To achieve a high system availability at minimal costs, relevant decisions include the choice of preventive maintenance frequency, spare part inventory levels and spare part repair capacity. We develop heuristics for the joint optimisation of these variables for (a) a single k-out-of-N system under condition-based maintenance and (b) an installed base of multiple identical k-out-of-N systems under block replacement. We show that a straightforward extension of the METRIC method for spare part inventory optimisation yields inferior results, because both the availability and costs are not necessarily monotonous functions of the decision variables. We develop an adjusted marginal analysis and show that it performs considerably better in numerical experiments.
Many of today's capital assets require a high availability, because the consequences of downtime can be serious. For example, the failure of a wafer stepper in the semiconductor industry usually leads to a production stop. This yields reduced output and hence reduced revenues, so the consequence of a failure is serious. The system availability is influenced by many tactical and operational decisions, such as the maintenance frequency, the amount of maintenance resources like service engineers and test equipment, and spare part inventories. A common approach is to decompose the overall trade-off in a set of subproblems. However, we can argue that there are clear relations between these decision variables.
For example, consider the interaction between spare part inventories and maintenance frequency. Demand for spare parts arises from both preventive and corrective maintenance. A higher preventive maintenance frequency leads to higher maintenance cost, but at the same time to a better predictable demand for spare parts and hence to a lower spare parts safety stock. Also, the interaction between repairable spare part inventories and the capacity needed to repair these spares cannot be neglected, see e.g. Sleptchenko et al., 2002 and Sleptchenko et al., 2003: low repair shop capacity means a high utilisation, so long spare part repair leadtimes. As safety stocks should cover the demand during the leadtime, this means that savings on repair capacity lead to a need for more spare parts and vice versa.
In this paper, we discuss heuristics for the joint optimisation of maintenance frequency, spare part inventories, and spare part repair capacity. We focus on k -out-of-N systems with hot stand-by redundancy. That is, a system consists of N identical components of which only k<Nk<N are required for system operation. The N-kN-k stand-by components have the same failure behaviour as the k operational components. We construct our optimisation heuristics based on approximations that we have developed before to calculate the system availability as function of the maintenance frequency, spare part inventories and repair capacity ( De Smidt-Destombes et al., 2004, De Smidt-Destombes et al., 2006 and De Smidt-Destombes et al., 2007). A complication is that the availability might not be a monotonous function of the maintenance frequency. When the frequency decreases, the probability that the system fails before maintenance starts increases and this pushes the availability down. On the other hand, the cycle length increases and the expected uptime in a cycle increases as well, which pushes the availability up. The aggregate effect may both be a decrease or an increase in the system availability. Therefore, the development of a joint optimisation method for spare part inventories, repair capacity and maintenance frequency is not straightforward.
The remainder of this paper is structured as follows. In the next section, we discuss the related literature. In Section 3, we develop an optimisation heuristic for a single k-out-of-N system with condition-based maintenance. We evaluate the quality of our heuristic in a numerical experiment in Section 4. We give our conclusions and directions for further research in Section 5.
