Generally weighted moving average monitoring schemes: Overview and perspectives

Abstract

An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution‐free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (ie, double GWMA, composite Shewhart‐GWMA, mixed GWMA‐CUSUM, and mixed CUSUM‐GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA‐related schemes (ie, 66 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.

Distribution‐free triple EWMA control chart for monitoring the process location using the Wilcoxon rank‐sum statistic with fast initial response feature

“…There are four different types of memory‐type control charts in the SPM literature and these are: (1) exponentially weighted moving average (EWMA) chart by Roberts, 2 (2) cumulative sum chart by Page, 3 (3) generally weighted moving average chart by Sheu and Lin, 4 and (4) homogeneously weighted moving average chart by Abbas 5 . For more detailed studies or literature reviews on the latter memory‐type schemes, see Hawkins and Olwell, 6 Ruggeri et al., 7 Mabude et al., 8 Nawaz and Han, 9 Abid et al., 10 Adegoke et al., 11 and Adeoti and Koleoso 12 . The focus of this paper is on improving the performance of the nonparametric EWMA‐type charts to monitor the process location, especially during start‐up period.…”

An EWMA signed ranks control chart with reliable run length performances

“…). Additionally, recent developments of distribution‐free EWMA‐type schemes can be found in Raza et al., 18 Alevizakos et al., 19 Mabude et al., 20 Perdikis et al 21 …”

Distribution‐free composite Shewhart‐GWMA Mann‐Whitney charts for monitoring the process location

“…The CUSUM and EWMA schemes have received thorough coverage in the SPM literature; see, for instance, Hawkins and Olwell 9 and Ruggeri et al 10 for some earlier reviews. Although the GWMA‐type schemes are relatively new as compared to the CUSUM‐type and EWMA‐type schemes, a literature review documenting 65 publications on this topic is done by Mabude et al 11 . The manner in which the Shewhart, EWMA, CUSUM, and GWMA schemes assign weights to recent and older observations is illustrated in Mabude et al 11 …”

“…Although the GWMA‐type schemes are relatively new as compared to the CUSUM‐type and EWMA‐type schemes, a literature review documenting 65 publications on this topic is done by Mabude et al 11 . The manner in which the Shewhart, EWMA, CUSUM, and GWMA schemes assign weights to recent and older observations is illustrated in Mabude et al 11 …”