# Optimal Preventive Maintenance Strategies for a Production System Subject to Random Shocks.

1994

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

Helmut Schneider

## Abstract

The failure rate of production equipment is usually increasing as wear accumulates with usage. An improved preventive maintenance approach is accomplished through predictive maintenance, where an indicator of wear, like vibration or heat, is measured and used to determine the optimal time of an adjustment (or maintenance) such as realignment, oil change or replacing seals. The state of the unit is restored into the same original "as new" state both after adjustment or failure (followed by a repair). This research will develop mathematical models for a single and two unit production system. In the development of the one unit model, a cost criterion and indicator variable will be used for deciding when adjustment should take place. The cost to be minimized is the long-run average cost of adjustments and failures. An optimal solution to this problem will be obtained via dynamic programming and compared to an approximate steady state solution based on renewal theory. This approximation (like other earlier works) disregards the fact that after failure (that has a small probability) the unit is restored to its original state. Both models provide an upper control limit (UCL) on the indicator variable which triggers an adjustment when exceeded. It will be shown that disregarding the restoration after failure in the cost approximation causes the UCL to be underestimated. The resulting cost penalty is considerable in most cases. For the two unit system, an optimizing mathematical model will be developed by monitoring an external variable for each unit and using this information collectively as a predictor for failure. The cost to be minimized is the long-run average cost of adjustments, system overhaul, and failures. In the general case, the system with n units, it is shown why the current approach becomes more intractable as n increases. An alternate methodology is suggested. Finally, using a simplified decision policy, a simulation model is offered as a safeguard that the mathematical model is realistic. Sensitivity and factor analysis results are also provided for both the single and two unit systems.

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