Repairable Systems Analysis Reference Example

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This example compares the results for a repairable systems analysis.

Reference Case

Crow, L.H., Reliability Analysis for Complex Repairable Systems, Reliability and Biometry: Statistical Analysis of Lifelength, pg. 385, 1974.

Data

Simulated Data for 3 Systems with End Time = 200 hours
System 1	System 2	System 3
4.3	0.1	8.4
4.4	5.6	32.4
10.2	18.6	44.7
23.5	19.5	48.4
23.8	24.2	50.6
26.4	26.7	73.6
74	45.1	98.7
77.1	45.8	112.2
92.1	72.7	129.8
197.2	75.7	136
	98.6	195.8
	120.1
	161.8
	180.6
	190.8

Result

Beta = 0.615, Lambda = 0.461

Results in Weibull++

Since [math]\displaystyle{ \,\!S_{1}=S_{2}=S_{3}=0 }[/math] and [math]\displaystyle{ \,\!T_{1}=T_{2}=T_{3}=200 }[/math] then the maximum likelihood estimates of [math]\displaystyle{ \,\!\hat{\beta} }[/math] and [math]\displaystyle{ \,\!\hat{\lambda } }[/math] are given by:

[math]\displaystyle{ \begin{align} \hat{\beta }=&\frac{\sum_{q=1}^{K}N_{q}}{\sum_{q=1}^{K}\sum_{i=1}^{N_{q}}ln \left(\frac{T}{N_{iq}}\right)}\\ \\ =&0.6153 \end{align}\,\! }[/math]

[math]\displaystyle{ \begin{align} \hat{\lambda }=&\frac{\sum_{q=1}^{K}N_{q}}{KT^{\hat{\beta }}}\\ \\ =&0.4605 \end{align}\,\! }[/math]