A control chart to monitor the process mean based on inspecting attributes using control limits of the traditional X-bar chart

Abstract

This paper proposes a new control chart, denoted by X¯tn, for evaluating the stability of a process mean, which is based on attribute inspection. In the X¯tn control chart, the mean of the quality characteristic of interest is controlled by a go-no-go gauge device that generates five categorizations. In equally-spaced times, samples of n items are collected, their categories are determined, and random values are generated according to a truncated normal distribution that corresponds to their categories. With these random values, the averages are estimated and the X¯tn control charts are built. Extensive computational experiments shown that the newly introduced X¯tn control charts perform similarly to the usual X¯ control chart in terms of average run length, provided that the sample sizes are raised by approximately three additional sample units. Because the X¯tn control charts use attributes, they can be considered a viable alternative to the traditional X¯ control chart.