Simple Stochastic Model for Planning the Inventory of Spare Components Subject to Wear-out

We treat an industrial system which comprises of a number of identical components subject to wear-out. To support the system maintenance an appropriate inventory of spare components is needed. In order to plan the sufficient inventory of spare components, two variants of a simple stochastic model are developed. In both variants, the aim is to determine how many spare components are needed at the beginning of a planning interval to meet demand for corrective replacements during this interval. Under the first variant the acceptable probability of spare shortage during the planning interval is chosen as a decision variable. While in the second variant the adequate spare inventory level is assessed by taking into account the expected number of component failures within the planning interval. A comparison of both variants of the model shows that calculations involved in the second variant are simpler. However, it can only be used when the inventory of spare components can be planned for a relatively long period of time.The determination of an adequate number of spare components according to both variants of our model depends on the form of the probability density function of component failure times. Since the components are subject to wear-out, this function exhibits a peak-shaped form that can be described by different statistical density functions. Advantages and disadvantages of using the normal, lognormal, Weibull, and Gamma density function in our model are discussed. Among the probability density functions studied, the normal density function is found to be the most appropriate for calculations in our model. The applicability of both variants of the model is given through numerical examples using field data on electric locomotives of Slovenian Railways.