### Abstract

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 |
---|---|

Number of pages | 9 |

Journal | Stochastics and Quality Control |

Publication status | Published - 19 Sep 2019 |

### Fingerprint

### Keywords

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

### Cite this

*Stochastics and Quality Control*.

**Quality analysis in acyclic production networks.** / Gutierrez Sanchez, Abraham; Müller, Sebastian.

Research output: Contribution to journal › Article › Research › peer-review

}

TY - JOUR

T1 - Quality analysis in acyclic production networks

AU - Gutierrez Sanchez, Abraham

AU - Müller, Sebastian

PY - 2019/9/19

Y1 - 2019/9/19

N2 - 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 randomlyto a machine. We assume that the production network is acyclic, that is, a part does not returnto a workstation where it previously received service. Furthermore, we assume that the quality ofthe end product is additive, that is, the sum of the quality contributions of the machines along theproduction 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 comparisonof the means and variances of machines in the same workstation. These comparisons then maylead to the identification of unreliable machines. We also discuss the asymptotic distributions ofthe estimators that allow the use of standard statistical tests and decision making.Keywords: direct acyclic graphs, production networks, quality estimation, anomaly detec-tion, variabilityAMS MSC 2010: 90B30, 90B15, 62M02, 62M05

AB - 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 randomlyto a machine. We assume that the production network is acyclic, that is, a part does not returnto a workstation where it previously received service. Furthermore, we assume that the quality ofthe end product is additive, that is, the sum of the quality contributions of the machines along theproduction 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 comparisonof the means and variances of machines in the same workstation. These comparisons then maylead to the identification of unreliable machines. We also discuss the asymptotic distributions ofthe estimators that allow the use of standard statistical tests and decision making.Keywords: direct acyclic graphs, production networks, quality estimation, anomaly detec-tion, variabilityAMS MSC 2010: 90B30, 90B15, 62M02, 62M05

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

UR - http://10.1515/eqc-2019-0014

M3 - Article

JO - Stochastics and Quality Control

JF - Stochastics and Quality Control

SN - 0940-5151

ER -