Grouped Data - Crow Extended Example

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This example appears in the Reliability Growth and Repairable System Analysis Reference book.

A reliability growth test was conducted for 200 hours. Some of the corrective actions were applied during the test while others were delayed until after the test was completed. The tables below give the data set and the effectiveness factors for the BD modes. Do the following:

1) Estimate the parameters of the Crow Extended model.

2) Determine the average effectiveness factor of the BC modes using the Function Wizard.

3) What percent of the failure intensity will be left in the system due to the BD modes after implementing the delayed fixes?

Grouped Failure Times Data
Number at Event	Time to Event	Classification	Mode
3	25	BC	1
1	25	BD	9
1	25	BC	2
1	50	BD	10
1	50	BD	11
1	75	BD	12
1	75	BC	3
2	75	BD	13
1	75	A
1	100	BC	4
1	100	BD	14
1	125	BD	15
1	125	A
1	125	A
1	125	BC	5
1	125	BD	10
1	125	BC	6
1	150	A
1	150	BD	16
1	175	BC	4
1	175	BC	8
1	175	A
1	175	BC	7
1	200	BD	16
1	200	BC	3
1	200	BD	17

Effectiveness Factors
BD Mode	Effectiveness Factor
9	0.75
10	0.5
11	0.9
12	0.6
13	0.8
14	0.8
15	0.25
16	0.75
17	0.8

Solution

1) The next figure shows the estimated parameters of the Crow Extended model.

Entered data and the estimated Crow Extended parameters.

2) Insert a general spreadsheet into the folio, and then access the Function Wizard. In the Function Wizard, select Average Effectiveness Factor from the list of available functions and under Avg. Eff. Factor select BC modes, as shown next. Click Insert and the result will be inserted into the general spreadsheet. The average effectiveness factor for the BC modes is 0.6983.

Calculate the average effectiveness factor for the BC modes using the Function Wizard.

3) The failure intensity left in the system due to the BD modes can be determined using the Failure Mode Strategy plot, as shown next. Therefore, the failure intensity left in the system due to the BD modes is 1.79%. 

 

Failure Mode Strategy plot.