### Abstract

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

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 language | English |
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Number of pages | 9 |

Journal | Stochastics and Quality Control |

Publication status | Published - 19 Sep 2019 |

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### Keywords

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

### Cite this

Gutierrez Sanchez, A., & Müller, S. (2019). Quality analysis in acyclic production networks.

*Stochastics and Quality Control*.