Abstract: - Control charts are generally used to detect mean process changes in continuous processes. However,

counting procedures that characterize product quality are popular in production processes, such as the number

of defects or the proportion of defective products. This research aims to investigate using the Modified

Exponentially Weighted Moving Average combined with a nonparametric Sign Rank control chart, namely

MEWMA-SR chart is a novel tool. Comparative analyses involving different run length measures are

conducted to evaluate the proposed scheme against MEWMA, MEWMA-SR, and classical EWMA charts. The

performance of the MEWMA-SR chart is assessed using Monte Carlo simulations based on its run-length

profiles. It was found that the proposed combination control chart was effective in detecting changes better than

other control charts along with presenting applications with real data. A study further validates the proposed

Good quality products that meet standards are the

main factors that make the industry successful.

Therefore, to make the products that meet the needs

of consumers, it is necessary to use process control

to control production and detect abnormalities or the

amount of waste in the production process which in

the industrial production process. Without loss of

of variations; natural variation which is a normal

variation that is hidden in the production process.

Another type of variation is variation due to

assignable causes, such as human, machine,

material, and method causes. Statistical process

[4]. Those two control charts, known as memory-

type charts, incorporate current and past sample

information into their charting structures. While

their performance detecting small to moderate shifts

is nearly identical, quality practitioners often favor

the EWMA chart's simplicity. The increasing

adoption of these flowcharts is attributed to their

heightened sensitivity to persistent modifications to

the process variables. Consequently, they are

regularly employed to identify subtle alterations in

superior efficacy in detecting subtle changes

compared to standard EWMA charts.

the presumption that the data come from a normal

distribution. However, if the finding stems from an

irregular distribution, utilizing the equivalents of

such control diagrams for tracking change in the

process becomes unsuitable. Consequently,

developing an adequate substitute is a

variance while creating location parameter charts.

encompass: In 1991, this research significantly

advanced the statistical process control domain by

demonstrating the effectiveness of the

nonparametric EWMA method for monitoring

processes with non-normal or heavy-tailed

distributions, [6]. Compared to conventional

EWMA schemes, the nonparametric approach

performed better in detecting shifts and identifying

sign test statistic. Given the EWMA chart's

sensitivity to subtle and enduring shifts, numerous

changes have been proposed and examined within

the nonparametric exponentially weighted moving

average (EWMA) charting structure. In 2011, [8],

introduced an EWMA chart based on an SR test

normal distribution and are independent, such as the

average amount of mineral water packed, the width

of the diameter of the piston ring, etc. But in

practice, the quality characteristics of interest may

have a non-normal distribution or a discrete

distribution, such as proportion. the proportion of

defective products or the number of defects, which

corresponds to a binomial distribution. Production

quality is sometimes measured by the number of

enumerated data or observed values that have a

discrete distribution such as the binomial (10, 0.1)

and Poisson(4) distributions. Combining the benefits

of both charts, it is a hybrid of the Sign-Rank

statistic and the MEWMA chart. The proposed

nonparametric control chart can solve problems with

processes where the distribution of observed values

is unknown or parameters cannot be estimated.

Conventional control charts currently in use cannot

simulations, employing the out-of-control average

run length (ARL1) metric as the evaluation

benchmarking. Additionally, practical applications

of the MEWMA-SR chart are demonstrated using

real-world data examples.

This segment introduces pertinent theory, organized

into three parts. Section 2.1 delves into the

nonparametric properties of the control chart.

control chart, transformed into an exponentially

weighted moving average sign rank (EWMA-SR)

control chart, and proposes the modified

exponentially weighted moving average sign rank

approaches infinity, the variance asymptotically is

EWMA chart is represented by L1, which

corresponds to the desired ARL0. This value can be

found to reach the desired ARL0 using the Monte

Carlo simulation method.

incorporating the additional term

EWMA statistic. This modification resulted in

MEWMA statistics surpassing the EWMA chart for

the identical dataset, [5]. The statistics of the

MEWMA chart are as follows:

similar form with k=1 (see details [5]). The mean

and deviation of MEWMAt for an in-control process

are as follows:

and

MEWMA chart are explained as follows:

asymptotic variance are as follows:

considered the most potent.

numerical outcomes for a binomial (10, 0.1)

distribution with a subgroup size of 5, resulting in

an average run length under in-control conditions

from 0.01 to 0.20, the EWMA chart outperforms all

other charts, according to the Monte Carlo method

analysis. Beyond that, when the process changes

more than 0.2, the MEWMA chart works well

found that when the magnitude size (

The data is collected weekly from April 1, 2021, to

May 31, 2021, totalling 61 points. The data exhibits

charts efficiently identify the data's mean variations.

Figure 1 demonstrates that the statistics of the

EWMA chart fall within the upper and lower

bounds, leading to the conclusion that the EWMA

chart is unable to detect changes in the data. The

MEWMA chart fails to detect changes in data like

Fig. 2: The performance of the MEWMA chart

distributions, achieving the least ARL1 compared to