The impracticality of homogeneously weighted moving average and progressive mean control chart approaches

Abstract

There is growing literature on new versions of “memory‐type” control charts, where deceptively good zero‐state average run‐length (ARL) performance is misleading. Using steady‐state run‐length analysis in combination with the conditional expected delay (CED) metric, we show that the increasingly discussed progressive mean (PM) and homogeneously weighted moving average (HWMA) control charts should not be used in practice. Previously reported performance of methods based on these two approaches is misleading, as we found that performance is good only when a process change occurs at the very start of monitoring. Traditional alternatives, such as exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, not only have more consistent detection behavior over a range of different change points, they can also lead to better out‐of‐control zero‐state ARL performance when properly designed.

A multivariate triple exponentially weighted moving average control chart

“…From Figure 6, it can be observed that for small 𝜆 the proposed MTEWMA scheme performs better under the time-varying case compared to the asymptotic one in terms of the ARL profile. This confirms the findings of Knoth et al 26 reporting the worst performance of the TEWMA scheme and other memory-type schemes with asymptotic control limits. For large 𝜆 values, the MTEWMA scheme performs similarly for both cases.…”

Progressive mean as a special case of exponentially weighted moving average: Discussion

“…Knoth et al 13 . were the first to mention a decline in the performance of PM chart through their CED curves, which can be confirmed from the conditional steady state ARL values of PM chart in Tables 2 and 3.…”

“…Here, constant $$q$$ becomes the sensitivity parameter of PM control chart that is, a smaller value of $$q$$ (i.e., close to 0) increases the sensitivity of PM chart and creates inertia problem at the same time, whereas a larger value of $$q$$ can reduce the severity of inertia problem at the cost of lower sensitivity. Knoth et al 13 . also pointed out the deficiency of PM control chart in monitoring the processes where shift does not occur at the start of monitoring.…”

“…Knoth et al 13 . showed in their study that the design parameter ($$\lambda $$) of EWMA chart can be set to outperform PM chart in terms of zero‐state ARL values.…”

Letter on statistical process monitoring research: Misdirections and recommendations

“…Many of the recently proposed methods, such as the triple multivariate exponentially weighted moving average chart of Malela-Majika et al, 2 lead to weighting patterns that violate this basic requirement. For many other examples, see Mahmoud and Woodall 3 and Knoth et al 4,5 The homogeneously weighted moving average (HWMA) chart of Abbas 6 gives a specified weight to the current data point and distributes equal weights to all past data values. Knoth et al 5 showed that this approach has poor performance even though the weight pattern restriction of Lai 1 is typically met after the first few observations.Methods should be compared based on steady-state average run length (ARL) performance, where it is assumed that any process shift is delayed.…”