Concurrent Operating Times - Crow Extended Example

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at RGA examples and RGA reference examples.

---

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

Three systems were subjected to a reliability growth test to evaluate the prototype of a new product. Based on a failure analysis on the results of the test, the proposed management strategy is to delay corrective actions until after the test. The tables shown next display the data set and the associated effectiveness factors for the unique BD modes.

Multiple Systems (Concurrent Operating Times) data
	System 1	System 2	System 3
Start Time	0	0	0
End Time	541	454	436
Times-to-Failure	83 BD37	26 BD25	23 BD30
	83 BD43	26 BD43	46 BD49
	83 BD46	57 BD37	127 BD47
	169 A45	64 BD19	166 A2
	213 A18	169 A45	169 BD23
	299 A42	213 A32	213 BD7
	375 A1	231 BD8	213 BD29
	431 BD16	231 BD25	255 BD26
		231 BD27	369 A33
		231 A28	374 BD29
		304 BD24	380 BD22
		383 BD40	415 BD7

Effectiveness factors
BD Mode	Effectiveness Factor
30	0.75
43	0.5
25	0.5
49	0.75
37	0.9
19	0.75
46	0.75
47	0.25
23	0.5
7	0.25
29	0.25
8	0.5
27	0.5
26	0.75
24	0.5
22	0.5
40	0.75
16	0.75

The prototype is required to meet a projected MTBF goal of 55 hours. Do the following:

1. Estimate the parameters of the Crow Extended model.
2. Based on the current management strategy what is the projected MTBF?
3. If the projected MTBF goal is not met, alter the current management strategy to meet this requirement with as little adjustment as possible and without changing the EFs of the existing BD modes. Assume an EF = 0.7 for any newly assigned BD modes.

Solution

1. The next figure shows the estimated Crow Extended parameters.
   

   Entered data and the estimated Crow Extended parameters.
2. There are a couple of ways to calculate the projected MTBF, but the easiest is via the Quick Calculation Pad (QCP). The following result shows that the projected MTBF is estimated to be 53.9390 hours, which is below the goal of 55 hours.
   

   Calculate the projected MTBF.
3. To reach our goal, or to see if we can even get there, the management strategy must be changed. The effectiveness factors for the existing BD modes cannot be changed; however, it is possible to change an A mode to a BD mode, but which A mode(s) should be changed? To answer this question, create an Individual Mode Failure Intensity plot with just the A modes displayed, as shown next. As you can see from the plot, failure mode A45 has the highest failure intensity. Therefore, among the A modes, this particular failure mode has the greatest negative effect on the system MTBF.
   

   Individual Mode Failure Intensity chart.

   Change A45 to BD45. Be sure to change all instances of A45 to a BD mode. Enter an effectiveness factor of 0.7 for BD45, and then recalculate the parameters of the Crow Extended model. Now go back to the QCP to calculate the projected MTBF, as shown below. The projected MTBF is now estimated to be 55.5903 hours. Based on the change in the management strategy, the projected MTBF goal is now expected to be met.

   

   Calculate the projected MTBF based on the change to the management strategy.