Ed Merlino
December 2nd, 2004, 02:29 PM
The feasibility analysis of a project usually uses Predicted Failure Rates (or MTBs) like from MIL-HNBK-217. When the project is implemented in the field then you start to collect field data. Because at the beginning the number of operating hours is small (and may be you have some failures) you want to combine the predicted and the field data. The Predicted and Field are two different statistical populations with different environments and also if I have a part that has a FRate of 1 FPMHs and in the field, after 2000 hours, I have a failure then the total MTBF is going to be VERY small if I combined the two populations.
What is the best way to merge these data ?
I know of two ways:
1) Use the formula given by PRISM (from PRISM Manual):
Lambda = a0 + A1 + ….an / b0 + B1 + … bn
where,
Lambda = The best estimate of the predicted failure rate
a0 = The equivalent number of failures of the "prior" distribution corresponding to the reliability prediction
a0=0.5
b0= The equivalent number of hours associated with the reliability prediction. Since a0 is set to 0.5, the value of b0 is calculated by PRISM as:
b0 = 0.5 / Lambda pred
where Lambda pred is the failure rate determined by PRISM (either via a RACRates model calculation, merged RAC Data, or a User Defined failure rate).
A1 thru an = The number of failures experienced in the test or field data. There may be "n" different types of datasets available. A dataset is defined as a matched pair of "ai" and "bi" values.
B1 thru bn = The corresponding number of cumulative hours (in millions) experienced from the empirical data. The user will need to convert these values to equivalent hours by accounting for the accelerating effects between the applied test conditions and the actual use conditions.
Here the term a0 = 0.5 is a concern.
2) Use Bayes Gamma function as explained by Dimitri Kececioglu book: Reliability & Life Testing Hndk, Vol 2, page 504 to 505, see Table 11.12, Assessment of Prior Inverted Gamma Dist. From Objective Prior Information (page 498), where MTBF is the random variable. The calculation of the prior gives the alpha and beta parameters for the Inverted Gamma distribution for a set of data, then the new updated data (field data) is calculating using the well know equations of posterior Inv Gammas. The problem here IF the data (the Field samples) DO NOT follow a Inv Gamma distribution then the formulas (11.94 for alpha, & 11.95 for beta) break down into negative values. A call to Dimitri confirmed these assumptions. Then the problem here is first to prove that the data is Inv Gamma distributed.
Question: How do you check that the data follows the Inv Gamma distribution ?
Any other ways to calculate this problem?
Thank you for your answers Reliasoft (Pantelis?).
What is the best way to merge these data ?
I know of two ways:
1) Use the formula given by PRISM (from PRISM Manual):
Lambda = a0 + A1 + ….an / b0 + B1 + … bn
where,
Lambda = The best estimate of the predicted failure rate
a0 = The equivalent number of failures of the "prior" distribution corresponding to the reliability prediction
a0=0.5
b0= The equivalent number of hours associated with the reliability prediction. Since a0 is set to 0.5, the value of b0 is calculated by PRISM as:
b0 = 0.5 / Lambda pred
where Lambda pred is the failure rate determined by PRISM (either via a RACRates model calculation, merged RAC Data, or a User Defined failure rate).
A1 thru an = The number of failures experienced in the test or field data. There may be "n" different types of datasets available. A dataset is defined as a matched pair of "ai" and "bi" values.
B1 thru bn = The corresponding number of cumulative hours (in millions) experienced from the empirical data. The user will need to convert these values to equivalent hours by accounting for the accelerating effects between the applied test conditions and the actual use conditions.
Here the term a0 = 0.5 is a concern.
2) Use Bayes Gamma function as explained by Dimitri Kececioglu book: Reliability & Life Testing Hndk, Vol 2, page 504 to 505, see Table 11.12, Assessment of Prior Inverted Gamma Dist. From Objective Prior Information (page 498), where MTBF is the random variable. The calculation of the prior gives the alpha and beta parameters for the Inverted Gamma distribution for a set of data, then the new updated data (field data) is calculating using the well know equations of posterior Inv Gammas. The problem here IF the data (the Field samples) DO NOT follow a Inv Gamma distribution then the formulas (11.94 for alpha, & 11.95 for beta) break down into negative values. A call to Dimitri confirmed these assumptions. Then the problem here is first to prove that the data is Inv Gamma distributed.
Question: How do you check that the data follows the Inv Gamma distribution ?
Any other ways to calculate this problem?
Thank you for your answers Reliasoft (Pantelis?).