Abstract
In recent decades, various adaptive X control charts with various variable parameters such as sampling interval,sample size, and control limits have been proposed to improve the efficiency of detecting the out-of-controlconditions for small, medium, and large shifts. The variable parameters (VP) adaptive chart is one of theseproposed charts that have an acceptable performance compared to other schemes especially for small shifts. Inthis article we proposed a modified version of VP chart with three stage variable chart parameters and havecompared it with some other adaptive charts. Here we used three mostly used indicators to evaluate theperformance of these charts which are Average Time to Signal (ATS), Average Number of Observations to Signal(ANOS) and Average Number of Samples to Signal (ANSS). Also we have calculated the optimal points fordifferent adaptive charts and compared them in these points according to the indicators mentioned above.
Highlights
In recent decades, various adaptive X control charts with various variable parameters such as sampling interval, sample size, and control limits have been proposed to improve the efficiency of detecting the out-of-control conditions for small, medium, and large shifts
The logic of these charts is based on the fact that if the current sample statistic plotted on the control chart is near the center line, there is probably no change happened in the process parameter, and, the sample will be taken from the process with a smaller sample size and/or a longer sampling interval and/or a larger control limit coefficient
If the current sample statistic is plotted near the control limits but still within them, it could indicate a kind of change in the parameter; sample will be taken from the process with a larger sample size and/or a shorter sampling interval and/or a smaller control limit coefficient in order to detect the possible shift as soon as possible
Summary
In today's competitive world, meeting customer’s expectation from quality point of view is a key to successful business conduct for any organization. Adaptive control charts allow at least one of their parameters (i.e. sample size n, sampling interval t and control limits coefficient k) to be variable in duration of operation and present superior economic and statistical performance compared to fixed parameter control charts. Prabhu et al (2001) and Costa (1997) combined VSI and VSS features and proposed variable sampling sizes and intervals (VSSI) X control charts. Adaptive control charts present superior performance in detecting small shifts than the SS control charts with fixed parameters because of their average time to signal (ATS) to alert any changes in the process is smaller than SS control charts. We compared the three stage VP chart with some other control charts in section 5 and, we calculated the optimal point in the proposed chart and its statistical performance improvements for different amounts of shifts.
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