Eleven systems from the field were chosen for the purposes of a fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3000 hours and assume a fixed effectiveness factor equal to 0.4. Do the following:
Estimate the parameters of the Crow Extended model.
Based on the analysis does it appear that the systems were randomly ordered?
After the implementation of the delayed fixes, how many failures would you expect within the next 4000 hours of fleet operation.
Table 10.9 - Fleet data for Example 5
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The estimated Crow Extended parameters are shown in Figure 10.8.
Upon observing the estimated parameter it does appear that the systems were randomly ordered since . This value is close to one. You can also verify that the confidence bounds on include one by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine if the systems were randomly ordered graphically using the System Operation plot as shown in Figure 10.9. Looking at the Cum. Time Line it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.
Figure 10.8: Estimated Crow Extended parameters
Figure 10.9: System Operation plot
This case study is based on the data given in the article "Graphical Analysis of Repair Data" by Dr. Wayne Nelson. The data in Table 10.10 represents repair data on an automatic transmission from a sample of 34 cars. For each car, the data set shows mileage at the time of each transmission repair, and the latest mileage. Car 1, for example, had a repair at 7068 miles and was observed until 26,744 miles. The + indicates the latest mileage observed without failure. Do the following:
Estimate the parameters of the Power Law model.
Estimate the number of warranty claims for a 36,000 mile warranty policy for an estimated fleet of 35,000 vehicles.
Table 10.10 - Automatic transmission data
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Figure 10.10: Entered transmission data and the estimated Power Law parameters
Figure 10.11: Cumulative number of failures at 36,000 miles
The estimated Power Law parameters are shown in Figure 10.10.
The expected number of failures at 36,000 miles can be estimated using the QCP as shown in Figure 10.11. The model predicts that 0.3553 failures per system will occur by 36,000 miles. This means that for a fleet of 35,000 vehicles, the expected warranty claims are 0.3553 * 35,000 = 12,436.
Field data has been collected for a system which begins its wearout phase at time zero. The start time for each system is equal to zero and the end time for each system is 10,000 miles. Each system is scheduled to undergo an overhaul after a certain number of miles. It has been determined that the cost of an overhaul is four times more expensive than a repair. The data is presented in Table 10.11. Do the following:
Estimate the parameters of the Power Law model.
Determine the optimum overhaul interval.
If , would it be cost efficient to implement an overhaul policy?
Table 10.11 - Field data
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The estimated Power Law parameters are shown in Figure 10.12.
The QCP can be used to calculate the optimum overhaul interval as shown in Figure 10.13.
If then it would not be cost efficient to implement an overhaul policy. Since , the systems are not wearing out. An overhaul policy only makes sense if the systems are wearing out. Otherwise, an overhauled unit would have the same probability of failing as a unit that was not overhauled.
Figure 10.12: Entered data and the estimated Power Law parameters
Figure 10.13: Calculate the optimum overhaul interval
See Also:
Fielded Systems
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