A special double sampling three-level control chart

Abstract

Three-level control charts have been developed for monitoring processes where the quality of products is characterized by classifying the product characteristic into three discrete levels. In this paper, a double sampling (DS) attribute control chart is developed for monitoring three-level products. The statistical performance of the proposed chart is evaluated using the statistical measures average run length (ARL) and average number of inspected items to signal (ANI). A Markov chain approach is applied to derive expressions for ARL and ANI. Using numerical examples, we illustrate the performance of the proposed control scheme and compare its efficiency with the other control schemes. The results approve the statistical efficiency of the proposed control scheme compared with the other control schemes.

Keywords:

• Average run length (ARL)
• double sampling (DS) control scheme
• Markov chain
• quality value function (QVF)
• three-level control chart

Acknowledgements

The Authors wish to acknowledge the help of the Editor-in-Chief, gratefully acknowledging the valuable suggestions and comments of GRA Edward Wayne Solomon and two reviewers who have guided in the publication of an improved version of the manuscript. The financial supports of the Natural Science and Engineering Research Council (NSERC) of Canada is also gratefully acknowledged.