How good must failure predictions be to make local spare parts stock superfluous?

Thanks to Industry 4.0 technologies, predictive algorithms can provide advance demand information on spare parts demand. Understanding how the goodness of predictions affects on-hand inventory and costs is important for decision makers before integrating these models into existing systems. We consider a spare parts inventory problem for multiple technical systems that are supported by one local stockpoint. Each system has a single critical component that is subject to random failures. Signals are generated to predict component failures. The signal that corresponds to a failure is generated a certain amount of time before the failure, referred to as the demand lead time. However, not every signal results in a failure and some failures are undetected. A component is replaced from the stock when a failure occurs. In case of stock-outs, an emergency shipment takes place. We formulate a discrete-time Markov decision process model to optimize the replenishment decisions with the objective of minimizing the long-run average cost per period. We investigate the effect of precision (i.e., the fraction of true signals among all signals) and sensitivity (i.e., the fraction of detected failures among all failures) of the predictions and the demand lead time on the costs, order-up-to levels, average on-hand inventory and emergency shipments under the optimal policy. In the worst case, the precision, sensitivity or demand lead time is zero. We show analytically that the optimal policy and optimal costs only depend on the sensitivity and the demand lead time through their product. In numerical experiments, we observe a Pareto principle for the reduction of costs in precision (e.g., a 30% perfectness in precision brings a 70% reduction in optimal cost compared to the worst case) and an inverse Pareto principle in the product of sensitivity and demand lead time (e.g., 70% perfectness in the sensitivity or demand lead time only brings 30% reduction in optimal cost compared to the worst case). Finally, we observe that the local spare parts stock only becomes superfluous when the signals are really close to perfect.