The exponentially weighted moving average (EWMA) control chart was introduced by Roberts in 1959, which is a good alternative to the Shewhart control chart when one is interested in small shifts. Several studies were made for the properties of ARL of EWMA control chart. Roberts (1959), using simulation developed monographs of ARL s for normally distributed observations. Robinson and Ho (1978) used a numeric procedure to determine the ARL, presenting several combinations of L and λ for change in the process mean with the help of an Edgeworth series expansion. Crowder (1987, 1989), presented tables for ARL of the EWMA chart, by solving a system of integral equations. Crowder (1987) has given a computer program that calculates the ARL of the EWMA chart for controlling the mean of a normal process. Lucas and Saccucci (1990) presented table and graph of ARL values for different values of L and λ. They have evaluated the run length properties of EWMA control schemes by representing the EWMA statistic as a continuous Markov chain. In the present paper, simulation is carried out to calculate the ARL values using Cprograms. Observing these values it is seen that approximately the same values of ARL are obtained by simulation method using C programming. That is, the Markov chain approach by Lucas, Saccucci and the present simulation technique yields the same ARL results.

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The Shewhart R-and S-charts are often used to monitor the variability of a quality characteristic of interest. In order to improve the sensitivity of these charting procedures to detecting small shifts in the process standard deviation, runs rules have been suggested. We evaluate the properties of the run length distributions of these charting procedures using a Markov chain approach. We show that the rules commonly used in practice based on the Western Electric Handbook do not have the statistical performance one might expect. Alternative runs rules are provided that provide the same in-control ARL's as the usual %-chart with runs rules. Average run 409

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