Monitoring the process mean based on attribute inspection when a small sample is available

Abstract

This paper proposes a new control chart, denoted by to evaluate the stability of a process mean when a small sample is available. This chart is based on attribute inspection rather than the physical measurements (taken with an instrument, such as a caliper or precision balance) of the quality characteristics of interest of the sampled items. The main goal is to recover measurements on a continuous scale by generating random measurements using the frequencies observed for the sample as inputs. The average sample obtained using these recovery measures () is calculated and used to draw the standard chart. The average sample can be shown to be a mixture of normal distributions. The values of the lower control limit (LCL) and the upper control limit (UCL) are chosen to minimize the average run length (ARL).

Keywords:

• quality
• control chart
• optimization
• attribute and variable control charts
• average run length

Acknowledgements

The authors would like to thank the anonymous referees for their constructive comments on the earlier version of this work, many of which led to substantial improvements. We also thank CNPq-Brazil for their partial financial support of this research.