Operational Testing Example

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

Consider two systems are placed into operational testing. The data for each system is given below. Do the following:

1. After estimating the parameters, verify the assumption of [math]\displaystyle{ \beta = 1\,\! }[/math].
2. Estimate the demonstrated MTBF of the system.
3. What is the projected MTBF if the delayed fixes are to be implemented?
4. What is the growth potential of the system?

Operational Testing Data

System #	1	2
Start Time (Hr)	0	0
End Time (Hr)	504	541
Failure Times (Hr)	21 BD43	83 BD37
	29 A42	83 BD43
	43 BD10	83 BD46
	43 BD11	169 A45
	43 A39	213 A18
	66 A20	299 A42
	115 BD34	375 A1
	159 BD49	431 BD16
	199 BD47
	202 BD47
	222 BD47
	248 BD14
	248 BD15
	255 BD41
	286 BD40
	286 BD48
	304 BD47
	320 BD13
	348 BD11
	364 BD44
	404 BD44
	410 BD4
	429 BD47

The BD modes are implemented at the end of the test and assume a fixed effectiveness factor equal to 0.6.

Solution

1. The entered operational testing data and the estimated parameters are given below.
   

   The assumption of [math]\displaystyle{ \beta = 1\,\! }[/math] can be checked by looking at the confidence bounds on [math]\displaystyle{ \beta\,\! }[/math] via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on [math]\displaystyle{ \beta\,\! }[/math] are shown next.

   

   Since the confidence bounds on [math]\displaystyle{ \beta\,\! }[/math] include one, then you can fail to reject the hypothesis that [math]\displaystyle{ \beta = 1\,\! }[/math].

2. As