The Inertial properties of EWMA control charts

Abstract

Since exponentially weighted moving average (EWMA) control charts combine information from the current and past samples, they are relatively more effective in detecting small process shifts than Shewhart control charts. A prevailing problem in control charts is the property of not responding quickly to process shifts, that is, showing statistical control of the process while a shift has occurred in the process parameter(s). This property of control charts, which is referred to as “inertia”, is an important issue in control charting and has been a major concern to engineers and statisticians. This study surveys the inertial properties of EWMA control charts in detail. First, the distribution of EWMA chart statistic and signal resistance probability (SRP) are studied for many different cases when there are undetected transient shifts. All measures are calculated and evaluated via a Markov chain approach. Then, an optimal scheme is proposed to minimize the out-of-control average run length (ARL) for a specified shift, subject to SRP constraints. The results reveal that the inertia can be sometimes a serious problem in EWMA control schemes that should not be overlooked. It is shown that an appropriate scheme based on both ARL and SRP measures could be useful for processes that may have sustained and/or transient out-of-control states.

Keywords:

• Average run length (ARL)
• exponentially weighted moving average (EWMA)
• inertial properties
• signal resistance probability (SRP)
• statistical process control