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5. Combining Predicted Failure Rate With Empirical Data
The user of this model is encouraged to collect as much empirical data as possible and use it in the assessment. This is done by mathematically combining the assessment made (based on the initial assessment and the process grades) with empirical data. This step will combine the best "pre-build" failure rate estimate obtained from the initial assessment (with process grading) with the metrics obtained from the empirical data. Bayesian techniques are used for this purpose. This technique accounts for the quantity of data by weighting large amounts of data more heavily than small quantities. The failure rate estimate obtained above forms the "prior" distribution, comprised of a0 and b0.
If empirical data (i.e., test or field data) is available on the system under analysis, it can be combined with the best pre-build failure rate estimate using the following equation.
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| where, |
| |
λ |
= |
The best estimate of the predicted failure rate |
| |
a0 |
= |
The equivalent number of failures of the prior distribution corresponding to the reliability prediction (after process grading has been accounted for) |
| a0 = 0.5 |
| |
b0 |
= |
The equivalent number of hours associated with the reliability prediction (after process grading). After a0 is calculated, the value of b0 can be calculated by |
| b0 = a0 / λp |
| |
a1 through an = The number of failures experienced in the empirical data. There may be "n" different types of data available. |
| |
| |
b1 through bn = The equivalent number of cumulative operating hours (in millions) experienced in the empirical data. These values must be converted to equivalent hours by accounting for the accelerating effects between the test and use conditions. |
If test data is available that was taken at accelerated conditions, it needs to be converted to the conditions of interest. A traditional reliability prediction can be performed at both the test and use conditions, and the equivalent number of hours (bi) can be determined from the failure rate ratio between the test and use temperatures.
(Click to Zoom)
| where, |
| |
HEq |
= |
The equivalent number of test hours |
| |
λ1 |
= |
Predicted failure rate at the test conditions obtained by performing a reliability prediction of system at the test condition |
| |
λ2 |
= |
Predicted failure rate at the use conditions obtained by performing a prediction at the use conditions |
| |
HT |
= |
Actual number of test hours |
Adding empirical data in the failure rate estimate...
- integrates all RAM data that is available at the point in time when the estimate is performed (analogous to the statistical process called "meta-analysis"),
- provides flexibility for the user to customize the reliability model with historical data.
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