Analysis Process Dispersion Variation Tracked using a Mixed

MA-EWMA Control Chart

SUGANYA PHANTU1, YUPAPORN AREEPONG2, SAOWANIT SUKPARUNGSEE2, *

1Faulty of Science, Energy, and Environment,

King's Mongkut University of Technology North Bangkok,

Rayong, 21120,

THAILAND

2Department of Applied Statistics, Faculty of Applied Science,

King Mongkut's University of Technology, North Bangkok,

Bangkok, 10800,

THAILAND

*Corresponding Author

Abstract: - This study aims to develop a combined Moving Average - Exponentially Weighted Moving Average

Control Chart with standard deviation based (MA-EWMAS chart) that can be used to identify changes in standard

deviation in processes under a normal distribution. The average run length (ARL), standard deviation of run length

(SRL), and median run length (MRL) are used to compare the performance of the proposed control chart with S,

MAS, and EWMAS control charts. This benchmark is assessed using Monte Carlo (MC) simulations. Furthermore,

actual data is used to apply the suggested control charts. For all levels of variation, the recommended control chart

outperforms S, MAS, and EWMAS control charts in terms of detection performance, as indicated by the

performance comparison results. Additionally, the MA-EWMAS chart demonstrates superior performance in

managing process variability for moderate and large subgroup sizes across all magnitudes of shift parameters. One

way to assess the control chart's effectiveness is to apply the suggested chart to track the fruit juice and wafer

coating production process and verify that it complies with standards. The results of the simulations were found to

align with the actual data.

Key-Words: - Dispersion, Performance, Detection, Mixed control chart, Change, Average run length

Received: March 2, 2024. Revised: May 24, 2024. Accepted: June 25, 2024. Published: July 29, 2024.

1 Introduction

Control charts are the primary tools used in statistical

process control (SPC). Control charts have practical

applications and are used extensively in a variety of

industries, including the healthcare sector. Methods of

production used in environmental science, etc.

Shewhart initially developed the control chart, which

is thought to be the main tool of SPC, using statistical

concepts, [1]. The production process is ascertained

by scatter plotting data from previous production

processes in what is commonly known as a Shewhart

control chart. Therefore, the plot distribution pattern

cannot be determined if the production process

remains largely unchanged. Therefore, using a

Shewhart control chart, it is possible to detect more

significant changes in a process. [2] and [3]

subsequently created control charts to detect

modifications in the production process, regardless of

how minor. Compared to Shewhart control chart also

known as cumulative sum (CUSUM) and

exponentially weighted moving average (EWMA)

control charts are more sensitive to identifying slight

to moderate changes in a process. [4], developed a

moving average (MA) control chart in 2004 to

ascertain the percentage of inconsistent observations.

The outcomes show that the MA control chart

outperforms the other charts. Making EWMA and MA

control charts for various scenarios is a common

research focus. In order to detect process averages in

the case of a lognormal distribution using integral

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equations and verify the accuracy of the results

obtained from simulation techniques, [5], presented

algorithms to design CUSUM control chart with time

series observations. It was discovered that the integral

equation outperformed the EWMA control chart, [6].

The EWMA-MA control chart was proposed in 2019

combined the EWMA and MA control charts, [7]. The

performance of the EWMA-MA control chart and the

MA-EWMA control chart are compared to detect

changes in the process average. Upon comparing the

suggested control chart with the MA-EWMA control

chart for both symmetric and asymmetric distributions

under all shift magnitudes, it is discovered that the

MA-EWMA control chart outperforms the EWMA-

MA control chart regarding parameter change

detection.

On the other hand, the comparison results show

that the ARL1 value of the EWMA-MA and MA-

EWMA control charts depend on the parameter of the

control chart mentioned above; that is, if the values of

λ change, ARL1 will not change, but the MA-EWMA

chart will vary ARL1 when the range size changes.

[8], looked into the use of moving average standard

deviation (MAS) control charts for process variation

detection. Process variation is tracked by comparing

the S control chart with the MAS control chart using a

moving average of the sample standard deviation. S

control chart is found to be less effective than MAS

control chart through comparisons. Using a MAS

control chart, small and large process variation

changes can be rapidly recognized as out-of-control

events.

This research aims to propose a new control chart,

called the MA-EWMAS control chart, which

combines the EWMAS and MAS control charts and

can be used to track a change in the standard deviation

process by comparing the chart performance. To

manage MA-EWMAS for process dispersion change,

use S, EWMAS, and MAS control charts. A control

chart with the lowest ARL1 performs best regarding

change detection. Verifying the inter-thread thickness

on real data can also be done with it. In addition,

information on fruit juice bottle packaging and wafer

surface coating quality inspection have been used to

compare the performance of the presented chart with

the original control chart.

2 Research Methodology

Let

12

, ,..., ,...

i

S S S

represent the standard deviation from

a set of subgroups following a normal distribution

(

2

( , )Normal



) [9], which

i

S

signifies the standard

deviation of the sample of subgroups i. Establishing a

control limit is imperative to ascertain the value of the

actual standard deviation

( ).



A value



is unknown in most cases and needs to

be estimated from prior data. The average sample

standard deviation

S

is typically determined from an

initial set of

k

subgroup standard deviations provided

by the unbiased estimator

4

ˆ/,Sc





, where

1

1,

k

i

SS

k



(1)

where

2

1

11

( ) , ,

1

k

i ij i i ij

jj

S X X X X

kk



  



and

1/2

4

21

( ) ( ( ) / ( ))

1 2 2

nn

cn



  



is a constant that depends

on the sample size

,k

including the following chats in

this research.

2.1 Control Chart for Standard Deviation (S

Chart)

The standard deviation control limits are usually

computed based on the

3



approach, i.e.,

3

SS





where

S



and

S



are the mean and standard

deviation of the process [9], respectively. Thus, the

upper and lower control limits of the chart, when



is

unknown, are given as:

2

14

ˆˆ

/1UCL LCL B c



  

(2)

where

1

B

is the factor of control limit of the S chart. A

sample point plot that deviates from the control limit

indicates instability in the process.

2.2 Moving Average for Standard Deviation

Control Chart (MAS chart)

The moving average standard deviation (MAS) control

chart was examined by [8] in order to look into the

control chart's middle movement for identifying

process variability which original presented from [10].

For minor and large process variability changes, the

MAS chart can quickly identify departures from

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control. The statistical values of the MAS chart can be

categorized into two cases as follows:

1 2 1

11

;

;.

i i i

ii i i

S S S ... S i

i

MA S S ... S i





  

   





  







(3)

Where



is the width of the MAS chart. The average

of the MAS statistic is denoted as

4ˆ

( ) .=

S

E MA c



(4)

Furthermore, the variance of the MAS statistic can be

split into the following two scenarios:

22

4

22

4

ˆ(1 ) ,

= ˆ

( ) (1 ) ,.

S

c

Var MA i

i

c

















(5)

As a result, the following is the upper and lower

control limit,

22

4

2

4

2

4

2

4

ˆ(1 )

ˆ,

=

ˆ

(

/

1)

ˆ,

Bi

i

Bi

c

UCL LCL c

c

























(6)

where

2

B

is the factor of control limit of the MAS

chart.

2.3 Exponentially Weighted Moving Average

for Standard Deviation Control Chart

(EWMAS chart)

[3], introduced the EWMA chart to track minute

parameter variations like process mean and standard

deviation. EWMA statistics for detecting the variation

of a process [9] are as follows

 

1

1 , 1,2,...

ii

S i S

EWMA S EWMA i





   

(7)

where



the weighting parameter of the past data has

a value from 0 to 1, and

i

S

the average standard

deviation at the time i. The expectation and variance

of EWMAS are:

 

4ˆ

i

S

E EWMA c





and

 

2

4

ˆ1 / 2 .

i

S

Var EWMA c

  

  

(8)

Therefore, the EWMAS chart's control limits are

 

2

4 3 4

ˆ

/ 1 / 2UCL LCL c B c

  

   

(9)

where

3

B

is the factor of control limit of the EWMAS

chart.

2.4 Moving Average - Exponentially Weighted

Moving Average for Standard Deviation

Control Chart (MA-EWMAS chart)

The MAS chart and the EWMAS chart are combined to

create the MA-EWMAS chart. As an input to the MAS

chart, let us consider the statistical data of the

EWMAS chart. Thus, the statistics of the MA-

EWMAS chart are as follows:

1 2 1

11

;

i

i i i

Si i i

Z Z Z ... Z i

i

MA EWMA Z Z ... Z i





  

   







  







(10)

where



is the span of the moving average of the

MA-EWMAS chart. The expectation and variance of

statistics MA-EWMAS are:

4

( = ˆ

)

S

E MA EWMA c





and

22

4

22

4

( ) 2

ˆ(1 ) ,

= ˆ(1 ) ,.

2

S

c

Var MA EW

i

ci

MA

















  















(11)

Therefore, the MA-EWMAS chart’s control limits are

4

22

44

4

22

4

ˆ(1 )

ˆ,

2

=

ˆ(

1)

ˆ,

2

/

c

UL

B

CL CL c

i

Bic







































(12)

where

4

B

is the factor of control limit of the MA-

EWMAS chart.

3 The Performance of the Control

Chart

The effectiveness of control charts can be evaluated

using a variety of techniques. This research uses three

values to consider the tracking performance of control

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charts with Monte Carlo (MC) simulation techniques,

including the following methods.

3.1 Average Run Length (ARL)

The Average Run Length (ARL) is a commonly used

metric to evaluate a control chart's effectiveness. ARL

measures the control chart's effectiveness in

identifying outliers in the production process. It

measures how quickly the process parameter shifts are

identified on the chart. The average number of data

points (ARL) that must be plotted before one point

indicates an out-of-control condition, which is

represented by ARL0 and ARL1, respectively,

representing the in-control and out-of-control

processes. The ARL can be determined as follows:

1

.

T

j

ARL RL T





(13)

In this case, the sample being examined before the

process surpasses the control limits for the first time is

indicated by RLj. T is set to 200,000, is the number of

experiment repetitions in the simulation during round

j.

3.2 Standard Deviation of Run Length (SRL)

The standard deviation of the run length (SRL) can be

computed as follows:

 

22.

j

SDRL E RL ARL

(14)

3.3 Median Run Length (MRL)

The middle of RLj points plotted on a chart before an

out-of-control signal is given is called the median run

length, or MRL. Thus, the MRL is calculated as

follows:

( ).

j

MRL Median RL

(15)

4 Numerical Results

The numerical results of this research are divided into

three parts. Part 1 focuses on assessing the efficiency

of the MA-EWMAS chart. Part 2 involves comparing

the efficiency of control charts, and Part 3 explores

the application of these charts to real-world data in

that order.

4.1 Average Run Length of MA-EWMAS

Chart

A performance metric is the average run length

(ARL). The estimated number of samples needed until

a control chart indicates an out-of-control condition is

indicated by the ARL0. A large ARL0 is desirable

when there is no change in the process variability.

However, in the scenario where the process variability

shifts from

0



to

1



,

10

,

 



a small ARL1 value is

preferred. Monte Carlo simulations estimate the

average run lengths of the MA-EWMAS chart that are

in control and out-of-control, considering different

shifts in the process standard deviation. The in-control

process is assumed to follow a normal distribution

with parameters Normal

2

( , ),



while the out-of-

control process is supposed to be normally distributed

as Normal

2

( , ).

 

The shift values are represented as

10

/

  



where



takes on values in the set {1.01,

1.025, 1.05, 1.10, 1.20, 1.50, 2.00}. It is assumed that



= 0 and

0



= 1, ensuring that the chart's in-control

average run length (ARL0) is approximately 370.

Table 1, Table 2 and Table 3 display the ARL of

the MA- EWMAS chart for sample sizes of

k

= 5, 10,

and 15, respectively, with the weighting parameter of

the data

()



as 0.5 and the width

()



of the MA-

EWMAS chart are 2, 5, 10 and 15. The results showed

that in Table 1, when the number of subgroups is 5,

the optimal width parameter

()



for the MA-

EWMAS chart, when the shift value is set to 1.01, is 2.

Next, in Table 2, the optimal width parameter

()



for

the MA-EWMAS chart, when the shift value is set to

1.025, is determined to be 5. Finally, in Table 3, the

optimal width parameter

()



for the MA-EWMAS

chart, when the shift value is greater than 1.05, the

value of width

()



is determined to be 15, resulting

in the lowest ARL1. Additionally, the number of

subgroups is 10 and 15. The result indicates that the

optimal width parameter

()



for the MA-EWMAs

chart, when the shift value is equal to 1.01, is found to

be 2, and when the shift value starts from 1.025 and

upwards, it is found to be 15.

Additionally, the efficiency of the MA-EWMAS

chart increases performance as the width

()



is

augmented across all levels of parameter changes. At

the same time, the subgroup size (k) does not impact

the proposed chart’s performance.

Table 4, Table 5 and Table 6 displays the

performance of the MA-EWMAS chart for sample

sizes of k = 5, 10, and 15, respectively, with the

weighting factor of the past data

()



based on the

value in the set {0.05, 0.2, 0.25, 0.50} and the width

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()



of the MA-EWMAS chart is 2. The results

demonstrate that in Table 4, if the number of

subgroups is 5, the optimal parameter of weighting

()



for the MA-EWMAS chart, when the shift value is

set from 1.01 to 1.20, is given to be 0.25. Next, in

Table 5, when the shift value is set from 1.50 to 2.00,

it is shown to be 0.2 and 0.25. In the scenario of the

number of subgroups being 10, the optimal parameter

of weighting

()



for the MA-EWMAS chart, when the

shift value is set from 1.01 to 1.20, is given to be 0.05.

Furthermore, when the shift value is set from 1.50 to

2.00, it is shown to be 0.05 to 0.52. In Table 6, the

number of subgroups is 15, and the optimal parameter

of weighting

()



for the MA-EWMAS chart, when the

shift value is set from 1.01 to 1.20, is given to be 0.25.

Finally, in Table 6, when the shift value is set from

1.50 to 2.00, it is found to be 0.05 to 0.52.

Furthermore, the MA-EWMA chart's efficiency

increases as weighting

()



decreases, where the

subgroup size affects the proposed chart’s

performance. When the subgroup size (k) is small, the

weighting

()



tends to increase; conversely, when the

subgroup size (k) is large, the weighting value

()



tends to decrease.

Table 1. Comparative ARL1 of MA-EWMAS chart when ARL0=370, k=5 and



=0.2.

Shift sizes

(



)



=2



=5



=10



=15

4

B

=5.316

4

B

=5.052

4

B

=4.808

4

B

=4.634

1.01

323.274

325.565

331.352

334.431

1.025

262.444

261.825

265.748

267.274

1.05

184.347

175.965

171.945

166.776

1.10

95.228

82.614

73.846

67.939

1.20

33.602

26.313

22.295

20.394

1.50

5.442

4.418

3.991

3.744

2.00

1.273

1.128

1.036

0.974

*bold is a minimum of ARL1

Table 2. Comparative ARL1 of MA-EWMAS chart when ARL0=370, k=10 and



=0.2.

Shift sizes

(



)



=2



=5



=10



=15

4

B

=5.236

4

B

=5.047

4

B

=4.815

4

B

=4.641

1.01

317.787

321.606

324.275

324.551

1.025

245.814

241.454

235.952

228.462

1.05

155.473

139.378

123.287

111.568

1.10

66.598

50.517

40.566

35.603

1.20

18.091

12.730

10.483

9.556

1.50

2.186

1.817

1.646

1.537

2.00

0.368

0.335

0.302

0.279

*bold is a minimum of ARL1

Table 3. Comparative ARL1 of MA-EWMAS chart when ARL0=370, k=15 and



=0.2.

Shift sizes

(



)



=2



=5



=10



=15

4

B

=5.219

4

B

=5.043

4

B

=4.809

4

B

=4.639

1.01

314.979

317.512

316.863

315.912

1.025

235.683

225.311

210.330

198.089

1.05

137.286

114.375

93.817

82.508

1.10

51.077

35.467

27.113

23.802

1.20

11.917

8.090

6.704

6.175

1.50

1.228

1.051

0.952

0.885

2.00

0.141

0.127

0.112

0.101

*bold is a minimum of ARL1

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Table 4. Comparative ARL1 of MA-EWMAS chart when ARL0=370, k=5, and



=2.

Shift sizes

(



)

𝜆 = 0.05

𝜆 = 0.2

𝜆 = 0.25

𝜆 = 0.50

4

B

=19.166

4

B

=9.207

4

B

=8.120

4

B

=5.316

1.01

323.256

323.216

323.204

323.274

1.025

262.435

262.394

262.386

262.444

1.05

184.346

184.315

184.312

184.347

1.10

95.228

95.219

95.217

95.228

1.20

33.601

33.599

33.598

33.602

1.50

5.442

5.441

5.442

2.00

1.273

1.272

1.273

*bold is a minimum of ARL1

Table 5. Comparative ARL1 of MA-EWMAS chart when ARL0=370, k=10, and



=2.

Shift sizes

(



)

𝜆 = 0.05

𝜆 = 0.2

𝜆 = 0.25

𝜆 = 0.50

4

B

=18.874

4

B

=9.068

4

B

=7.997

4

B

=5.236

1.01

317.048

317.268

317.103

317.787

1.025

245.307

245.509

245.347

245.814

1.05

155.144

155.283

155.163

155.473

1.10

66.465

66.515

66.476

66.598

1.20

18.066

18.076

18.069

18.091

1.50

2.185

2.00

0.368

*bold is a minimum of ARL1

Table 6. Comparative ARL1 of MA-EWMAS chart when ARL0=370, k=15, and



=2.

Shift sizes

(



)

𝜆 = 0.05

𝜆 = 0.2

𝜆 = 0.25

𝜆 = 0.50

4

B

=18.815

4

B

=9.042

4

B

=7.971

4

B

=5.219

1.01

314.872

315.643

314.866

314.979

1.025

235.578

236.139

235.576

235.683

1.05

137.235

137.538

137.234

137.286

1.10

51.068

51.156

51.062

51.077

1.20

11.917

11.932

11.916

11.917

1.50

1.228

2.00

0.141

*bold is a minimum of ARL1

4.2 Comparison Performance of the Control

Chart

This section compares the MA-EWMAS chart's

efficiency to that of the S, MAS, and EWMAS charts.

The standard deviation of run length (SRL), median

run length (MRL), and average run length (ARL)

were among the metrics used to assess the

effectiveness of control charts. The control chart

exhibiting the lowest values for ARL1, SRL, and

MRL was deemed the most efficient. When the

process is under control, it is given that ARL0 = 370,

the width

()



for the MA-EWMAS chart is two, and

the weighting factor of the data is 0.2. Table 7 shows

that the number of subgroups is 5, indicating that the

MAS chart performs best when the shift parameter is

1.01 to 1.02. Next, the shift parameter (



) is 1.05 to

1.20, and the EWMAS chart achieves the most.

Finally, if the shift parameter exceeds 1.50, the MA-

EWMAS chart detects change most effectively. Table

8 for the number subgroup is 10, showing that when

the shift parameter is 1.01, the MAS chart is the best

performing. Next, the shift parameter is 1.02, and the

EWMAS chart performs the most. Furthermore, if the

shift parameter is greater than 1.05, the MA-EWMAS

chart detects change most effectively. Additionally,

Table 9 for the number of subgroups is 10,

demonstrating that when the shift parameter is

greater than 1.01, the MA-EWMAS chart is the best

performing.

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Table 7. The comparison of control chart when ARL0 = 370, k = 5,



= 0.2, and



= 2.

Shift sizes

(



)

S

MAS

EWMAS

MA-EWMAS

1

B

= 3.19

2

B

= 3.07

3

B

= 3.19

4

B

= 5.32

ARL1

SRL

MRL

ARL1

SRL

MRL

ARL1

SRL

MRL

ARL1

SRL

MRL

1.01

330

0.83

243

323

0.82

237

324

0.94

219

323

0.82

237

1.02

276

0.73

196

262

0.70

186

263

0.81

171

262

0.70

186

1.05

203

0.57

142

184

0.52

128

181

0.59

115

184

0.52

128

1.10

114

0.33

79

95

0.28

66

90

0.29

58

95

0.28

95

1.20

44

0.13

30

33

0.10

23

31

0.09

22

33

0.10

23

1.50

7

0.23

5

6

0.02

4

6

0.02

5

0.01

4

2.00

1

0.01

1

0.01

1

2

0.01

2

1

0.01

1

*bold is a minimum of ARL1, SRL, and MRL

Table 8. The comparison of control chart when ARL0 = 370, k = 10,



= 0.2 and



= 2.

Shift

sizes

(



)

S

MAS

EWMAS

MA-EWMAS

1

B

= 3.07

2

B

= 3.02

3

B

= 3.58

4

B

= 5.24

ARL1

SRL

MRL

ARL1

SRL

MRL

ARL1

SRL

MRL

ARL1

SRL

MRL

1.01

319

0.81

232

317

0.81

231

355

1.27

232

317

0.81

232

1.02

253

0.69

179

245

0.67

174

321

0.67

173

245

0.67

174

1.05

170

0.49

119

155

0.44

108

239

0.45

45

155

0.45

108

1.10

82

0.24

57

66

0.19

46

100

0.42

37

66

0.19

46

1.20

25

0.07

17

18

0.05

14

24

0.09

15

18

0.05

12

1.50

2

0.01

2

0.01

1

4

0.01

4

2

0.01

1

2.00

0.5

0.01

0

0.5

0.01

0

1

0.01

1

0.3

0.01

0

*bold is a minimum of ARL1, SRL, and MRL

Table 9. The comparison of control chart when ARL0 = 370, k = 15,



= 0.2, and



= 2.

Shift

sizes

(



)

S

MAS

EWMAS

MA-EWMAS

1

B

= 3.047

2

B

= 3.014

3

B

= 4.291

4

B

= 5.219

ARL1

SRL

MRL

ARL1

SRL

MRL

ARL1

SRL

MRL

ARL1

SRL

MRL

1.01

317

0.81

230

315

0.80

230

385

1.39

232

314

0.80

230

1.02

244

0.67

172

235

0.65

166

404

1.36

171

235

0.65

166

1.05

155

0.45

108

137

0.39

96

431

1.36

96

137

0.39

96

1.10

66

0.19

46

51

0.15

36

51

1.03

84

51

0.15

36

1.20

17

0.05

12

11

0.03

8

41

0.15

24

11

0.04

8

1.50

1.6

0.01

1

1.2

0.01

1

4.3

0.01

4

1.2

0.01

1

2.00

0.2

0.01

0

0.1

0.01

0

1.5

0.01

0

0.1

0.01

0

*bold is a minimum of ARL1, SRL, and MRL

4.3 Comparison Performance of the Control

Chart

This section describes how the control chart is

applied to real data to inspect and manage production

process quality and meet predetermined standards.

The standard deviation is the value used to assess the

performance of both data sets. The data is divided

into two sets as follows:

4.3.1 Application I: Fruit Juice Volume

Data from the production process will be collected to

inspect the quantity of fruit juice packages, which

will involve 15 sample groups, each containing ten

bottles. The measurement consists of assessing the

height of the fruit juice level in the bottles compared

to standard quality. The interpretation is as follows: if

the measured height is 0, it indicates that the

packaging quantity is equal to the normal amount. A

positive or negative estimated height signifies that

the packaging quantity is higher or lower than the

standard quantity, [9].

The efficiency of detecting changes in the

standard deviation values of S, MAS, EWMAS, and

MA-EWMAS charts can be illustrated as follows. In

Figure 1, the change detection performance for the S

chart reveals no data from the sample group of fruit

juice bottles exceeding the control limits. Next,

Figure 2, Figure 3 and Figure 4 illustrate the change

detection performance of the MAS, EWMAS, and

MA-EWMAS charts, respectively. The results of the

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control chart performance measurements reveal that

sample group no. At Sixth the fruit juice bottles

exceed the control limits of the chart. Therefore,

these charts detect changes faster than the S chart.

Additionally, the comparative results indicate that

MAS, EWMAS, and MA-EWMAS control charts

exhibit comparable efficiency in detecting changes in

the data's standard deviation.

Fig. 1: The performance of the S chart for fruit juice

Fig. 2: The performance of the MAS chart for fruit

juice

Fig. 3: The performance of the EWMAS chart for

fruit juice

Fig. 4: The performance of the MA-EWMAS chart

for fruit juice

4.3.2 Application II: The Coating on Wafers

Quality control is essential in semiconductor

manufacturing, which involves hardback processes.

The thickness of the surface coating on wafers is

examined by sampling five units from each of the 20

groups to observe whether the production process is

under control. The sampling intervals are set to be 1

hour apart for each instance, [9].

The efficiency of detecting changes in the

standard deviation values of S, MAS, EWMAS, and

MA-EWMAS charts can be explained as follows.

Figure 5, Figure 6 and Figure 7 present the

performance evaluation of the S, MAS, and EWMAS

control charts. The results indicate that these charts

cannot detect changes in the data because no data

from the sample group exceeds the control limits.

The performance of the MA-EWMAS chart is finally

displayed in Figure 8. The outcomes demonstrated

that the MA-EWMAs chart can detect data changes

immediately. For this reason, compared to the S,

MAS, and EWMAS charts, the MA-EWMAs chart is

better at tracking changes in the data's standard

deviation.

Fig. 5: The performance of the S chart for the coating

on wafers

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Fig. 6: The performance of the MAS chart for the

coating on wafers

Fig. 7: The performance of the EWMAS chart for the

coating on wafers

Fig. 8: The performance of the MA-EWMAS chart

for the coating on wafers

5 Conclusion and Future Work

In order to monitor process variability, this study

substitutes the moving average statistic for the MAS

and EWMAS charts. For the chart, control limit

factors are given for a range of sample sizes and

width parameters. Through simulation procedures,

the average run length (ARL), standard deviation of

run length (SRL), and median run length (MRL)

values are used to assess the performance of the MA-

EWMAS chart. The S, MAS, and EWMAS charts for

process variability monitoring are compared with the

ARL1, SRL, and MRL values. The comparison

shows that the MA-EWMAS chart is superior to all

charts when the shift parameter is significant, and the

number of subgroups is small. The MA-EWMAS

chart also performs best in process variability for

moderate and large subgroup sizes (k) of all shift

parameters. In all the above research, the MA-

EWMAS chart primarily excels in rapidly identifying

signals of process variability shift, even slight ones

that could be crucial. Organizations value this

capability as early detection of such variability can

enhance overall process quality. The aspiration is for

the MA-EWMAS chart to be seen as a compelling

substitute for the traditional S chart, particularly

among quality control operators dealing with minor

to moderate shifts in process variability.

Acknowledgment:

The authors would like to express the Department of

Applied Statistics for supporting materials and

superhigh-performance computers. Besides, we

would like to thank King Mongkut's University of

Technology North Bangkok and Thailand Science

Research and Innovation, Ministry of Higher

Education, Science, and Research for supporting the

research fund with contract no. KMUTNB-FF-67-B-

18.

References:

[1] W. A. Shewhart, “Statistical control,” in

Economic Control of Quality Manufactured

Product,” NY: D. Van Nostrand Company,

(1931).

[2] E. S. Page, "Continuous Inspection Scheme,"

Biometrika, 41(1-2), 100–115, (1954).

[3] S. W. Roberts, “Control Chart Tests Based on

Geometric Moving Average,” Techmometrics,

1, 239–250, (1959).

[4] A. A. Olatunde, A. A. Abayomi and B. A.

Femi, “Monitoring Process Variability Using

Double Moving Average Control Chart,”

Communications in Statistics – Theory and

Methods, 46, 6980–6993, (2017), doi:

10.1080/03610926.2016.1139132.

[5] W. Peerajit, “Computation of ARL on a

CUSUM Control Chart for a Long-Memory

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Seasonal Autoregressive Fractionally

Integrated Process with Exogenous Variables,”

Journal of Physics: Conference Series, 1,

012003, (2014), doi: 10.1088/1742-

6596/2014/1/012003.

[6] N. Khan, M. Aslam and C-H. Jun, “An EWMA

Control Chart for Exponential Distributed

Quality Based on Moving Average Statistics,”

Quality and Reliability Engineering

International, 32, 1179–1190, (2015),

doi.org/10.1002/qre.1825.

[7] S. Sukparungsee, Y. Areepong and R.

Taboran, “Exponentially weighted moving

average-Moving average charts for monitoring

the process mean,” PLoS ONE, 15, 1–24,

(2020), doi: 10.1371/journal.pone.0228208.

[8] A. A. Olatunde and J. O. Olaomi, “A moving

average S control chart for monitoring process

variability,” Quality Engineering, 28, 212–

219, (2016), doi:

10.1080/08982112.2015.1104542.

[9] D. C. Montgomery, “Introduction to Statistical

Quality Control Case Study,” NY: John Wiley

and Sons, (2009).

[10] M. B. C. Khoo. “Moving average control chart

for monitoring the fraction non-conforming,”

Quality and Reliability Engineering

International, 20, 617–635, (2004), doi:

10.1002/qre.576.

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

- P. S.: writing an original draft, software, data

analysis, data curation, proof, and validate.

- Y. A.: investigation, methodology, validate,

reviewing

- S. S.: conceptualization, investigation, funding

acquisition, project administration, reviewing and

editing.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

Besides, we would like to thank King Mongkut's

University of Technology North Bangkok and

Thailand Science Research and Innovation, Ministry

of Higher Education, Science, and Research for

supporting the research fund with contract no.

KMUTNB-FF-67-B-18.

Conflict of Interest

The authors have no conflict of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_

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