8.
Assessing Product Reliability
8.4. Reliability Data Analysis 8.4.5. How do you fit system repair rate models?
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The Power Law (Duane) model has been very successful in modeling industrial reliability improvement data |
Brief Review of Power Law Model and Duane Plots
Recall that the Power Law is a NHPP
with the expected number of fails,
The parameter
If a system is observed for a fixed time of |
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MLE's for the Power Law model are given |
Estimates for the Power Law Model
Computer aided graphical estimates can easily be obtained by doing a
regression fit of
However, better estimates can easily be calculated. These are modified
maximum likelihood estimates (corrected to eliminate bias). The formulas
are given below for a fixed time of |
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Approximate confidence bounds for the MTBF at end of test are given |
Approximate Confidence Bounds for the MTBF at End of Test
We give an approximate 100(1- |
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Fitting the power law model to case study 1 failure data |
This case study
was introduced in section 2, where we did various plots of the data, including a Duane Plot.
The case study was
continued
when we discussed trend tests and verified that significant improvement had
taken place. Now we will complete the case study data analysis.
The observed failure times were: 5, 40, 43, 175, 389, 712, 747, 795,
1299 and 1478 hours, with the test ending at 1500 hours.
We estimate Estimate ofThe analyses in this section can can be implemented using R code. |