Crow-AMSAA Discrete Model Example

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This example appears in the Reliability Growth and Repairable System Analysis Reference book.

A one-shot system underwent reliability growth development testing for a total of 68 trials. Delayed corrective actions were incorporated after the 14th, 33rd and 48th trials. From trial 49 to trial 68, the configuration was not changed.

• Configuration 1 experienced 5 failures,
• Configuration 2 experienced 3 failures,
• Configuration 3 experienced 4 failures and
• Configuration 4 experienced 4 failures.

The objectives are:

1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimation.

2) Estimate the unreliability and reliability by configuration.

Solution

1) The solution from the MLE equations for discrete models yield [math]\displaystyle{ \lambda = 0.5954\,\! }[/math] and [math]\displaystyle{ \beta =0.7801\,\! }[/math].

2) The following table displays the results for probability of failure and reliability, and these results are displayed in the next two plots.

Estimated Failure Probability and Reliability by Configuration

Configuration([math]\displaystyle{ i\,\! }[/math])	Estimated Failure Probability	Estimated Reliability
1	0.333	0.667
2	0.234	0.766
3	0.206	0.794
4	0.190	0.810