Test-Fix-Find-Test

Traditional reliability growth models provide assessments for two types of testing and corrective action strategies: test-fix-test and test-find-test. In test-fix-test, failure modes are found during testing and corrective actions for these modes are incorporated during the test (Crow-AMSAA model). In test-find-test, modes are found during testing but all of the corrective actions are delayed and incorporated after the completion of the test (also called the Crow-AMSAA Projection model). However, a common strategy involves a combination of these two approaches, namely some corrective actions are incorporated during the test and some corrective actions are delayed and incorporated at the end of the test. This strategy is referred to as test-fix-find-test. Test-fix-find-test is a special case of the Crow Extended reliability growth model.

Recall that B failure modes are all failure modes that will receive a corrective action. In order to provide the assessment and management metric structure for corrective actions during and after a test, two types of B modes are defined. BC failure modes are corrected during the test and BD failure modes are delayed until the end of the test. A type failure modes are defined as before; i.e. those failure modes that will not receive a corrective action, either during or at the end of the test.

Development of the Extended Reliability Growth Model

Let denote the constant failure intensity for the BD failure modes and let h(t|BD) denote the first occurrence function for the BD failure modes. In addition, as before, let K be the number of BD failure modes, let di be the effectiveness factor for the ith BD failure mode and let be the average effectiveness factor.

The extended reliability growth model projected failure intensity is given by:

(9)

where is the achieved failure intensity at time T.

The extended reliability growth model projected MTBF is:

This is the MTBF after the delayed fixes have been implemented. Under the extended reliability growth model, the demonstrated failure intensity before the delayed fixes is the first term, . The demonstrated MTBF at time T before the delayed fixes is given by:

If you assume that there are no delayed corrective actions (BD modes) then the model reduces to the special case of the Crow-AMSAA model (the first term only in Eqn. 9) and the achieved MTBF equals the projection. That is, there is no jump. If you assume that there are no corrective actions during the test (BC modes) then the model reduces to the test-find-test scenario described in the Test-Find-Test section.

Estimation of the Extended Reliability Growth Model

In the general estimation of the Crow Extended model, it is required that all failure times during the test are known. However, it is only required that the distinct BD failure modes are designated. The BD failure modes must be known, but it is not necessary to distinguish among the A and BC failure modes. In the calculation of a number of the management metrics discussed in the Failure Mode Management Strategy section, it is required that the A and distinct BC failure modes are known.

The estimate of the projected failure intensity for the extended reliability growth model is given by:

(10)

where Ni is the total number of failures for the ith BD mode and di is the corresponding assigned EF. In order to obtain the first term, , fit all of the data (regardless of mode classification) to the Crow-AMSAA model to estimate and , thus

The remaining terms are calculated as the Crow Extended model, which is applied to only the BD data.

is the unbiased estimated of for the Crow-AMSAA model based on the first occurrence of M distinct BD modes.

The structure for the Crow Extended model includes the following special data analysis cases:

1. Test-fix-test with no failure modes known or with BC failure modes known. This is the data for the traditional Crow-AMSAA analysis.

2. Test-find-test with BD failure modes known. (This is also referred to as the Crow-AMSAA Projection model.)

3. Test-fix-find-test with BC and BD failure modes known.

Reliability Growth Potential and Maturity Metrics

The growth potential and some maturity metrics for the Crow Extended model are calculated as follows.

Initial system MTBF and failure intensity

and

where and are the estimators of the Crow-AMSAA model for all data regardless of the failure mode classification (i.e. A, BC or BD).

A mode failure intensity and MTBF

Initial BD mode failure intensity
BC mode initial failure intensity and MTBF
Failure intensity h(T|BC) and instantaneous MTBF M(T|BC) for new BC failure modes at the end of test T

where and are the estimators of the Crow-AMSAA model for the first occurrence of distinct BC modes.

Average effectiveness factor for BC failure modes

where NBC is the total number of observed BC modes, MBC is the number of unique BC mode and is the MLE for the first occurrence of distinct BC modes. If then equals zero.

Growth potential failure intensity and growth potential MTBF

(11)