Example 4 - Fielded Systems Analysis
[Download RGA7 Example File (*.rga7)]
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 A modes (where a fix will not be applied) and BD modes (where a delayed fix will be applied after the termination time). 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 be changing 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 Crow Extended 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.
Background
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 | ||||
Analysis and Results
A Standard Folio Data Sheet using the Repairable Systems data type is created by selecting the Fielded and Repairable options in the New Data Sheet Setup window Expert view, as shown next.
Projections columns are added to the Data Sheet. The data set is then entered and analyzed using the Power Law model, as shown next.
The resulting beta of 2.3829 is clearly greater than 1, but the confidence bounds on beta also must be checked to see if they include beta = 1. This can be done by specifying the confidence bounds in the Quick Calculation Pad and then clicking the Parameter Bounds icon, as shown next.
The lower confidence bound on beta, 1.4907, does not include 1. This violates the assumption associated with the Crow Extended model and the model cannot be applied to this data set. However, this assumption may not be violated if the data set is considered from a fleet perspective. To this end, the data set is transferred to a Fleet Data Sheet by choosing Data > Transfer to New Data Type and selecting the Fleet - Fielded Systems option in the Transfer to New Data Type window. The new Data Sheet is added to the Folio. A constant interval of 8000 hours is chosen for grouping the data. This provides a sufficient number of groups (11) for the analysis. The goodness-of-fit tests also return favorable results. This analysis yields a beta value of 1.0937, as shown next.
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.
NOTE: While unbiased calculations are recommended for analysis conducted using the Crow Extended model, this setting does not affect fleet data due to the grouping of the data. Therefore, the overall parameter results for fleet data will not change with the setting of the Calculate Biased Beta option on the Calculations page of the User Setup.
A conservative effectiveness factor (EF) for the BD modes is chosen, such that EF = 0.4, as shown next.
This represents the expected reduction in the failure intensity associated with each BD mode from applying the corrective actions. In other words, 60% of each BD mode’s failure intensity will remain in the system after the corrective actions have been implemented. The resulting Growth Potential MTBF plot is shown next.
The demonstrated MTBF for the fleet is equal to 2630.9032 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 2630 hours of fleet operation. Given the proposed corrective actions, the fleet MTBF is expected to jump to 3386.6754 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.
