Failure Discounting

During a reliability growth test, once a failure has been analyzed and corrective actions for that specific failure mode have been implemented, the probability of its recurrence is diminished, as given in Lloyd [4]. Then for the success/failure data that follow, the value of the failure for which corrective actions have already been implemented should be subtracted from the total number of failures. However, certain questions arise, such as to what extent should the failure value be diminished or discounted, and how should the failure value be defined? One answer would be to use engineering judgment (e.g., a panel of specialists would agree that the probability of failure has been reduced by 50% or 90% and therefore, that failure should be given a value of 0.5 or 0.9). The obvious disadvantage of this approach is its arbitrariness and the difficulty of reaching an agreement. Therefore, a statistical basis needs to be selected, one that is repeatable and less arbitrary. Failure discounting is applied when using the Lloyd-Lipow, logistic, and the standard and modified Gompertz models.

The value of the failure, $$f\,\!$$, is chosen to be the upper confidence limit on the probability of failure based on the number of successful tests following implementation of the corrective action. The failure value is given by the following equation:


 * $$f=1-{{(1-CL)}^{\tfrac{1}}}\,\!$$

where:


 * $$CL\,\!$$ is the confidence level.
 * $${{S}_{n}}\,\!$$ is the number of successful tests after the first success following the corrective action.

For example, after one successful test following a corrective action, $${{S}_{n}}=1\,\!$$, the failure is given a value of 0.9 based on a 90% confidence level. After two successful tests, $${{S}_{n}}=2\,\!$$, the failure is given a value of 0.684, and so on. The procedure for applying this method is illustrated in the next example.

Example