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The concept of the proposed R chart is based on the sum of chi squares (χ²). The average run lengths (ARLs) of the proposed R chart are computed and compared with the ARLs of a standard R chart, Shewhart variance chart proposed by Chang and Gan, a CUSUM range chart (with and without FIR feature) proposed by Chang and Gan and also with an EWMA range chart proposed by Crowder and Hamilton for various chart parameters. This paper aims to show that only FIR CUSUM schemes perform better than the proposed R chart but other CUSUM and EWMA schemes are less efficient than the proposed R chart.

The concept of the proposed R chart is based on the sum of chi squares (χ²). The proposed R chart divides the plot area into three regions, namely: outright rejection region; outright acceptance region; and transition region. The NULL hypothesis is rejected if a point falls beyond the control limit, and accepted if it falls below the warning limit. However, when a point falls beyond the warning limit, but not beyond the control limit, the decision is taken on the basis of individual observations of the previous H samples, which are considered to evaluate statistic U, that is the sum of chi squares. The NULL hypothesis is rejected if U exceeds a predefined value (U*) and accepted otherwise.

The comparisons also show that the CUSUM, EWMA and proposed R charts outperform the Shewhart R chart by a substantial amount. It is concluded that only FIR CUSUM schemes perform better than the proposed R chart, as it is second in ranking. The other CUSUM and EWMA schemes are less efficient than the proposed R chart.

CUSUM and EWMA charts can catch a small shift in the process average but they are not efficient to catch a large shift. Many researchers have also pointed out that these charts' applicability is limited to the chemical industries. Another limitation of CUSUM and EWMA charts is that they can catch the shift only when there is a single and sustained shift in the process average. If the shift is not sustained, then they will not be effective.

Many difficulties related to the operation and design of CUSUM and EWMA control charts are greatly reduced by providing a simple and accurate proposed scheme. The performance characteristics (ARLs) of the proposed charts described in this paper are very much comparable with FIR CUSUM, CUSUM, EWMA and other charts. It can be concluded that, instead of considering many chart parameters used in CUSUM and EWMA charts, it is better to consider a simple and more effective scheme, because a control chart loses its simplicity with multiple parameters. Moreover, practitioners may also experience difficulty in using these charts in production processes.

It is a modification of the Shewhart Range Chart but it is more effective than the Shewhart Range chart, as shown in the research paper.

The purpose of this paper is to introduce a new design of an R chart to catch smaller shifts in the process dispersion as well as maintaining the simplicity so that it may be applied at shopfloor level.

Here a new R chart has been proposed which can overcome the limitations of Shewhart, CUSUM and EWMA range charts. The concept of this R chart is based on chi‐square (χ²) distribution. Although CUSUM and EWMA charts are very useful for catching the small shifts in the mean or standard deviation, they can catch the process shift only when there is a single and sustained shift in process average or standard deviation.

It was found that the proposed chart performs significantly better than the conventional (Shewhart) R chart, CUSUM range schemes proposed by Chang and Gan for most of the process shifts in standard deviation. The ARLs of the proposed R chart is higher than ARLs of CUSUM schemes for only ten cases out of 40. The performance of the proposed R chart has also been compared with the variance chart proposed by Chang and Gan for various shifts in standard deviation. The ARLs of the proposed R chart are compared with Chang's R chart for sample sizes of 3 and it can be concluded from the comparisons that the proposed R chart is much better than Chang's variance chart for all shift ratios for sample size of three. Many difficulties related to the operation and design of CUSUM and EWMA control charts are greatly reduced by providing a simple and accurate proposed R chart scheme. The performance characteristics (ARLs) of the proposed charts are very comparable to a great degree with FIR CUSUM, simple CUSUM and other variance charts. It can be concluded that, instead of considering many parameters, it is better to consider single sample size and single control limits because a control chart loses its simplicity with a greater number of parameters. Moreover, practitioners may also find difficulty in applying it in production processes. On the other hand, CUSUM control charts are not effective when there is a single and sustained shift in the process dispersion.

A lot of effort has been done to develop the new range charts for monitoring the process dispersion. Various assumptions and factors affecting the performance of the R chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and the performance of the proposed R chart may be studied.

The research findings could be applied to various manufacturing and service industries as it is more effective than the conventional (Shewhart) R chart and simpler than CUSUM charts.

The purpose of this paper is to study the effect of correlation on the performance of CUSUM and EWMA charts. The performance of the CUSUM and EWMA charts is measured in terms of average run lengths (ARLs) for the positively correlated data. The ARLs at various set of parameters of the CUSUM and EWMA charts are computed, using MATLAB. The behavior of the CUSUM and EWMA chart at the various shifts in the process mean is studied, analyzed and compared at different levels of correlation (Φ). The optimum schemes for both the charts are suggested for various levels of correlation (Φ).

Positively correlated observations having normal distribution are generated with the help of the MATLAB. Performance of both the charts in terms of ARLs is measured and compared at various levels of correlation (Φ). The optimal schemes of charts which give the desired in‐control ARLs are suggested for various levels of correlation (Φ).

For each level of correlation (Φ) various schemes of both the charts are suggested. Moreover those suggested schemes which give quick response to the shifts in the process mean is termed as optimal scheme. It is concluded that CUSUM schemes are preferred as compared to the EWMA schemes for quicker response. The optimal schemes of CUSUM and EWMA chart are also compared with the EWMAST chart suggested by Winkel and Zhang (2004).

Both the schemes are optimized by assuming the autocorrelated numbers to be normally distributed. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover sample size of four is taken while developing these schemes; various other schemes can also be developed for different sample sizes. Control charts for attribute type of data can also be developed for different level of correlation (Φ).

For a specific control chart, if the in‐control ARL of the process outputs of any industry is in accordance with the simulated in‐control ARL. It means the process outputs must have same level of correlation (Φ) corresponding to the simulated in‐control ARL and the suggested optimal schemes, corresponding to that level of correlation (Φ), must be adopted to avoid the false alarm rate. The correlation among the process outputs of any industry can be find out and corresponding to that level of correlation the suggested control chart parameters can be applied. Thus false alarms generated, will be minimum for the suggested schemes at different level of correlation (Φ).

If the optimal CUSUM schemes are employed in process/service industry, there will be a considerable amount of saving in time and money expended in search of causes behind frequent false alarms. The rejection level of products in the industries can be reduced by designing the better control chart schemes which will also reduce the loss to the society, as suggested by Taguchi.

The research findings could be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.

The cusum (cumulative sum) chart is a type of graph which takes a little longer to draw than one of the traditional kind but which gives a lot more information. It is particularly useful for plotting the evolution of processes like recruitment, promotion and wastage because it presents information in a way that enables the eye to separate true trends and changes from a background of random variation. It may be used both for retrospective analysis and for monitoring; in the latter role it can give early warning of changes in (for example) wastage rates. Though the technique is not one which demands masses of data as a prerequisite, it offers its richest rewards in the field of large computer‐based data banks.

The application of condition-based maintenance on selected equipment can allow online monitoring using fixed, half-fixed or portable sensors. The collected data not always allow a straightforward interpretation and many false alarms can happen. The paper aims to discuss these issues.

Statistical techniques can be used to perform early failure detection. With the application of Cumulative Sum (CUSUM) Modified Charts and the Exponentially Weighted Moving Average (EWMA) Charts, special causes of variation can be detected online and during the equipment functioning. Before applying these methods, it is important to check data for independence. When the independence condition is not verified, data should be modeled with an ARIMA (p, d, q) model. Parameters estimation is obtained using the Shewhart Traditional Charts.

With data monitoring and statistical methods, it is possible to detect any system or equipment failure trend, so that we can act at the right time to avoid catastrophic failures.

In this work, an electro pump condition is monitored. Through this process, an anomaly and four stages of aggravation are forced, and the CUSUM and EWMA modified control charts are applied to test an online equipment monitoring. When the detection occurs, the methodology will have rules to define the degree of intervention.

The purpose of this paper is to introduce a new design of the X¯ chart to catch smaller shifts in the process average as well as to maintain the simplicity like the Shewhart X¯ chart so that it may be applied at shopfloor level.

In this paper, a new X¯ chart with two strategies is proposed which can overcome the limitations of Shewhart, CUSUM and EWMA charts. The Shewhart chart uses only two control limits to arrive at a decision to accept the Null Hypothesis (H₀) or Alternative Hypothesis (H₁), but in the new X¯ chart, two more limits at “K” times sample standard deviation on both sides from center line have been introduced. These limits are termed warning limits. The first strategy is based on chi‐square distribution (CSQ), while the second strategy is based on the average of sample means (ASM).

The proposed X¯ chart with “strategy ASM” shows lower average run length (ARL) values than ARLs of variable parameter (VP) X¯ chart for most of the cases. The VP chart shows little better performance than the new chart; but at large sample sizes (n) of 12 and 16. The VSS X¯ chart also shows lower ARLs but at very large sample size, which should not be used because, as far as possible, samples should be taken from a lot produced under identical conditions. The inherent feature of the new chart is its simplicity, so that it can be used without difficulty at shopfloor level as it uses only a fixed sample size and fixed sampling interval but it is very difficult to set the various chart parameters in VP and VSS X¯ charts.

A lot of effort has been expended to develop the new strategies for monitoring the process mean. Various assumptions and factors affecting the performance of the X¯ chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and performance of the proposed chart may be studied.

The research findings could be applied to various manufacturing and service industries as it is more effective than the Shewhart chart and simpler than the VP, VSS and CUSUM charts.

In 1973, Goel and Wu presented an algorithm for the economic design of cusum charts to control the mean of a process with a normally distributed quality characteristic. They employed the two‐dimensional pattern search technique to determine the optimal values of the sample size, the sampling interval and the decision limit. Proposes a search algorithm required to use the one‐dimensional pattern search technique to get the optimal values of design parameters instead of the two‐dimensional pattern search technique. So, our search algorithm is not only accurate and efficient but also simpler to solve than that of Goel and Wu.

The majority of quality control charts are employed for normally distributed data. In reality this assumption is not always valid. This paper aims to consider an alternative the truncated normal.

Having derived integral equations for the average run length (ARL), a key measure of the performance of a control chart, approximate solutions are derived using Gaussian quadrature.

Polynomials closely approximating the ARL for the three most popular control charts, using their usual parameterization, are obtained.

An obvious extension is to other distributions and hopefully this work will encourage real world applications.

These charts are widely applicable within engineering, finance, medicine, environmental statistics, and many other fields. These problems are typically said to fall in the domain of risk management. It is hoped that this paper will add to the body of practitioners already employing this technique.

Control charts are widely employed, however applications are usually restricted to the normal distribution. This is the first time it has been applied to the truncated normal distribution and original polynomials derived for the ARL.

Despite being a widely used management technique, cumulative sum (CUSUM) analysis remains almost unheard of in professional sport. To address this, CUSUM analysis of soccer match data from the English Premier League (EPL) was performed. The primary objective of the study was to evaluate CUSUM as a tool for assessing “on-field” team performance. As a secondary objective, the association between managerial change and team performance was evaluated.

CUSUM was applied retrospectively to goal difference data for six EPL teams (Arsenal, Chelsea, Everton, Liverpool, Manchester United and Tottenham) over 23 consecutive seasons from 1995 to 2018. This was supplemented with change point analysis to identify structural changes in mean goal difference. Succession was evaluated by mapping historical managerial changes onto the CUSUM plots for the respective clubs.

CUSUM analysis revealed the presence of structural changes in four clubs. Two structural change points were identified for both Chelsea and Everton, one for Manchester United and Tottenham and none for Arsenal and Liverpool. Relatively few managerial changes coincided temporally with structural changes in “on-field” performance, with most appointments having minimal impact on long-term team performance. Other factors (e.g. changes in ownership) appear to have been influential.

The study was limited by the fact that only successful teams were investigated.

CUSUM analysis appears to have potential as a tool for executive decision-makers to evaluate performance outcomes in professional soccer.

The study is the first of its kind to use CUSUM analysis to evaluate team performance in professional soccer.

Proposes cusum‐cuscore procedures that consider equal weight past sample mean values and past sample score values. The objective is to compare the performance of the cusum‐cuscore and the ewma‐cuscore and in particular to investigate the number of past sample mean values needed to make a significant impact on the performance of the schemes. It will be shown by average run length calculations that the two schemes complement each other very well and that they perform significantly better than standard Shewhart, cuscore and cusum procedures.