Evaluatiok of optimum weights and average run lenghts in ewma control schemes

Abstract

In this paper, a two sided exponentially weighted moving average (EWMA) control scheme of Roberts (1959) is studied. By using a continuous time model, explicit formulae for the average run lengths are obtained. Using these results, a formula for the optimal weight in the EWMA is obtained by minimizing the out of control average run length for a given reference value and in control average run length [ARL ₀), which is assumed to be large. These optimunl weights are found to be very close to the optimum weights obtained by Lucas and Saccucci(1990) for the discrete time model using the Markov chain method. It is shown that the EWMA scheme performs almost as well as the CUSUM for moderate ARL_O. Another important finding that emerges from this study is that the EWMA scheme is less sensitive to the choice of a reference value as compared to the CUSIJM. We also provide very accurate formulae for the ARL _O and ARL _μ of the two-sided CUSUM procedure.

Keywords:

• average run lengths
• CUSUM procedure
• exponentially weighted moving average
• shift in the mean
• two-sided procedures