# Quality analysis in acyclic production networks

## TL;DR

This paper develops statistical estimators for comparing machine quality contributions in acyclic production networks, enabling the identification of unreliable machines through pairwise and multiple comparisons.

## Contribution

It introduces new estimators for means and variances of machine quality contributions and discusses their asymptotic distributions for reliable statistical testing.

## Key findings

- Estimators enable effective comparison of machine quality metrics.
- Asymptotic distributions facilitate standard statistical tests.
- Method helps identify unreliable machines in production networks.

## Abstract

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.