Test-Find-Test Data Reference Example

This example validates the results for test-find-test data in RGA.

International Standard IEC 61164 (Reliability Growth in Product Design and Test – Statistical Test and Estimation Methods), Example 4, pg. 32.

For this example, the following will be calculated:
 * Parameters of the Crow Extended model
 * Unseen BD mode failure intensity
 * Cramér-von Mises (CVM) goodness of fit for BD modes
 * Demonstrated MTBF (DMTBF)
 * Projected PMTBF (PMTBF)

The following table shows the data.

The book has the following results:


 * BetaBD (UnB) = 0.7472, LambdaBD = 0.0326


 * Unseen BD Mode Failure Intensity = 0.0030/hr


 * Goodness of fit for BD modes: CVM = 0.085, critical value = 0.171 with significance level = 0.1. Since CVM < critical value can fail to reject hypothesis that the model fits the data.


 * DMTBF = 88.9 hours


 * PMTBF = 135.1 hours

In RGA, the Crow Extended model with the maximum likelihood estimation (MLE) method was used to calculate the results.

For a test-find-test, the assumption is $$\,\!\beta =1$$. Therefore:


 * $$\begin{align}

DMTBF=&\frac{T}{N}\\ \\ =&\frac{4000}{45}\\ \\ =&88.8889\; \; \mathrm{hours} \end{align}\,\!$$


 * The model parameters are:






 * $$\begin{align}

\lambda _{p}=&\lambda _{A}+\sum_{i=1}^{N_{BD}}\left ( 1-d_{i} \right )\lambda _{i}+\bar{d}h\left ( T \right )\\ \\ =&\frac{N_{A}}{T}+\sum_{i=1}^{N_{BD}}\left ( 1-d_{i} \right )\frac{N_{i}}{T}+\bar{d}\lambda _{BD}\beta _{BD}T^{\beta -1}\\ \\ =&\frac{13}{4000}+0.002+\left ( 0.7188 \right )\left ( 0.032572 \right )\left ( 0.74715 \right )\left ( 4000 \right )^{0.7472-1}\\ \\ =&0.007398\\ \\ PMTBF=&\frac{1}{\lambda _{p}}\\ \\ =&135.17 \; \; \mathrm{hours} \end{align}\,\!$$


 * The growth potential MTBF plot: