## Modeling and Forecasting the Demand for Aircraft Recoverable Spare PartsThis report explores issues in forecasting and modeling the demand for aircraft recoverable spare parts to improve the Air Force's estimation of spares and repair requirements over quarterly, annual, and longer planning horizons. Specifically, it demonstrates the utility of approaches that account explicitly for nonstationarity and their superiority over current methods used by the Air Force Materiel Command for these purposes. The authors recommend using a weighted regression, a special case of the Kalman filter, for forecasting demand for high-demand items. This approach is a logical extension of Bayesian statistics, which explicitly accounts for nonstationarity in stochastic processes, assigning greater weight to more recent than to less recent demands. Coupled with an improved approach to variance estimation that assigns greater uncertainty to longer planning horizons than to shorter ones, this holds the promise of reducing the cost of spares investments while achieving adequate levels of system performance. |

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### Contents

SOME EXPLORATIONS OF BASELEVEL | 30 |

ALTERNATIVE APPROACHES TO DEMAND | 39 |

VARIANCE ESTIMATION | 67 |

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### Common terms and phrases

action quantities greater AFMC's Air Force Air Force's aircraft spare approach to demand base base-level demand Bayesian binomial probability distribution Bitburg data cannibalization compound Poisson compound Poisson process current system demand modeling demand process demands for aircraft described discussed effects eight quarters eight-quarter moving average evaluations expected value explanatory variables explored exponential smoothing Feeney and Sherbrooke flying hours forecast variance forecasting methods function Geisler important improved techniques inventory system Kalman filter model lateral supply line items mands mean absolute deviation Mean Squared Error measurement equation nonstationarity NRTS Forecaster NRTS rate number of items observed VTMRs parameter period planning horizons Poisson distribution predictions probability distribution problem RAND research recoverable spares repair requirements estimation resupply root mean squared spares and repair spares requirements specified stochastic process stochastic variability stock levels tion transformation true demand rate underlying variance estimation variance-to-mean ratio VTMR estimator wartime weighted regression forecaster WRSK