Abstract
AbstractAverage number of samples to signal (ANSS) and average time to signal (ATS) are the most widely used criterion for comparing the efficiencies of the quality control charts. In this study the method of evaluating ANSS and ATS values of the multivariate exponentially weighted moving average (EWMA) control charts with Markov chain approach was presented when the production process is in control state or out of control state. Through numerical results, it is found that when the number oftransient state is less than 50, the calculated ANSS and ATS values are unstable; and ¬Þs tends to be stabilized when is greater than 100; in addition, when the properties of multivariate EWMA control chart is evaluated using Markov chain method, the number of transient state requires bigger values when the smoothing constatnt A becomes smaller. Key words: Asymptotic ATS, Control Chart, Markov Chain Method 1. Introduction 1 The main purpose of statistical process control (SPC) is to improve the quality and productivity. One of the efficient methods for checking shifts or variations in the production process is control chart. Average run length (ARL), ANSS and ATS are the most widely used criterion for comparing the efficiency of the quality control charts. The ability of a control chart detecting process changes is determined by the length of time required for the chart to signal. Thus, a good control chart detects any changes quickly in the process while producing few false alarms. In traditional control chart, the run length (RL) is defined as the random number of samples required for the chart to signal and the ARL is the expected value of the RL. Therefore, the expected time to signal is simply the product of the ARL and the length of the fixed sampling interval in fixed sampling interval (FSI) chart, so the ARL can be thought of as the expected time to signal. If there are no changes in the process then the ARL should be large so that the frequency of false alarm
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