Prediction model selection and spare parts ordering policy for efficient support of maintenance and repair of equipment

The prediction model selection problem via variable subset selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors, but there is uncertainty about which subset to use. Several papers have dealt with various aspects of the problem but it appears that the typical regression user has not benefited appreciably. One reason for the lack of resolution of the problem is the fact that it has not been well defined. Indeed, it is apparent that there is not a single problem, but rather several problems for which different answers might be appropriate. The intent of this paper is not to give specific answers but merely to present a new simple multiplicative variable selection criterion based on the parametrically penalized residual sum of squares, which performs consistently well across a wide variety of variable selection problems. This criterion allows one to select a subset model for prediction of a demand for spare parts, in support of maintenance and repair of equipment. The past data of prediction errors are used at each stage to determine an adaptive spare parts ordering policy for a providing an adequate yet efficient supply of spare parts. In order to optimize the adaptive spare parts ordering policy at each stage under parametric uncertainty, the invariant embedding technique is used. Practical utility of the proposed approach is demonstrated by examples.