A test for suitability of the preliminary samples for constructing control limits of X¯ chart

Abstract

Unless the preliminary m subgroups of small samples are drawn from a stable process, the estimated control limits of X¯ chart in phase I can be erroneous, due to which the performance of the chart in phase II can be significantly affected. In this work, a quantitative approach based on extraction of the shape features of control chart patterns in the X¯ chart is proposed for evaluating the stability of the process mean, while the preliminary samples were drawn and thus, the subjectivity associated with the visual analysis of the patterns is eliminated. The effectiveness of the test procedure is evaluated using simulated data. The results show that the proposed approach can be very effective for m≥48. The power of the test can be improved by identifying a new feature that can more efficiently discriminate the cyclic pattern of smaller periodicity from the natural pattern and by redefining the test statistic.

Keywords:

• preliminary samples
• control limits of X¯ chart
• process stability
• control chart patterns
• shape features