Repairable Systems Analysis Reference Example

This example compares the results for a repairable systems analysis.

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

For this example, the Power Law model parameters will be calculated.

The following table shows the data.

The book has the following results:

Beta = 0.615, Lambda = 0.461

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


 * $$\begin{align}

\hat{\beta} =&\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 )}\\ \\ =&0.6153 \end{align}\,\!$$


 * $$\begin{align}

\hat{\lambda }=&\frac{KT^{\hat{\beta }}}\\ \\ =&0.4605 \end{align}\,\!$$

The model parameters are: