Modified Synthetic Control Chart for One-Step Markov-Dependent Processes

Abstract

Quality measurement by the attributes method often does not result in independent random variables for the count of non conformities or non conforming units. A model based on Markovian dependence can be considered as a practical option in such situations. For a Markovian production process, Adnaik et al. (in press) have proposed the “Single Attribute Control Charts” (SACCs) using two criteria. The first one is by controlling the error probabilities being (α*, β*) and the second, by using the ATS criterion. In this article, we propose a “Modified Synthetic Single Attribute Control Chart” for one-step Markovian Dependent process using ATS criterion (MSyn-SACC-MD).

Zero state as well as the steady-state performance of the chart is studied. It is numerically illustrated that the proposed chart is more efficient than SACC-MD-A as proposed by Adnaik et al. (in press).

Keywords:

• Average time to signal
• Conforming run length
• Markovian dependence
• np chart
• Serial correlation
• Steady state
• Synthetic control chart

Mathematics Subject Clssification:

• 62P30

Acknowledgment

We are very thankful to both reviewers for their valuable suggestions and comments, which helped a lot in improving the manuscript significantly. We also thank the editor for encouraging us to revise the manuscript.