Problem definition: We examine and analyze a strategy for forecasting the demand for replacement devices in a large Wireless Service Provider (WSP) that is a Fortune 100 company. The Original Equipment Manufacturer (OEM) refurbishes returned devices that are offered as replacement devices by the WSP to its customers, and hence the device refurbishment and replacement operations are a closed-loop supply chain.

Academic/practical relevance: We introduce a strategy for estimating failure time distributions of newly launched devices that leverages the historical data of failures from other devices. The fundamental assumption that we make is that the hazard rate distribution of the new devices can be modeled as a mixture of historical hazard rate distributions of prior devices.

Methodology: The proposed strategy is based on the assumption that different devices fail according to the same age-dependent failure distribution. Specifically, this strategy uses the empirical hazard rates from other devices to form a basis set of hazard rate distributions. We then use a regression to identify and fit the relevant hazard rates distributions from the basis to the observed failures of the new device. We use data from our industrial partner to analyze our proposed strategy and compare it with a Maximum Likelihood Estimator (MLE).

Results: To evaluate our forecasting strategies, we use the Kolmogorov-Smirnov (KS) distance between the estimated Cumulative Distribution Function (CDF) and the true CDF, and the Mean Absolute Scaled Error (MASE). Our numerical analysis shows that both forecasting strategies perform very well. Furthermore, our results indicate that our proposed forecasting strategy also performs well (i) when the size of the basis is small and (ii) when producing forecasts early in the life cycle of the new device.

Managerial implications: A forecast of the failure time distribution is a key input for managing the inventory of spares at the reverse logistics facility. A better forecast can result in better service and less cost (see Calmon and Graves (2017)). Our general approach can be translated to other settings and we validate our hazard rate regression approach in a completely different application domain for Project Repat, a social enterprise that transforms old t-shirts into quilts.

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ERIM Report Series Research in Management
Erasmus Research Institute of Management

Lemmens, S, Calmon, A, & Graves, S.C. (2023). Data-Driven Failure Time Estimation in a Consumer Electronics Closed-Loop Supply Chain (No. ERS-2023-002-LIS). ERIM Report Series Research in Management. Retrieved from