Generally weighted moving average monitoring schemes: Overview and perspectives

TL;DR: An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided in this article, where a number of possible future GWMA-related schemes are documented and categorized in such a manner that it is easy to identify research gaps.

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 (i.e. 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 (i.e. 61 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.

Summary

1. Introduction

• In any field, a literature review is essential as it gives an overview of what investigations have been conducted and what are some of the possible research ideas that can be pursued.
• Thus, the tradition emphasized by the latter articles is continued with the generally weighted moving average (GWMA) monitoring schemes in this paper.
• The basic properties of the GWMA scheme and its existing enhancements as well as a detailed outline of how the review is structured are provided in Section 2.

2.1 Operation of the GWMA scheme and its enhancements

• (independent and identically distributed) normally distributed random variables with in-control (IC) mean and standard deviation √ .
• The operation of the GWMA scheme and its enhancements are illustrated for the subgroup mean.
• Thus, the asymptotic upper and lower control limits (denoted as and ): EQUATION Following a similar line of argument, it follows that the charting statistics, design parameters and control limits of the DGWMA, Shewhart-GWMA, GWMA-CUSUM and CUSUM-GWMA ̅ schemes are as shown in Table 1 .
• An illustration of different charting statistics, design parameters and control limits of the GWMA scheme and its existing enhancements when the characteristic of interest is the process mean, also known as Table 1.

Asymptotic

• Note that when the underlying process parameters are known (i.e. Case K), control limits can easily be calculated and the process monitoring can take place immediately; however, when process parameters are unknown (i.e. Case U), a two phases approach needs to be implemented, see Jensen et al 18 and Psarakis et al 19 .
• In Phase II, monitoring schemes are implemented prospectively to continuously monitor any departures from an IC state using the parameters estimated in Phase I. Even though Table 1 and Figure 1 provide properties pertaining to GWMA-related schemes for the process mean only, other types of statistics can be done in a similar manner.

.2 Outline of the review

• The journals or proceedings that have published researches on GWMA-related schemes and / or their enhancements are provided in Table 4 (as well as the total number of publications in each journal or proceedings).
• In Table 5 , the list of researchers with at least two publications on GWMA-related schemes and / or their enhancements have been provided, including their corresponding affiliations.

Process mean

• Apart from introducing the GWMA scheme to the SPM literature, Sheu and Lin 9 showed that when =1, the GWMA ̅ scheme reduces to the EWMA ̅ scheme; whereas when =1 and =0 it reduces to the Shewhart ̅ scheme.
• Apart from showing that the GWMA ̅ scheme outperforms the corresponding EWMA ̅ scheme in many situations, Sheu and Lin 9 demonstrated that it also outperforms the Shewhart ̅ scheme with and without runs-rules.
• For processes with start-up problems, a FIR approach is also incorporated and it is shown that it uniformly outperforms the basic GWMA scheme; however, it outperforms the EWMA ̅ scheme with AIB in most situations.
• The abovementioned articles in this subsection are based on i.i.d. observations used to compute the process mean.
• Using ARL and SDRL metrics, this extension is shown to be superior to the GWMA ̅ scheme in detecting medium-to-large shifts; but for small shifts, the converse is true.

Process median

• Unlike the process mean, the process median tends to be preferred in some situations due to its outlier-resistant property.
• Sheu and Yang 29 showed that the GWMA median scheme outperforms the corresponding EWMA (including the one with FIR) and the Shewhart median schemes in many situations.
• Note though, the GWMA ̅ scheme has a better OOC detection ability while the GWMA median scheme performs best when the process is subjected to outliers.
• Moreover, the quality cost model implemented with contaminated normal distribution shows that the GWMA median scheme is more economical with respect to the average quality cost as compared to the GWMA ̅ scheme.

Time-between-events

• To ensure ARL-unbiased OOC performance, Chakraborty et al 30 proposed a one-sided GWMA scheme for monitoring time-between-events (TBE) based on the gamma distribution for Cases K and U.
• It is observed that the estimation of the unknown parameter from an IC Phase I sample affects the GWMA TBE scheme"s performance in Phase II.
• Also, it has a better steady-state ARL performance than the DEWMA TBE scheme for smallto-moderate shifts; but the converse is true for other shifts.
• In some situations, the GWMA TBE scheme has a slight advantage over the DGWMA TBE scheme for (very small)-to-small shifts, but the converse is true for other shifts.

Attributes data

• When the characteristic to be monitored is in the form of count data and under the assumption of a Poisson distribution; using simulation, Sheu and Chiu 31 showed that while the GWMA scheme outperforms the corresponding Shewhart and EWMA schemes in detecting all shifts values, it outperforms the DEWMA scheme in detecting small-to-moderate shifts only.
• Moreover, the simulation approach tends to be time consuming in terms of CPU time as compared to Markov chain approach, i.e. takes 10-to-60 minutes per case study for simulation as compared to 1-to-2 minutes for Markov chain approach.
• When the characteristic to be monitored is in the form of number nonconforming and under the assumption of a binomial distribution; using both Markov chain and simulation approaches, Sukparungsee 35 proposed the GWMA scheme and showed that it outperforms the corresponding EWMA scheme for small shifts.
• In the case of high quality processes, where a large number of zero nonconforming observations exist, the and schemes result in excessive false alarms, hence a zero-inflated Poisson (ZIP) distribution is often used to model and monitor count data with such a large number of zeros.
• A comparison with the corresponding upper-sided Shewhart, CUSUM and DEWMA schemes indicates that, in many situations, the GWMA ZIP scheme is more effective when both parameters are monitored.

3.1.2 Variability

• Sheu and Tai 40 proposed the GWMA scheme and showed that it outperforms the corresponding EWMA scheme in detecting OOC observations especially for small shifts.
• Next, Sheu and Lu 41 used an unbiased estimator of the process variance to propose the one-sided GWMA scheme and showed that it yields better ARLs than the basic EWMA and exponential weighted mean square deviation schemes.
• Next, Ali and Haq 42 proposed a one-and two-sided GWMA schemes which are based on applying the normal approximation to the distributions of the logarithms of the weighted sum of chi-squared random variables.
• It is observed that a properly designed one-or two-sided GWMA scheme has a better OOC performance than the corresponding EWMA schemes in detecting small shifts.
• Finally, it is worth mentioning that Chakraborty et al 30 briefly discussed how the GWMA TBE scheme can be used to monitor downwards shifts in the variance for normally distributed data in Case K and they commented on how this can be extended to the Case U scenario.

Mean and variance using separate charting statistics

• Next, the corresponding studies to jointly monitor the process mean and variability of residuals & autocorrelated actual observations were investigated in Sheu and Lu 45, 46 , respectively; assuming an ARMA(1,1) model for the time series data.
• In each investigated instance, the GWMA schemes were shown to have a better OOC ARL performance than the corresponding EWMA schemes.

Mean and variance using a single charting statistic

• The transformed mean and variance values of the Max statistic are obtained using an inverse standard normal distribution and a chi-square distribution, respectively.
• Max scheme can be found in Nguyen et al 49 and Hsu et al 50 using the thickness of the coating layer of tablets and the quality of displays from Thin Film Transistor -Liquid Crystal Display (TFT-LCD) datasets, respectively.
• In many situations, the results showed that the GWMA Max scheme has lower false alarm rates (or similarly, higher IC ARLs) for more levels of skewness when compared to the EWMA Max scheme.
• Max scheme; note though, the diagnostic analysis was not considered.

Coefficient of variation

• For processes where the mean and variability parameters vary in a fixed proportional way when the process is IC, it is more reasonable to monitor the coefficient of variation (CV).
• Using the ARL, SDRL and ratios of the ARLs, it is shown that, in many situations, the GWMA CV scheme has a better OOC performance as compared to the EWMA and DEWMA CV schemes.
• Hong et al 60 incorporated a FIR feature to the GWMA CV scheme and they showed that it has a significantly improved OOC performance compared to the DEWMA and GWMA schemes without a FIR feature.

3.2 Nonparametric schemes

• Currently, the only contributions that consider the monitoring of a nonparametric statistic using a GWMA scheme are all dedicated to the monitoring of the process location.
• Taking into account the shapes of the Normal, Student"s -and Gamma distribution, Chen et al 62 used the ARL and ASS metrics to show that the GWMA sign scheme with repetitive sampling outperforms the corresponding EWMA scheme based on SRS and repetitive sampling methods as well as the GWMA scheme based on SRS in detecting small shifts.
• As an alternative to the two-sample location shift parametric t-test, the Exceedance (EX) and Wilcoxon rank-sum (WRS) tests are usually recommended when the underlying process distribution is non-normal.
• Next, the GWMA WRS scheme was proposed by Mabude et al 66 , with the Normal, Student"s t-, Gamma, Log-logistic and Weibull distributions used to show the IC robustness and to study the OOC performance.
• Also, the effect of the Phase I reference sample size on the Phase II test samples" OOC performance is provided.

4.2 Nonparametric schemes

• The research works that exist for DGWMA-type nonparametric schemes are on monitoring the location parameter only.
• Lu 73 proposed a DGWMA sign scheme and showed that it is more sensitive than the corresponding EWMA, GWMA and DEWMA schemes in many situations.
• Phanyaem 74 briefly discussed the DGWMA sign scheme with repetitive sampling and showed that it is more sensitive than the corresponding DEWMA sign scheme in many situations.
• The same distributions as those in Chakraborty et al 65 are considered and the DGWMA EX scheme is observed to have more favourable results than the GWMA and EWMA EX schemes.

5. Shewhart-GWMA schemes

• Currently, no research work exists for nonparametric Shewhart-GWMA schemes.
• For parametric ones, some based on monitoring location as well as location and variability exist.

6. GWMA-CUSUM schemes and its reverse version

• Currently, no research work exist for nonparametric statistics using GWMA-CUSUM schemes.
• For parametric ones, some based on monitoring location and monitoring variability exist.

6.1 Location

• Lu 16 proposed the mixed GWMA-CUSUM ̅ scheme and its reverse version (CUSUM-GWMA ̅ scheme) to monitor individual observations.
• It is shown (using ARL only) that, in many situations, this scheme provides better OOC detection ability than the basic GWMA, EWMA and CUSUM schemes, as well as the mixed EWMA-CUSUM and CUSUM-EWMA ̅ schemes.
• Moreover, the CUSUM-GWMA scheme is shown to yield a slightly better OOC ARL performance over the corresponding GWMA-CUSUM scheme in many situations.
• At the same time, but independently, Ali and Haq 17 also proposed the GWMA-CUSUM ̅ scheme to monitor the process mean; however, of subgroup observations.
• Note though, Ali and Haq 17 did not consider the reverse CUSUM-GWMA ̅ scheme.

6.2 Variability

• Ali and Haq 78 proposed the mixed GWMA-CUSUM scheme (with and without FIR) to monitor upwards shifts for subgroup observations and showed that it yields better OOC detection ability than the CUSUM and mixed CUSUM-EWMA schemes.
• Note that Ali and Haq 78 did not consider the mixed CUSUM-GWMA scheme.
• Next, Huang et al 79 proposed the mixed GWMA-CUSUM scheme and the reverse version to monitor upwards shifts using individual observations.
• Both of the mixed schemes have better small shifts detection ability than many competitors, including those discussed in Ali and Haq 42 and, Sheu and Lu 41 .
• More importantly, it is observed that the CUSUM-GWMA scheme has a slight advantage over the corresponding GWMA-CUSUM scheme in many situations.

7. Concluding remarks

• The GWMA scheme is an extended version of the EWMA scheme with an additional adjustment parameter.
• Note that, with the aid of computer programs, the complexity in implementation can be significantly simplified.
• Effort needs to be paid to demonstrating how to monitor real-life datasets using the different GWMA-related schemes discussed herein.

3. As observed in

• Only a few attribute GWMA monitoring schemes have been proposed.
• There is no study on the economic and economic-statistical designs of the GWMA monitoring schemes that has been done in the literature so far.
• Therefore, researchers are encouraged to investigate these topics under both i.i.d. and correlated observations as well as for Case U. 12.
• Only one publication on multivariate schemes is available in the literature.
• The weight structure of the observations for the EWMA and GWMA schemes are similar, i.e., geometrically decreasing; however, the weights structure or weight function kurtosis used by the GWMA scheme differs from that EWMA scheme due to the additional adjustment parameter.

5. The design parameter found in

• Step 4 is called the optimal design parameter.
• Record the optimal and its corresponding control limits.
• Calculate the charting statistic(s) and compare to the control limit(s) found in Step 5.
• Then record the number of subgroups plotted until an OOC signal occurs.
• This number represents one value of the distribution.

Figures

Figure 1: Flow chart illustrating the operational procedure of the GWMA scheme and its enhancements in Phase I and Phase II

Table 2: Outline of the review by section

Table 4: Journals / conference proceedings that published researches on GWMA-related monitoring schemes

Table 5: Researchers in SPM with at least two publications on GWMA-related monitoring schemes and their corresponding affiliations

Table 1: An illustration of different charting statistics, design parameters and control limits of the GWMA scheme and its existing enhancements when the characteristic of interest is the process mean

Full text

HAL Id: hal-03321174
https://hal.archives-ouvertes.fr/hal-03321174
Submitted on 17 Aug 2021
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Generally weighted moving average monitoring schemes:
Overview and perspectives
Kutele Mabude, Jean-claude Malela-majika, Philippe Castagliola, Sandile
Shongwe
To cite this version:
Kutele Mabude, Jean-claude Malela-majika, Philippe Castagliola, Sandile Shongwe. Generally
weighted moving average monitoring schemes: Overview and perspectives. Quality and Reliability
Engineering International, Wiley, 2021, 37 (2), pp.409-432. �10.1002/qre.2765�. �hal-03321174�

1
Generally Weighted Moving Average monitoring schemes – Overview and Perspectives
1
Mabude K.,
1
Malela-Majika J.-C.,
2
Castagliola P. and
1*
Shongwe S.C.
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 (i.e. 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 (i.e. 61 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.
Keywords: Generally weighted moving average, GWMA, Memory-type scheme, Run-length, Monte
Carlo Simulation.
1. Introduction
In any field, a literature review is essential as it gives an overview of what investigations have been
conducted and what are some of the possible research ideas that can be pursued. In statistical process
monitoring (SPM) there have been a number of literature reviews that have shed some light on the
current state of a particular topic and in doing so, made way for many publications thereafter; see for
instance
1,2,3,4,5
. Thus, the tradition emphasized by the latter articles is continued with the generally
weighted moving average (GWMA) monitoring schemes in this paper. The exponentially weighted
moving average (EWMA) monitoring scheme with an additional adjustment parameter was discussed
in Sheu and Griffith
6
, Sheu
7,8
as an enhancement procedure to further improve the sensitivity of the
EWMA scheme towards small shifts in the process mean. Thereafter, Sheu and Lin
9
formally
introduced this enhancement procedure as a stand-alone monitoring scheme which is simply called the
GWMA control chart; and they defined it as a moving average of past data where a specific weight is
assigned to each data point. Moreover, the moving average tends to be a representation of the more
recent process performance, as larger weights are allocated to the most recent observations. In
addition, Sheu and Lin
9
derived the properties that are required to compute the run-length distribution
and they discussed its importance as well as illustrated its implementation.
The purpose of this literature review is to acquaint SPM researchers as well as practitioners about
GWMA schemes which were supposed to be, in essence, replacements of the EWMA-type schemes;
however, this is not really the case in the literature or in practice; because there are actually way more
*
Corresponding author. S.C. Shongwe. E-mail: sandile@tuks.co.za.
1
Department of Statistics, College of Science, Engineering and Technology, University of South Africa;
Pretoria, South Africa;
2
Département Qualité Logistique Industrielle et Organisation, Université de Nantes &
LS2N UMR CNRS 6004, Nantes, France.

2
research output that have been reported on EWMA schemes than on the GWMA schemes from 2003
to mid-year 2020. Based on different authors who have commented on the latter predicament, they
have indicated that the implementation of the EWMA scheme is easier as compared to that of the
GWMA one. By conducting this review, it is also meant to convince researchers and practitioners
alike that GWMA schemes are not as complex as they are thought to be and to further explain that
they provide fascinating results when compared to other well-known monitoring schemes, more
especially, the EWMA monitoring scheme.
Since 2003, the year of publication of the first article, there have been a total of 61 publications on the
GWMA-related monitoring schemes and their enhancements. So far, the existing known
enhancements of the GWMA-related scheme are:
 the double GWMA scheme – denoted as DGWMA scheme;
 the composite Shewhart-GWMA scheme;
 the mixed GWMA-CUSUM scheme and its reverse version, the mixed CUSUM-GWMA
scheme.
A DGWMA scheme is a weighted moving average of a weighted moving average; which implies that
the smoothing process is done twice (this concept was first introduced by Shamma and Shamma
10
for
the double EWMA (DEWMA) scheme). A composite Shewhart-GWMA scheme is a combination of
the Shewhart and GWMA schemes which is an efficient way of harnessing the benefits of these two
schemes (this concept was first introduced by Lucas
11
and Lucas and Saccucci
12
for the Shewhart-
CUSUM and Shewhart-EWMA schemes, respectively). The mixed GWMA-CUSUM scheme is a
combination of the GWMA and CUSUM schemes where the GWMA statistic is used as input in the
CUSUM scheme; however, the CUSUM-GWMA scheme uses the CUSUM statistic as input in the
GWMA scheme (this concept was first introduced by Abbas et al
13
for the EWMA-CUSUM scheme
and the reverse version was introduced by Zaman et al
14
).
The basic properties of the GWMA scheme and its existing enhancements as well as a detailed outline
of how the review is structured are provided in Section 2. Thereafter, the publications discussing
research works on GWMA, DGWMA, Shewhart-GWMA and GWMA-CUSUM (as well as its
reverse version) schemes are reviewed in Sections 3, 4, 5 and 6, respectively. Section 7 provides
concluding remarks and some possible future research ideas. Finally, Appendices A and B provide an
illustration of how the weight function kurtosis varies for different design parameters and an outline
of how the run-length properties are determined for GWMA-related monitoring schemes,
respectively.

3
2. Basic propeties of GWMA schemes and their enhancements
2.1 Operation of the GWMA scheme and its enhancements
The weight structure of the GWMA 

scheme as compared to the corresponding EWMA scheme for
various design parameters are discussed in Appendix A. Assume that the quality characteristic of
interest is a subgroup mean, then 


are i.i.d. (independent and identically distributed) normally
distributed random variables with in-control (IC) mean 

and standard deviation




. In this section,
the operation of the GWMA scheme and its enhancements are illustrated for the subgroup mean. The
charting statistic of the GWMA 

scheme is given by



󰇛



󰇜



 
󰇛



󰇜



  
󰇛



󰇜



 
󰇛



󰇜









 















 








  󰇡

󰇛󰇜


 




󰇢


 






󰇡

󰇛󰇜


 




󰇢




 







(1)
where 

is defined in Appendix A, 

 and 

> 0. The expected value and standard
deviation of 

are given by

󰇛


󰇜


and 
󰇛


󰇜









(2)
where


󰇡

󰇛󰇜


 




󰇢




(3)
Hence, the time-varying upper and lower control limits (denoted as 


and 


) of the GWMA


monitoring scheme are calculated as (with 

> 0, i.e. a width parameter):








󰇛


󰇜
 


󰇛


󰇜

(4)
When , Equation (3) reduces to the following limiting constant


󰇡

󰇛󰇜


 




󰇢




Thus, the asymptotic upper and lower control limits (denoted as 

and 

):







 







(5)
The above derivations given in Equations (1) to (5) are summarized in Table 1. Following a similar
line of argument, it follows that the charting statistics, design parameters and control limits of the
DGWMA, Shewhart-GWMA, GWMA-CUSUM and CUSUM-GWMA 

schemes are as shown in
Table 1. For more details on the properties summarized in Table 1, refer to Sheu and Lin
9
, Lin
15
, Lu
16
and, Ali and Haq
17
.

4
Table 1: An illustration of different charting statistics, design parameters and control limits of the GWMA scheme and its existing enhancements when the
characteristic of interest is the process mean
Scheme
Charting statistics
Design
parameters
Time-varying
control limits
Asymptotic
control limits
GWMA


󰇡

󰇛

󰇜


 




󰇢




 








> 0,


,


> 0








 








with


󰇡

󰇛

󰇜


 




󰇢









 







with


󰇡

󰇛

󰇜


 




󰇢




DGWMA









   





with


󰇡

󰇛

󰇜


 




󰇢󰇡

󰇛

󰇜


 

󰇛󰇜


󰇢




 0,




,




 0








 






 










 







with


 




Shewhart-GWMA




󰇡

󰇛

󰇜


 




󰇢




 






OR












> 0,


,


> 0,


> 0








 








OR








 











 







OR








 





GWMA-CUSUM





󰇛

 

 








󰇜  










󰇛

 








 

󰇜  







 0,


,


> 0
 0




















CUSUM-GWMA





󰇡

󰇛

󰇜


 




󰇢




 











󰇡

󰇛

󰇜


 




󰇢




 








> 0,


,


> 0








 














 








Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Generally weighted moving average monitoring schemes: overview and perspectives" ?

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. 

Q2. Why is the use of a composite Shewhart-GWMA scheme not advised?

Due to the complexity in implementation and excessive false alarms along with a very minor OOC improvement, the use of composite Shewhart-GWMA ̅ schemes with runs-rules is not advised. 

Q3. What distributions are used to show that the GWMA sign scheme has a better O?

Using the Normal, Student‟s -, Logistic and Uniform distributions, it is shown that the GWMA signed-rank scheme outperforms the GWMA sign scheme in many situations; however, when using the Laplace distribution, the GWMA sign scheme has a slightly better small shifts detection ability. 

Q4. What are the main statistics used for GWMA monitoring?

For joint monitoring of the process mean and variability, there are many test statistics used (i.e.Max, Semi-circle, Sum of squares, separate charting statistics, etc.). 

Q5. what is the relevance of multivariate schemes in real-life applications?

Given the relevanceof multivariate schemes in real-life applications, there is a lot of research works on GWMA schemes that need to be done based on parametric and nonparametric settings. 

Q6. What is the common example of a random shock in a ZIP model?

In a ZIP model, some random shocks occur independently with probability and the number of nonconformities follows a Poisson distribution with parameter . 

Q7. What are the main characteristics of the GWMA scheme?

Using the ARL and average sample size (ASS) metrics, it is shown that it outperforms the corresponding GWMA and hybrid EWMA schemes based on the SRS method in detecting small shifts. 

Q8. What is the significance of the moving average?

the moving average tends to be a representation of the more recent process performance, as larger weights are allocated to the most recent observations. 

Q9. What are the other options for adaptive EWMA schemes?

adaptive EWMA schemes also exist in SPM literature (i.e. variable sample size (VSS), variable sample interval (VSI), variable sampling size and interval (VSSI)). 

Q10. What is the significance of the GWMA-CUSUM scheme?

More importantly, the GWMA-related monitoring schemes can be useful for quality practitioners in a variety of applications where the EWMA-related schemes are being currently used, as replacements. 

Q11. How many publications have been published on GWMA?

Since 2003, the year of publication of the first article, there have been a total of 61 publications on the GWMA-related monitoring schemes and their enhancements. 

Q12. Is it recommended to use it in real-life applications?

Since the implementation of the composite ShewhartGWMA scheme is relatively complex, it is neither not advised to use it in real-life applications. 

Q13. What is the corresponding steady-state performance of the GWMA scheme?

The corresponding steady-state performance is discussed in Chiu and Lu 69 , where it is shown that it is preferred for downward shifts, while the GWMA scheme is more competitive for upward shifts. 

Q14. What are the different types of defects in a ZIP?

For instance, defects are classified in terms of categories or classes, e.g. „Very serious‟, „Serious‟, „Moderately serious‟ and „Minor‟. 

Q15. How can the GWMA scheme be extended to the case U scenario?

it is worth mentioning that Chakraborty et al 30 briefly discussed how the GWMA TBE scheme can be used to monitor downwards shifts in the variance for normally distributed data in Case K and they commented on how this can be extended to the Case U scenario. 

Q16. What are the alternatives to the two-sample location shift parametric t-test?

As an alternative to the two-sample location shift parametric t-test, the Exceedance (EX) and Wilcoxon rank-sum (WRS) tests are usually recommended when the underlying process distribution is non-normal. 

Q17. What are the known enhancements of the GWMA-related scheme?

So far, the existing known enhancements of the GWMA-related scheme are: the double GWMA scheme – denoted as DGWMA scheme; the composite Shewhart-GWMA scheme; the mixed GWMA-CUSUM scheme and its reverse version, the mixed CUSUM-GWMAscheme. 

Q18. What is the way to study the GWMA Max scheme?

Using the ARL and SDRL, it is shown that the GWMA schemes have a better detection ability than the corresponding EWMA schemes, especially for small shifts; however, they have similar diagnostics abilities. 

Q19. What is the need for GWMA monitoring?

R programs or any other commercial / open source statistical software for any general charting statistic need to be made readily available so that more research can be fast-tracked for GWMA-related monitoring schemes.