we revisit the original problem. First, Mr. Rowland is using a well-known Weibull property [1,2,3,4,5]: if its shape parameter (Beta) is unit, Weibull reduces to an Exponential with mean, the scale parameter (Alpha). But Mr. Rowland is working with a sample, not with the population. Hence, there is a sampling error in his point estimation of the shape parameter Beta, which is a function of two factors: the sample size and other Weibull parameters (e.g. mean, variance, and scale). Therefore, without having access to Mr. Rowland's sample there is no way to say whether 0.952 is good enough to assume Beta is unit (and Exponentiality of the data) or whether it is not.


Subject: Weibull Beta Confidence
Reply Posted by: Joe Dzekevich ( )
Organization: Raytheon
Date Posted: Tue Nov 5 16:45:14 US/Eastern 2002
All good points made. I agree. Now, just like you can construct confidence bounds around the Weibull characteristic life, you can also construct confidence bounds around the shape factor, Beta. That should help you to see how far the spread is above and below 1.0.

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