How do we account for variation in design or operating context when performing reliability analysis and building CBM optimization models, for example:

*Identical equipment working in different operational contexts – can they be treated as a single group of similar units for purposes of reliability analysis?**Ten identical pumps deliver different volumes and pressures. Can they be treated as the same item group in order to enlarge the sample?**Some of the ten pump sets have different brands of electric motors with slightly different characteristics. Would the ten pump sets be still be treated as a single item?*

These are realistic questions. Let’s try to frame them in reliability analysis terms. A sample is a collection of life cycles and coincident CBM observations that we believe reflect the failure behavior of the population. We seek a rule or algorithm that will predict failure in the population. We wonder whether a given sample that includes life cycles of items of varying equipment models, configurations, and operating contexts is a “good” sample upon which to build a predictive model based upon their similarities.

It would depend on the condition monitoring variables that are available for modeling and prediction. Those variables may account for the variations (for example, between one operating context and another) in the sample. If so, then the sample would contain the required *predictive content* regardless of its non-homogeneity. Consider, for example, a fleet of identical pumps operating at locations where they are subject to different environments, differing operational requirements, duty cycles, and operating parameters. They would probably suffer from different failure mechanisms and exhibit different failure rates. Certain failure modes could dominate in each subgroup of pumps.

It is important to keep in mind that a predictive model is “tuned” to a failure mode and to the monitored variables that influence the probability of that failure mode. The model would tend to predict its target failure mode more frequently among certain of the pumps in the sample, and not so frequently in pumps whose context is less conducive to the occurrence of that particular failure mode.

Say that that a predictive model targets the failure mode “excessive impeller wear”. Then its monitored influential variables could include suction side pressure, volume rates, etc. A second model aimed at predicting circuit board failures could trigger more frequently on pumps subjected to wide pressure and volume variations, stops and starts, amperage surges, dust, heat, and humidity. A modeling analysis would confirm or refute the significance of those variables. The analyst might propose a load factor reflective of the differing contexts.

The analysis may statistically reject a given variable for prediction. This does not necessarily mean that it is not a significant predictor. It just means that its variation is amply reflected in other variables retained in the proposed predictive model. The rejected variable does not add any additional predictive capability.

A haul truck fleet may have units assigned to different pits whose conditions vary. Some pits will have steep grades and rough terrain while others may have relatively mild grades and smaller bumps. Considering the failure mode “Final-drive case failure due to fatigue cracking” the significant monitored variables could include unbalance as recorded by suspension strain gauges, shocks as recorded by accelerometers, fuel consumption, rpm surges, clutch slippage, and so on. Monitored variables reflecting the varying contexts and therefore could predict the occurrence of a variety of failure modes regardless of sample variability.

The purpose of a predictive modeling analysis is to discover the *significant* monitored variables related to the failure modes of interest. Secondly it must determine the precise relationship between those variables and the probability of each targeted failure mode. Various statistical tests test the hypothesis of the significance of candidate monitored variables.

The *types* of the variables mentioned in the pump and truck scenarios are a mixture of “internal” and “external” variables. External variables such as loading, shock, terrain, etc. contribute to the *causes *of failure, while internal variables such as oil debris, vibration, and thermographic data can reveal some *effects *of failure. External variables influence failure. Internal variables reflect impending failure *probability*. We may combine external and internal variables for CBM prediction and decision optimization, since both are accounted for, statistically, in exactly the same way.