Ansell, J.I., Archibald, T.W. and Thomas, L.C.
The elixir of life: using a maintenance repair and replacement model based on operating age in the water industry
IMA Journal of Management Mathematics, 15, (2), . (doi:10.1093/imaman/15.2.151).
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Processing equipment in the water industry is subject to decay and requires maintenance, repair and eventual replacement. The challenge of competition within the water industry and the accompanying regulatory regime requires that actions be integrated and cost effective. This is an industry, which has considerable data on the failure of its equipment, but until recently very few models of the maintenance process have been built.
This paper describes the context of this problem for clean water processing where the equipment is that required to purify water. It proposes a model based on the virtual and operating age of the components. The operating age reflects the true age of the equipment while the virtual age allows for the cumulative effect of maintenance actions performed on the equipment. The model also allows for different types of equipment by describing degradation by Cox's proportional hazards model. Thus the special features of the equipment and environment in which the equipment operates are described by a set of characteristics, which modify the hazard rate of the failure time of the equipment. This approach using Cox's model with virtual and operating age can be applied to other processing industries including the gas industry and the ‘dirty water’ side of the water industry.
The model is formulated as a stochastic dynamic programming or Markov decision process and the form of the optimal policy is determined. This shows that repair and replacement should only be performed when the equipment has failed and describes general conditions when replacement is appropriate. The optimal policy is calculated numerically using the value iteration algorithm for a specific example based on data on failure.
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