Using Information in Addition to Book Value in Sample Designs for Inventory Cost Estimation.

Abstract Stratified sampling for inventories, as discussed in the literature, usually employs the recorded book value as the stratification variable (Neter and Loebbecke 1975; Roshwalb et al. 1987). Stratification by book value along with an appropriate estimator provides a cost effective and precise estimate of the total inventory cost. Other stratification variables, such as volume of activity, provide information not provided by the book value about the variability of the errors in inventories, but little is known about the effectiveness of designs based on them. Greater improvement in efficiency may be possible by simultaneously including book value and volume into one sample design. In this paper, the effectiveness of volume is investigated as a stratification variable. A bivariate stratification method based on a model-based sampling framework is developed which effectively folds both book value and volume into one collective and simple stratification scheme. Using a bivariate sample design is not without any cost, because it requires that both the book and the volume values for an item to be positive. However, another extension of the model is proposed to include all items with zero book value or zero volume into a single stratified design. To examine the effectiveness, sample designs based on book value alone, volume alone, and the bivariate method are constructed for three inventory populations. Since the errors are known for every item in these inventories, the exact efficiency of a sample design can be determined. By designing a sample to achieve a specified precision with known reliability, the resulting sample size is a measure of efficiency. The design for a population with the smallest sample size is the most efficient and cost effective. To test whether the sampling methodologies actually achieve their precision and reliability targets, the audit sampling process is repeated in a simulation. Random samples are repeatedly selected from the inventories using the alternative sample designs, estimates for the inventory total are calculated using each set of sample data, and the accuracy of the estimates are recorded. Designs based on the bivariate stratification method required up to 62.5 percent fewer items to achieve the same level of precision and reliability than designs based on book value alone or volume alone. The simulation results show that these bivariate stratified designs attain the same target level of precision and reliability as designs based on book value alone or volume alone. In some cases, the bivariate designs improve the actual confidence interval coverage more than designs based on book value alone.