Repairable Systems Analysis Reference 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 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

The following table shows the 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

The book has the following results:

Beta = 0.615, Lambda = 0.461

Results in RGA

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}{X_{iq}}\right)}\\ \\ =&0.6153 \end{align}\,\! }[/math]

[math]\displaystyle{ \begin{align} =\frac{\underset{q=1}{\overset{K}{\mathop \sum }}N_{q}}{\underset{q=1}{\overset{K}{\mathop \sum }}\underset{i=1}{\overset{N^{q}}{\mathop \sum }}\ln \left ( \frac{T}{X_{iq}} \right )} \end{align}\,\! }[/math]

[math]\displaystyle{ \begin{align} \hat{\lambda }=&\frac{{\underset{i=1}{\overset{N}{\mathop \sum }}N_{q}}}{KT^{\hat{\beta }}}\\ \\ =&0.4605 \end{align}\,\! }[/math]

The model parameters are:

Repairable Systems Analysis Reference Example

Navigation menu

Search