Crow-AMSAA Discrete Model Example

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This example appears in the Reliability growth reference.

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.

Do the following:

1. Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimation.
2. Estimate the unreliability and reliability by configuration.

Solution

1. The parameter estimates for the Crow-AMSAA model using the parameter estimation for discrete data methodology yields [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