Crow-AMSAA Discrete Model Grouped Data Example: Difference between revisions

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!Failures in Interval
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!Cumulative Trials
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Revision as of 16:46, 14 May 2014

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


The table below shows the number of failures of each interval of trials and the cumulative number of trials in each interval for a reliability growth test. For example, the first row indicates that for an interval of 14 trials, 5 failures occurred.

Mixed Data
Failures in Interval Cumulative Trials
5 14
3 33
4 48
0 52
1 53
0 57
1 58
0 62
1 63
0 67
1 68


Using the RGA software, the parameters of the Crow-AMSAA model are estimated as follows:

[math]\displaystyle{ \hat{\beta }=0.7950\,\! }[/math]

and:

[math]\displaystyle{ \hat{\lambda }=0.5588\,\! }[/math]

As we have seen, the Crow-AMSAA instantaneous failure intensity, [math]\displaystyle{ {{\lambda }_{i}}(T)\,\! }[/math], is defined as:

[math]\displaystyle{ \begin{align} {{\lambda }_{i}}(T)=\lambda \beta {{T}^{\beta -1}},\text{with }T\gt 0,\text{ }\lambda \gt 0\text{ and }\beta \gt 0 \end{align}\,\! }[/math]

Using the parameter estimates, we can calculate the instantaneous unreliability at the end of the test, or [math]\displaystyle{ T=68.\,\! }[/math]

[math]\displaystyle{ {{R}_{i}}(68)=0.5588\cdot 0.7950\cdot {{68}^{0.7950-1}}=0.1871\,\! }[/math]

This result that can be obtained from the Quick Calculation Pad (QCP), for [math]\displaystyle{ T=68,\,\! }[/math] as seen in the following picture.

Instantaneous unreliability at the end of the test.

The instantaneous reliability can then be calculated as:

[math]\displaystyle{ \begin{align} {{R}_{inst}}=1-0.1871=0.8129 \end{align}\,\! }[/math]