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Software Used: Software Used: ALTA PRO
Download Example File for Version 10 (*.rsgz10) or Version 9 (*.rsr9)
When applying the Crow Extended model for fielded system analysis (with both the Repairable and Fleet data types), the underlying assumption is that beta = 1. This is the underlying assumption associated with the Crow Extended model when the data set contains only A modes (where a fix will not be applied) and BD modes (where a delayed fix will be applied after the test). This assumption implies that the system is in a relatively steady state as it is being used; it is neither wearing out nor exhibiting reliability growth.
However, the failure intensity of a fielded system might change over time (e.g., increasing if the system exhibits wear-out, in which case beta > 1) and this would violate the assumption of beta = 1 that is required for the model. But if you consider the data from a fleet perspective (where the number of fleet failures versus fleet time is modeled), the failures might become random. Therefore, the Fleet data type can be used when the underlying assumption of beta = 1 does not hold true for repairable systems analysis and you wish to apply the Crow Extended model to analyze the improvement from fixing the BD failure modes.
In this example, the purpose of the analysis is to project the improvement in a system based on the implementation of planned fixes for some failure modes. This example is based on the following data from 22 fielded systems. All systems have a start time of 0, and the final failure time for each system is considered to be the system’s end time.
| System | Failure1 | Failure2 | Failure3 | ||||||
| Time | Classification | Mode | Time | Classification | Mode | Time | Classification | Mode | |
| 1 | 1396 | BD | 1 | ||||||
| 2 | 4497 | BD | 2 | ||||||
| 3 | 2132 | BD | 3 | ||||||
| 4 | 3698 | BD | 4 | ||||||
| 5 | 2514 | BD | 5 | ||||||
| 6 | 2024 | BD | 3 | ||||||
| 7 | 2100 | BD | 3 | 5822 | A | ||||
| 8 | 5371 | A | |||||||
| 9 | 4233 | BD | 2 | 4234 | BD | 6 | 4877 | BD | 5 |
| 10 | 1877 | BD | 1 | 2527 | A | ||||
| 11 | 1420 | BD | 7 | 1980 | BD | 8 | |||
| 12 | 5079 | BD | 9 | ||||||
| 13 | 1023 | BD | 2 | ||||||
| 14 | 3163 | BD | 8 | ||||||
| 15 | 4767 | BD | 5 | ||||||
| 16 | 3795 | BD | 1 | 4375 | A | 6228 | BD | 7 | |
| 17 | 2156 | A | |||||||
| 18 | 5630 | A | |||||||
| 19 | 1841 | BD | 10 | ||||||
| 20 | 3385 | BD | 4 | 5852 | BD | 10 | |||
| 21 | 3556 | A | |||||||
| 22 | 3956 | A | 5425 | BD | 6 | ||||
A standard folio data sheet configured for exact failure times data type is created by selecting Fielded > Repairable in the RGA Folio Data Sheet Setup window, as shown next.
Figure 1: Selecting the data type for the new folio.
The Crow Extended model is selected so the analysis can take the failure mode information into account. Then the data is entered one system at a time. The failure times for System 9 (selected in the Systems panel) are shown next.
Figure 2: Data set entered in the standard folio.
Before the data can be analyzed, an effective factor must be entered for each BD mode. It is estimated that 40% of the failure intensity of each BD mode will be removed after the delayed fix is implemented, so a fixed factor of 0.4 is used for all the modes.
Figure 3: Effectiveness Factor window with a constant factor of 0.4 entered.
After analyzing the data, the resulting beta of 2.3829 is clearly greater than 1 and therefore violates the beta = 1 assumption, as shown next. (The assumption is shown on the Beta (hyp) line and assumed value is shown in red to indicate the the assumption is invalid. The calculated beta is shown on the Beta line.)
However, the confidence bounds on beta also must be checked to see if they include 1. This can be done with the Quick Parameter Estimator, as shown next. The results show that the 90% lower one-sided confidence bound is still higher than 1. Therefore, the assumption associated with the Crow Extended model is not valid, and the model cannot be applied if the data set is entered as Fielded Repairable data.
Figure 4: QCP showing that the bounds on beta do not include 1.
However, this assumption may not be violated if the data set is considered from a fleet perspective. To this end, the data set is automatically transferred to a new data sheet in the folio configured for the Repairable Fleet data type.
When the analysis is performed from a fleet perspective, a constant interval of 8,000 hours is chosen for grouping the data. This provides a sufficient number of groups (11) for the analysis. This analysis yields a Beta value of 1.0937, as shown next. The result of the Chi-Sqgoodness-of-fit test also shows a favorable result.
Using the QCP to calculate the parameter bounds as described above, we find that the lower confidence bound on beta is 0.8302, which includes 1. Given this, we can accept the hypothesis that beta = 1. Therefore, the analysis can proceed with the application of the Crow Extended model.
Figure 5: QCP showing that the bounds on beta do include 1.
The resulting Growth Potential MTBF plot is shown next.
Figure 6: Growth Potential MTBF plot showing the demonstrated (blue line) and projected (red point) MTBFs.
The demonstrated MTBF for the fleet is about 2,631 hours. Therefore, based on the current configuration of the system in the fleet, a failure within the fleet is expected to occur once for every 2,630 hours of fleet operation. Given the proposed corrective actions, the fleet MTBF is expected to jump to about 3,387 hours. This jump in the fleet’s MTBF, a 29% improvement over the demonstrated MTBF, is the projected improvement based on the 12 proposed corrective actions.
