A two-stage mathematical series selection procedure for improving prediction reliability of statistical distribution functions in supply chain networks

Effective prediction of data behavior is essential for supply chain agility. Data science models in production systems typically follow a three-step process to (1) define and select suitable statistical distribution functions (SDFs) for modeling the system, (2) improve the reliability of the selected SDFs, and (3) apply advanced techniques to predict the system behavior. While much of the literature has focused on defining suitable SDFs and developing prediction techniques, little work is devoted to improving SDFs’ reliability. This deficiency is a significant limitation of the current research on lean and agile production systems in supply chain networks (SCNs). This study focuses on using mathematical series as a tool for improving the reliability of SDFs in SCNs. A two-stage procedure utilizes a variant of Analysis of Variance (ANOVA) to assess the significance of different mathematical series for improving the reliability of a given set of SDFs in the first stage and a new compatibility index to select the most suitable mathematical series in the second stage. A case study demonstrates the applicability of the proposed method in manufacturing by considering several widely used SDFs (i.e., exponential, gamma, Weibull, normal, and log-normal distribution functions) and mathematical series (i.e., exponential, Maclaurin, Taylor, and Fourier series). We show that the Fourier series is the most influential mathematical series for improving SDFs. The proposed procedure can be adapted to successfully improve reliability in a wide range of data modeling problems and applications.