Quality analysis in acyclic production networks
Abraham Gutierrez Sebastian Mueller






Magnetic Cataclysmic Variables discovered in hard X-rays

    
M. Falanga1,
D. de Martino2,
F. Bernardini3,2,
K. Mukai4,5
          
    Received: date / Revised version: date
==========================================================================







The production network under examination consists of a number of workstations. Each workstation is a parallel configuration of machines performing the same kind of tasks on a given part. Parts move from one workstation to another and at each workstation a part is assigned randomly to a machine. We assume that the production network is acyclic, that is, a part does not return to a workstation where it previously received service. Furthermore,  we assume that the quality of the end product is additive, that is, the sum of the quality contributions of the machines along the production path. The contribution of each machine  is modeled by a separate random variable. 

Our main result is the construction of estimators that allow pairwise and multiple comparison of the means and variances of machines in the same workstation. These comparisons then may lead to the identification of unreliable machines.  We also discuss the asymptotic distributions of the estimators that allow the use of standard statistical tests and decision making.

Keywords: direct acyclic graphs, production networks,  quality estimation, anomaly detection, variability


AMS MSC 2010: 90B30, 90B15, 62M02, 62M05







§ INTRODUCTION





In order to maintain  competitiveness, industrial manufacturers have to pursue new sources to enhance process agility. In parallel production networks, the quality of the end product depends on various intermediate production steps. Therefore,  a recent  challenge is to achieve a level of visibility into the production flows that allow to optimize throughput by guaranteeing at the same time given quality standards. The challenge to maintain a visibility across all parallel workflows and  to identify eventual sources of errors becomes particularly difficult in situations where the qualities of single machines are not observable.  

