Quality analysis in acyclic production networks

Abraham Gutierrez Sanchez, Sebastian Müller

Research output: Contribution to journalArticle


The production network under examination consists of a number of workstations. Each work-
station 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 detec-
tion, variability
AMS MSC 2010: 90B30, 90B15, 62M02, 62M05
Original languageEnglish
Number of pages9
JournalStochastics and Quality Control
Publication statusPublished - 19 Sep 2019


  • direct acyclic graphs, production networks, quality estimation, anomaly detection, variability

Cite this