Statistics of fault indicator and maintenance for repairable fleet

#1
There is a fleet of repairable units and the units have system health measurements which consist primarily of vibration amplitudes. The health monitoring system is "new", so the thresholds are based on standard deviations of "normal" operations. So, the thresholds are clearly too low. Measurements above the threshold are classified as warning or non operation fault indicators depending on the threshold. There are trends of increasing frequency (count) of fault indicators, and there may be some trends of increasing amplitude. Currently, the unscheduled maintenance is performed in response to observations (operational or inspections). We are "endeavoring" to correlate the faults recorded with unscheduled maintenance performed. Correlating the faults with unscheduled maintenance is challenging for several reasons, including the large number of unscheduled repairs, and the lack of consistent description of the repair, and for other challenges.

Started to use a contingency table for the fault and an associated repair, with rows of fault threshold exceeded / not exceeded and columns of maintenance performed / not performed. But am having trouble with counting the non-events. The faults can occur multiple times during a single operation usage cycle (off/on/off cycle). But how to count the number of times the fault doesn't occur. Count a usage cycle, and only track the maximum exceedances faults (one per usage), then we could have a countable number of non faults corresponding to the number of off/on/off cycles that had no fault. That will be a very large number. For the maintenance side, we could count the number of off/on/off cycles that were followed by corrective maintenance actions (a very small number) and also the number of off/on/off cycles that were not followed by corrective maintenance actions (a very large number). The goals are to determine the usefulness, precision and reliability of the fault indicator.

All the data is in R.
 
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