Adaptive EWMA Control Charts with a Time Varying Smoothing Parameter

It is known that time-weighted charts like EWMA or CUSUM are designed to be optimal to detect a specific shift. If they are designed to detect, for instance, a very small shift, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to circumvent this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper has as main goal to propose some adaptive EWMA control charts (AEWMA) based on the assessment of a potential misadjustment, which is translated into a time-varying smoothing parameter. The resulting control charts can be seen as a smooth combination between Shewhart and EWMA control charts that can be efficient for a wide range of shifts. Markov chain procedures are established to analyze and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of the proposals.