SRC Forum - Message Replies

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

Original Message:

Posted by: LE GALLIOT (david.le.galliot@sonovision-itep.fr )
Organization:SONOVISION-ITEP
Date posted: Mon Apr 23 10:58:21 US/Eastern 2007
Subject: Use of level confidence with NPRD-95
Message:
Hello, I have a question about use of confidence level with NPRD-95: According to NPRD-91 and 95, "the natural logarithm of the observed failure rates is normally distributed with a sigma=1.5. This indicates that 68% of actual failure rates will be between 0.22 and 4.5 times the mean value". Or, if the parameters of the lognormal distribution are mu and sigma, then the median of the distribution is given by exp(mu) and the mean is given by exp(mu+0.5*sigma*sigma). This indicates, for sigma =1.5, that 56% of actual failure rates will be between 0.2 and 4.5 times the mean value and 68% of actual failure rates will be between 0.2 and 4.5 times the median value. I think that there is an error in NPRD-91 an NPRD-95: either it would be necessary to read “This indicates that 56% of actual failure rates will be between 0.22 and 4.5 times the mean value", either it would be necessary to read “This indicates that 68% of actual failure rates will be between 0.22 and 4.5 times the median value". Is anyone could tell me what really represent all listed failure rates on the both NPRD-91 an NPRD-95: the medians or the means of the lognormal distributions?

Reply:

Subject: Use of level confidence with NPRD-95
Reply Posted by: David Dylis (ddylis@alionscience.com )
Organization: Alion SRC
Date Posted: Thu Jun 7 13:09:28 US/Eastern 2007
Message:
The failure rates presented in NPRD-91 and NPRD-95 are means. At the summary level geometric means for each component type were determined using the following approach:

Deriving the geometric mean of all the failure rates associated with records having failures and multiplying the derived failure rates by the proportion: [observed hours with failures/total observed hours]. For example, if 70 percent of the total part hours correspond to records with failures, the geometric mean of failure rates from the data records with failures would be multiplied by 0.7. This option is appealing, since the geometric mean will inherently apply less weight to failure rates that are significantly greater than the others for the same part type. The merged failure rate should be representative of the population of parts since it takes into consideration all observed operating hours, regardless of whether or not there were observed failures. The algorithm used to calculate means of merged data is presented on page 1-16 of NPRD-95. For the purposes of merging data, those data entries with only failure rates presented (no failures and hours reported) were assumed to have one million operating hours. Roll-ups performed on only zero failure data records are accomplished simply by summing the total operating hours, calculating a failure rate by assuming one failure, and denoting the resulting upper bound failure rate with a “<” sign.

The procedure that you identified in your question was performed as a test only to determine variation in the observed failure rates and was not used in the calculation of any failure rates presented in NPRD. Alion has released a new product named SPIDR (System and Part Integrated Data Resource) that updates NPRD, EPRD, FMD, and VZAP with more than double the data previously contained by these products. Check our web site for more information on SPIDR

If you have any additional questions, feel free to contact me.