Test-Fix-Test Data Reference Example

This example compares the results for test-fix-test data (time terminated).

Crow, L.H., Confidence Interval Procedures for the Weibull Process with Applications to Reliability Growth, U.S. Army Material Systems Analysis Activity, 1981.

The following table shows the data.

The book has the following results:


 * Beta = 0.413, Lambda = 1.769


 * DMTBF = 52.7


 * Confidence Bounds on DMTBF (CL = 80%) = (35.6, 82.9)

In RGA, the Crow-AMSAA (NHPP) model with the maximum likelihood estimation (MLE) method was used to calculate the results. The following equations are used to calculate $$\beta\,\!$$ and $$\lambda\,\!$$.


 * $$\begin{align}

\hat{\beta }=&\frac{N}{N\ln T^{*}-\underset{i=1}{\overset{N}{\mathop \sum }}\,T_{i}}\\ \\ =&\frac{23}{{23\cdot \ln \left ( 500 \right )}-87.2106}\\ \\ =&0.4127 \end{align}\,\!$$


 * $$\begin{align}

\hat{\lambda }=&\frac{N}{T^{*\beta }}\\ \\ =&\frac{23}{500^{0.4127}}\\ \\ =&1.7691 \end{align}\,\!$$


 * The model parameters are:




 * The instantaneous MTBF and its two-sided 80% confidence bounds are: