On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

Abstract

On-line process control consists of inspecting a single item for every m (integer and m ≥ 2) produced items. Based on the results of the inspection, it is decided whether the process is in-control (the fraction of conforming items is p ₁; State I) or out-of-control (the fraction of conforming items is p ₂ < p ₁; State II). If the inspected item is non conforming, it is determined that the process is out-of-control, and the production process is stopped for an adjustment; otherwise, production continues. As most designs of on-line process control assume a long-run production, this study can be viewed as an extension because it is concerned with short-run production and the decision regarding the process is subject to misclassification errors. The probabilistic model of the control system employs properties of an ergodic Markov chain to obtain the expression of the average cost of the system per unit produced, which can be minimised as a function of the sampling interval, m. The procedure is illustrated by a numerical example.

Keywords:

• Economic design
• Markov chain
• Misclassification errors
• On-line process control using attributes
• Short-run production

Mathematics Subject Classification:

• 62P30
• 60J05
• 60J20
• 60J10

Acknowledgment

The authors would like to acknowledge CNPq for partial financial support. The authors would like also to acknowledge the suggestions given by the anonymous referees that certainly have contributed the improvement of this new version.