Example 3 - Developmental Testing with Corrective Actions Implemented During the Test and Delayed Fixes
[Download RGA7 Example File (*.rga7)]
This example is based on the paper An Extended Reliability Growth Model For Managing And Accessing Corrective Actions by Dr. Larry Crow, presented at the 2004 RAMS. [Click here to download the paper (*.pdf, 238 KB)].
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:
- Some are corrected during the test (which will be referred to as BC modes).
- Some will be corrected after the end of the test phase (i.e. delayed fixes, which will be referred to as BD modes).
- Some will be left (uncorrected) in the system (which will be referred to as A modes).
The Crow Extended model is used in these cases.
Background
A product undergoes 400 hours of developmental testing. During testing, the observed failure modes are identified. The data set is given next:
Failure Time |
Failure |
|
Failure Time |
Failure |
|
Failure Time |
Failure |
| 0.7 | BC17 | 121.9 | BC22 | 285 | BD13 | ||
| 3.7 | BC17 | 125.5 | BD9 | 304 | BD9 | ||
| 13.2 | BC17 | 133.4 | BD10 | 315.4 | BD4 | ||
| 15 | BD1 | 151 | BC23 | 317.1 | A | ||
| 17.6 | BC18 | 163 | BC24 | 320.6 | A | ||
| 25.3 | BD2 | 164.7 | BD9 | 324.5 | BD12 | ||
| 47.5 | BD3 | 174.5 | BC25 | 324.9 | BD10 | ||
| 54 | BD4 | 177.4 | BD10 | 342 | BD5 | ||
| 54.5 | BC19 | 191.6 | BC26 | 350.2 | BD3 | ||
| 56.4 | BD5 | 192.7 | BD11 | 355.2 | BC26 | ||
| 63.6 | A | 213 | A | 364.6 | BD10 | ||
| 72.2 | BD5 | 244.8 | A | 364.9 | A | ||
| 99.2 | BC20 | 249 | BD12 | 366.3 | BD2 | ||
| 99.6 | BD6 | 250.8 | A | 373 | BD8 | ||
| 100.3 | BD7 | 260.1 | BD1 | 379.4 | BD14 | ||
| 102.5 | A | 263.5 | BD8 | 389 | BD15 | ||
| 112 | BD8 | 273.1 | A | 394.9 | A | ||
| 112.2 | BC21 | 274.7 | BD6 | 395.2 | BD16 | ||
| 120.9 | BD2 | 282.8 | BC17 |
Furthermore, an effectiveness factor based on engineering assessment has been assigned for each of the BD failure modes (delayed fixes). These are given in the following table. The effectiveness factor is the expected fractional decrease in failure intensity of a failure mode after the implementation of a corrective action.
BD |
Effectiveness |
| 1 | .7 |
| 2 | .7 |
| 3 | .8 |
| 4 | .8 |
| 5 | .9 |
| 6 | .9 |
| 7 | .5 |
| 8 | .9 |
| 9 | .9 |
| 10 | .7 |
| 11 | .7 |
| 12 | .6 |
| 13 | .6 |
| 14 | .7 |
| 15 | .7 |
| 16 | .5 |
Analysis and Discussion
When using the Crow Extended model, it is common practice to calculate the unbiased beta. To do so, choose File > User Setup, then select Calculate Unbiased Beta, as shown next.
A Standard Folio Data Sheet using the Failure Times data type is created by selecting the Developmental and Failure Times options in the New Data Sheet Setup window Expert view, as shown next.
The Crow Extended model is selected and the data set is then entered.
An effectiveness factor to each BD failure mode is assigned, as shown next.
Effectiveness Factors
Finally, the time at which the test terminates is specified:
The calculated data set is shown next:
Results and Discussion
The achieved MTBF for this system is 7.8471 hours, which is the result of the corrective action taken during the test (BC modes). This can be seen in the "DMTBF" line of the Results area.
If the 16 delayed corrective actions are implemented (BD modes), the MTBF is projected to be 11.3182 hours. This can be seen on the Extended Calculations tab of the Quick Calculation Pad (QCP) and by calculating the Projected MTBF with no confidence bounds, as shown next.
If testing continues with the current management strategy in place (i.e. modes corrected vs. modes not corrected) and with the current effectiveness of each corrective action, then the maximum attainable MTBF is 15.00 hours. This is called the Growth Potential MTBF. The following plot illustrates these results.
The management strategy can be summarized in the Average Failure Mode Strategy plot.
This plot breaks down the failure intensity into contributing factors. It shows that 9.48% have been left in the system (A modes), while 14.167% were removed during testing (BC - Seen modes). From the analysis, failure modes accounting for an estimated 31.042% of the failure intensity were not observed during the testing, but would have been corrected if they had been observed (BC - Unseen modes). In addition, failure modes accounting for an estimated 8.761% of the failure intensity will be removed after the delayed corrective actions are implemented (BD - Removed modes) and failure modes accounting for an estimated 33.226% of the failure intensity have not yet been observed but will be removed by the delayed corrective actions (BD - Unseen modes). Finally, failure modes accounting for an estimated 3.323% of the failure intensity will remain (BD - Remain modes).
The MTBF of each individual failure mode can be plotted and the failure modes with the lowest MTBF can be identified. These are the failure modes that cause the majority of the system failures. This is illustrated in the next plot.
