Approximate multivariate distribution of key performance indicators through ordered block model and pair-copula construction

Key Performance Indicators (KPIs) play an important role in comprehending and improving a manufacturing system. This article proposes a novel method using Ordered Block Model and Pair-Copula Construction (OBM-PCC) to approximate the multivariate distribution of KPIs. The KPIs are treated as random variables in the OBM and studied under the stochastic queuing framework. The dependence structure of the OBM represents the influence flow from system input parameters to KPIs. Based on the OBM structure, the PCC is employed to simultaneously approximate the joint probability density function represented by KPIs and quantify the KPI values. The OBM-PCC model removes the redundant pair-copulas in traditional modeling, at the same time enjoying the flexibility and desirable analytical properties in KPI modeling, thus efficiently providing the accurate approximation. Extensive numerical studies are presented to demonstrate the effectiveness of the OBM-PCC model.