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ReliaSoft's RGA - Case Studies
Software for Repairable System
and Reliability Growth Analysis

Case Study 3: Developmental Testing with Corrective Actions Implemented During the Test and Delayed Fixes	Software Used: RGA 6 PRO
*Download RGA 6 Example File (.rga)**

Case Study 3

This case study 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)]

A product undergoes 400 hours of developmental testing. During testing, the observed failure modes are identified and:

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 data set is given next:

Failure Time	Failure Mode	Failure Time	Failure Mode
0.7	BC1	192.7	BD11
3.7	BC1	213	A
13.2	BC1	244.8	A
15	BD1	249	BD12
17.6	BC2	250.8	A
25.3	BD2	260.1	BD1
47.5	BD3	263.5	BD8
54	BD4	273.1	A
54.5	BC3	274.7	BD6
56.4	BD5	282.8	BC11
63.6	A	285	BD13
72.2	BD5	304	BD9
99.2	BC4	315.4	BD4
99.6	BD6	317.1	A
100.3	BD7	320.6	A
102.5	A	324.5	BD12
112	BD8	324.9	BD10
112.2	BC5	342	BD5
120.9	BD2	350.2	BD3
121.9	BC6	355.2	BC12
125.5	BD9	364.6	BD10
133.4	BD10	364.9	A
151	BC7	366.3	BD2
163	BC8	373	BD8
164.7	BD9	379.4	BD14
174.5	BC9	389	BD15
177.4	BD10	394.9	A
191.6	BC10	395.2	BD16

Furthermore, an effectiveness factor based on engineering assessment has been assigned for the BD failure modes (delayed fixes). This is 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 Mode	Effectiveness Factor
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

Data Entry
A new Data Entry Spreadsheet is created using the Data Type Expert by selecting the following option.

Data Type Expert

Once the Data Entry Spreadsheet has been created, the model is changed to Crow Extended and the data are entered. An effectiveness factor is then assigned to each BD failure mode, as shown next. (Note that when using the Crow Extended model, it is common practice to calculate the unbiased beta. You can specify to calculate the unbiased beta via the User Setup.)

[Click to Enlarge]

Finally, the time at which the test terminates is specified:

Termination Time Window

Results and Discussion
The achieved MTBF for this system is 7.85 hr, 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 11.32 hr.

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 hr. This is called the Growth Potential MTBF. The following plot illustrates these results.

The management strategy can be summarized in the Failure Mode Strategy plot.

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 13.4% were removed during testing (BC - Seen modes). From the analysis, an estimated 31.81% of the failure intensity were not observed during testing, but would have been corrected if they had been observed (BC - Unseen modes). In addition, 8.76% will be removed after the delayed corrective actions are implemented (BD - Removed modes) and 33.23% have not yet been observed but will be removed by the delayed corrective actions (BD - Unseen modes), while 3.32% 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.