Crow Extended

The most widely used traditional reliability growth tracking model, Crow-AMSAA, was presented in the Crow-AMSAA (N.H.P.P.) chapter. Using this model for reliability growth analysis assumes that the corrective actions for the observed failures modes are incorporated during the test (test-fix-test). However, in actual practice, fixes may be delayed until after the completion of the test (test-find-test) or some fixes may be implemented during the test while others are delayed (test-fix-find-test). At the end of a test phase two reliability estimates are of concern: demonstrated reliability and projected reliability. The demonstrated reliability, which is based on data generated during the test phase, is an estimate of the system reliability for its configuration at the end of the test phase. The projected reliability measures the impact of the delayed fixes at the end of the current test phase. Most of the reliability growth literature has been concerned with procedures and models for calculating the demonstrated reliability and very little attention has been paid to techniques for reliability projections. The procedure for making reliability projections utilizes engineering assessments of the effectiveness of the delayed fixes for each observed failure mode. These effectiveness factors are then used with the data generated during the test phase to obtain a projected estimate for the updated configuration by adjusting the number of failures observed during the test phase. The process of estimating the projected reliability is accomplished using the Crow Extended model. The Crow Extended model allows for a flexible growth strategy that can include corrective actions performed during the test, as well as delayed corrective actions. The test-find-test and test-fix-find-test scenarios are simply subsets of the Crow Extended model.

This chapter includes the following sections:

Crow Extended Model Background

When a system is tested and failure modes are observed, management can make one of two possible decisions, either to fix or not fix the failure mode. Therefore, the management strategy places failure modes into two categories; A modes and B modes. A modes are all failure modes such that when seen during the test no corrective action will be taken. This accounts for all modes for which management determines that it is not economically or otherwise justified to take 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 modes are corrected during the test and the corrective actions for BD modes are delayed until the end of the test. The management strategy is defined by how the corrective actions, if any, will be implemented. In summary, the classifications are defined as follows:

A indicates that no corrective action was or will be performed (management chooses not to address for technical, financial or other reasons).
BC indicates that the corrective action was implemented during the test. (BC modes were also referred to as C modes.) The analysis assumes that the effect of the corrective action was experienced during the test (as with other test-fix-test reliability growth analyses).
BD indicates that the corrective action will be delayed until after the completion of the current test. (BD modes were also referred to as B modes.)

Figure 9.1 shows an example of data entered for the Crow Extended model.

Figure 9.1: Failure Times data for a single system in cumulative format, including classification and mode information.

As you can see, each failure is indicated with A, BC, or BD in the Classification column. In addition, any text can be used to specify the mode. In the figure above, numbers were used in the Mode column for simplicity, but you could just as easily use "Seal Leak," or whatever designation you deem appropriate for the failure.

Reliability growth is achieved by decreasing the failure intensity. The failure intensity for the A failure modes will not change. Therefore, reliability growth can only be achieved by decreasing the BC and BD mode failure intensity. It is also clear that, in general, the only part of the BD mode failure intensity that can be decreased is that which has been seen during testing. BC failure modes are corrected during test and the BC failure intensity will not change any more at the end of test.

It is very important to note that once a BD failure mode is in the system it is rarely totally eliminated by a corrective action. After a BD mode has been found and fixed, a certain percentage of the failure intensity will be removed, but a certain percentage of the failure intensity will generally remain. For each BD mode, an effectiveness factor (EF) is required to estimate how effective you will be in eliminating the failure intensity due to the failure mode. The EF is the fractional decrease in a mode's failure intensity after a corrective action has been made and must be a value between 0 and 1. A recent study on EFs showed that an average EF d was about 70 percent. However, individual EFs for the failure modes may be larger or smaller than the average. Therefore, typically about 30 percent, i.e. 100 (1 - d) percent, of the BD mode failure intensity will remain in the system after all of the corrective actions have been implemented. Figure 9.2 displays RGA's Effectiveness Factor window where the effectiveness factors for each unique BD failure mode can be specified.

Figure 9.2: Effectiveness factors defined for each unique BD mode

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