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Software Used: Software Used: ALTA PRO
Download Example File for Version 10 (*.rsgz10) or Version 9 (*.rsr9)
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 decide whether or not to 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 that are discovered during the test but will not be fixed. This accounts for all modes which management determines are not justified to fix for economic or other reasons. 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:
The Crow Extended model is used to analyze data that includes these failure classifications.
A product undergoes 400 hours of developmental testing. During testing, the observed failure modes are identified. The data set is given in the next three tables, where the Failure Mode column combines the mode classification with the mode’s numerical identifier. (Identifiers were not assigned to A modes since they will not be addressed.)
| Failure Time | Failure Mode | Failure Time | Failure Mode | Failure Time | Failure Mode | ||
| 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 |
An effectiveness factor based on engineering assessments is also assigned to the BD modes. This factor is the expected fractional decrease in failure intensity of a failure mode after the implementation of a corrective action (e.g., 0.7 means 70% of the mode’s failure intensity will be removed by the fix). The factors for each BD mode are shown next.
| BD Mode | Effectiveness Factor |
| 1 | 0.7 |
| 2 | 0.7 |
| 3 | 0.8 |
| 4 | 0.8 |
| 5 | 0.9 |
| 6 | 0.9 |
| 7 | 0.5 |
| 8 | 0.9 |
| 9 | 0.9 |
| 10 | 0.7 |
| 11 | 0.7 |
| 12 | 0.6 |
| 13 | 0.6 |
| 14 | 0.7 |
| 15 | 0.7 |
| 16 | 0.5 |
The Crow Extended model uses the maximum likelihood estimation (MLE) method to calculate the parameters, which is known to produce a biased value for beta. If the software is not configured to remove this bias, the option to remove it should be selected in the Application Setup.

Figure 1: Application Setup window showing that the the bias will be removed from beta.
A standard folio data sheet configured for exact failure times is created by selecting Times-to-Failure Data > Failure Times in the RGA Folio Data Sheet Setup window.

Figure 2: Selecting the data type for the new folio.


Figure 4: Effectiveness Factor window with the specified factors for each BD mode.
Finally, it is specified that the tested ended at 400 hours. (If it were “failure terminated” it would end at the time of the last failure, which in this case is 395.2 hours.)

Figure 5: Termination Time window showing a time of 400.
After analyzing the data, a summary of results on the control panel shows the parameters of the fitted model.

The summary of results shows that the demonstrated MTBF (DMTBF) for this system at the end of the test is 7.8471 hours, which is the result of the corrective action taken during the test (BC modes).
If the 16 delayed corrective actions are implemented (BD modes), the MTBF is projected to be 11.3182 hours. This can be calculated using the Quick Calculation Pad (QCP).

Figure 5: QCP showing the expected MTBF after BD modes are fixed.
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 about 15 hours. This is called the growth potential MTBF. The following plot illustrates shows the projected MTBF (red), growth potential MTBF (red) and the demonstrated MTBF (blue).

Figure 6: Growth Potential MTBF plot showing the demonstrated, projected and growth potential MTBFs.
The management strategy is summarized in the Failure Mode Strategy chart.
