Coefficient Of Variation Chart Research Articles

New adaptive EWMA CV control chart with application to the sintering process

This research presents a new adaptive exponentially weighted moving average control chart, known as the coefficient of variation (CV) EWMA statistic to study the relative process variability. The production process CV monitoring is a long-term process observation with an unstable mean. Therefore, a new modified adaptive exponentially weighted moving average (AAEWMA) CV monitoring chart using a novel function hereafter referred to as the "AAEWMA CV" monitoring control chart. the novelty of the suggested AAEWMA CV chart statistic is to identify the infrequent process CV changes. A continuous function is suggested to be used to adapt the plotting statistic smoothing constant value as per the process estimated shift size that arises in the CV parametric values. The Monte Carlo simulation method is used to compute the run-length values, which are used to analyze efficiency. The existing AEWMA CV chart is less effective than the proposed AAEWMA CV chart. An industrial data example is used to examine the strength of the proposed AAEWMA CV chart and to clarify the implementation specifics which is provided in the example section. The results strongly recommend the implementation of the proposed AAEWMA CV control chart.

Economic Statistical Design of the Variable Sampling Interval CV Chart with Known Shift Size

Control charts are essential in Statistical Process Control (SPC) to enhance the product quality by identifying assignable causes within the process. Extensive study on coefficient of variation (CV) charts has been conducted in recent years, indicating their growing significance in a variety of scientific applications. In order to monitor the quality characteristic, it should be noted that the statistical properties and economic perspectives are both indispensable factors. For the economic design, the optimal design parameters that minimise the expected cost function are obtained. However, this design has a major weakness, where it overlooks the statistical performance of the control chart. Therefore, it is of greater importance to examine the economic statistical design, which includes statistical constraints on the cost model. Although the existing variable sampling interval (VSI) CV chart has excellent statistical qualities, it is deficient in taking into account the economic aspects that are necessary for cost-effective process monitoring. In response, this research proposes the economic statistical design of the variable sampling interval (VSI) CV chart with known shift size. Moreover, the study includes sensitivity analyses of the optimal cost and the optimal design parameters for various input parameters. The effects of misspecification of the shift size on the performance of the VSI CV chart are investigated. Additionally, the comparisons in terms of the economic statistical performance between the VSI CV, Shewhart CV and EWMA CV charts are conducted. In comparison with Shewhart CV and EWMA CV charts, the findings clearly demonstrate that the VSI CV chart performs better in all numerical examples. As a result, this research advocates the use of the economic statistical design of the VSI CV chart in process monitoring and provides insightful information for quality practitioners seeking cost-effectiveness and optimal performance in their processes.

Triple exponentially weighted moving average control charts without or with variable sampling interval for monitoring the coefficient of variation

The coefficient of variation (CV) chart is widely used in the process where the standard deviation is proportional to the mean. In this work, two separate one-sided triple exponentially weighted moving average control charts are proposed to monitor the CV squared (denoted as TEWMA- γ 2 chart). By adding the variable sampling interval (VSI) feature to the proposed - γ 2 charts, the VSI TEWMA- γ 2 charts are further proposed to improve the performance of the TEWMA- γ 2 charts. Through extensive Monte Carlo simulations, the zero-state and steady-state run length (RL) performances are presented. The comparisons with the existing CV charts, based on several run length metrics show the superiority of the proposed charts, especially for small shifts. Moreover, the overall measure, expected ARL (EARL), also shows the outperformance of the γ 2 charts. In addition, based on the average time to signal (ATS) and adjusted ATS (AATS), it is shown that the VSI strategy makes the TEWMA- γ 2 charts detect the shifts more quickly. An illustrative example from the sintering process is finally provided to display the application of the proposed charts.

COEFFICIENT OF VARIATION CONTROL CHART BASED ON CONDITIONAL EXPECTED VALUES FOR THE MONITORING OF CENSORED RAYLEIGH LIFETIMES

This article deals with the monitoring of type-I censored data using coefficient of variation (CV) control chart based on conditional expected values (CEVs) for Rayleigh lifetimes under type-I censoring. In particular, the censored data is replaced by the CEV to develop an efficient design structure. The main focus is to detect shifts in the mean of Rayleigh lifetimes assuming censored data. The performance of the proposed CEV based CV chart is evaluated by the average run length (ARL). Besides the simulation study, monitoring of a real-life dataset of 30 average daily wind speeds (in kilometers/hour) for the month of November 2007 at Elanora Heights is also discussed. Keywords: CEV, CV, type І censored, ARL, Average Run Length (ARL); Control Charts; Conditional Expected Values; type-I Censoring.

The performance of double exponentially weighted moving average control charts for monitoring the coefficient of variation

The coefficient of variation (CV) is one of the most important quality characteristics in industrial applications. There have been some control charts for monitoring this dimensionless and normalized characteristic. This paper presents three double exponentially weighted moving average (DEWMA) charts for monitoring the CV. Many numerical simulations are performed and the results are given in several tables to show the properties of the proposed DEWMA CV charts. Through comparisons with other existing exponentially weighted moving average (EWMA) CV charts using the average run length (ARL) metric, it is shown that the proposed DEWMA CV charts perform better than the existing EWMA CV charts for small shifts, especially when the smoothing parameter increases. In addition, a detailed comparison among the proposed three DEWMA CV charts is also presented. A real date example from industry is used to show the implementation of the proposed charts.

Monitoring of coefficient of variation with function‐based adaptive exponentially weighted moving average control chart

AbstractIn this paper, a new adaptive control chart is presented to study the relative process variability, which is called the coefficient of variation (CV). The CV study is the monitoring of a process with an unstable mean value over time. So, a function‐based adaptive exponentially weighted moving average (FAEWMA) CV control chart is proposed to detect the infrequent changes in the process CV, named as “FAEWMA CV” control chart. The function is suggested to adapt the smoothing constant (SC) of the plotting statistic as per arising process shift size in CV. The efficiency is examined through the run‐length values, which are computed through the Monte Carlo (MC) simulation method. The FAEWMA CV chart outperformed the existing AEWMA CV charts. A real‐life example is studied to explain implementation details in the example section.

Monitoring the process coefficient of variation without subgrouping

The coefficient of variation (CV), a measure of relative variability, is an important quality characteristic for a manufacturing process especially when the variance becomes a function of the mean. In this paper, for the first time, we develop four memory-type control charts for monitoring the CV of a normal process using individual observations, namely Crosier CUSUM (CC), EWMA, adaptive CC and adaptive EWMA charts. In addition, the sensitivities of these CV charts are also enhanced via an auxiliary information based CV estimator. The run length characteristics of these control charts are computed using Monte Carlo simulations. The proposed CV charts are also applied on a real dataset related to dowel pins.

Monitoring Coefficient of Variation Using Variable Sampling Interval Double Exponentially Weighted Moving Average Charts

As a measure of relative variability, the coefficient of variation (CV) is a valuable charting statistic in statistical process control. Great efforts have been devoted to monitoring CV efficiently. To further improve the performance of CV charts, this paper proposes three Double Exponentially Weighted Moving Average (DEWMA) charts by incorporating Variable Sampling Interval (VSI) strategies to monitor the CV squared. The run length properties of the proposed charts are evaluated via Monte Carlo simulations. Comparative studies show that the proposed VSI DEWMA CV charts detect the process shifts faster than the existing CV charts. A real data example is presented to illustrate the VSI DEWMA CV charts.

Evaluation of Variable Parameter MCV Control Chart in Downward Process Shifts

Previous studies revealed that the coefficient of variation (CV) is important in ensuring process quality, especially for monitoring a process where its process mean and variance are highly correlated. The fact that almost all industrial process monitoring involves a minimum of two or more related quality characteristics being monitored simultaneously. The existing adaptive charts for monitoring the multivariate CV are focused on detecting upward process shifts. The downward process monitoring is crucial since it shows process improvement. Very little research works are available on the downward adaptive multivariate CV chart. This makes it difficult for the quality engineer who wishes to implement the adaptive multivariate CV chart on the downward process monitoring. Therefore, this paper filled the research gap by proposing a downward variable parameter chart for the multivariate coefficient of variation. The performance measures of the proposed charts are derived based on the Markov-chain approach. Numerical comparisons between the proposed and existing charts have been made, in terms of the average time to signal criterion. The findings reveal that the proposed charts outperform the existing charts for detecting small and moderate downward process shifts

Monitoring the coefficient of variation using a double-sampling control chart

Coefficient of variation (CV) control charts are widely used to monitor processes in which the mean of process characteristic varies and its standard deviation changes with the mean. However, such charts are generally insensitive to small shifts. In the present paper, a double-sampling (DS) CV chart is proposed to effectively detect the CV shifts. An optimization model is developed to obtain the values of parameters in the DS CV chart. The performance of the DS CV chart is then compared with those of the variable parameter (VP) and the exponentially weighted moving average (EWMA) CV charts. Based on our study, the DS CV chart outperforms the VP CV chart in detecting all shift sizes. In addition, the EWMA CV chart outperforms the DS CV chart only for very small shifts, but the DS CV chart generally has better detection ability than the EWMA CV chart for small, medium and large shifts. A real example of integrated circuit lead electroplating is provided for illustration of applications and this example confirms that the DS CV chart has superior performance when compared with the other two charts.

Evaluating the Steady-state Performance of the Synthetic Coefficient of Variation Chart

The synthetic coefficient of variation (CV) chart is attractive to practitioners as it allows for a second point to fall outside the control limits before deciding whether the process is out-of-control. The existing synthetic CV chart is designed with a head-start feature, which shows an advantage under the zero-state assumption where shifts happen immediately after process monitoring has started. However, this assumption may not be valid as shifts may happen quite some time after process monitoring has started. This is called the steady-state condition. This paper evaluates the performance of the chart under the steady-state condition. It is shown that the steady-state out-of-control average run length (ARL1) is substantially larger than the zero-state ARL1, hence larger number of samples are needed to detect the out-of-control condition. From the comparison with other CV charts, the steady-state synthetic CV chart does not show better performance, especially for small sample sizes and shift sizes. Hence, the synthetic CV chart is not recommended to be adopted under the steady-state condition, and its good performance is only applicable under the zero-state assumption. The results of this paper enable practitioners to be aware that the performance of the synthetic CV chart may be inferior under actual application (when shifts do not happen at the beginning of process monitoring) compared to its zero-state performance.

An Optimal Adaptive Variable Sample Size Scheme for the Multivariate Coefficient of Variation

Development of an efficient process monitoring system has always received great attention. Previous studies revealed that the coefficient of variation (CV) is important in ensuring process quality, especially for monitoring a process where its process mean and variance are highly correlated. The fact that almost all industrial process monitoring involves a minimum of two or more related quality characteristics being monitored simultaneously, this paper incorporates the salient feature of the adaptive sample size VSS scheme into the standard multivariate CV (MCV) chart, called the VSS MCV chart. A Markov chain model is developed for the derivation of the chart’s performance measures, i.e the average run length (ARL), the standard deviation of the run length (SDRL), the average sample size (ASS), the average number of observations to signal (ANOS) and the expected average run length (EARL). The numerical comparison shows that the proposed chart prevails over the existing standard MCV chart for detecting small and moderate upward and downward MCV shifts.

An Optimal Design of the Synthetic Coefficient of Variation Chart Based on the Median Run Length

The synthetic coefficient of variation (CV) chart is currently evaluated based only on the average run length (ARL), but this paper evaluates the chart based on different percentiles of the run length, which shows that false alarms frequently happen earlier than that shown by the in-control ARL (ARL[Formula: see text], and for small sample sizes and shift sizes, the out-of-control condition is frequently detected before what is shown by the out-of-control ARL (ARL[Formula: see text]. Furthermore, the run lengths show large variations. Hence, the chart’s performance could not be interpreted only in terms of the ARL. This paper proposes the median run length (MRL)-based design for the synthetic CV chart, which is not available in the literature. The MRL-based design shows larger MRL0and ARL0, smaller MRL1and ARL1, and less variation in the out-of-control run lengths compared to existing ARL-based designs. However, the in-control run lengths show more variation. Comparisons show that the synthetic chart outperforms the VSS and Shewhart charts, while comparison with the Exponentially Weighted Moving Average (EWMA) chart shows that although it outperforms the synthetic chart based on the ARL for small shift sizes, the synthetic chart shows better performance in terms of the MRL. The MRL-based synthetic chart is then implemented on an industrial example.

Efficient monitoring of coefficient of variation with an application to chemical reactor process

AbstractControl chart is a useful tool to monitor the performance of the industrial or production processes. Control charts are mostly adopted to detect unfavorable variations in process location (mean) and dispersion (standard deviation) parameters. In the literature, many control charts are designed for the monitoring of process variability under the assumption that the process mean is constant over time and the standard deviation is independent of the mean. However, for many real‐life processes, the standard deviation may be proportional to mean, and hence it is more appropriate to monitor the process coefficient of variation (CV). In this study, we are proposing a design structure of the Shewhart type CV control chart under neoteric ranked set sampling with an aim to improve the detection ability of the usual CV chart. A comprehensive simulation study is conducted to evaluate the performance of the proposed chart in terms of , and measures. Moreover, the comparison of chart is made with the existing competitive charts, based on simple random sampling, ranked set sampling (RSS), median RSS, and extreme RSS schemes. The results revealed that the proposed chart has better detection ability as compared to all existing competitive charts. Finally, a real‐life example is presented to illustrate the working of the newly proposed CV chart.

Side‐sensitive modified group runs charts with and without measurement errors for monitoring the coefficient of variation

AbstractThe coefficient of variation (CV) is used in process monitoring when the process mean and standard deviation are proportional to each other. In this work, a side‐sensitive modified group runs CV (SSMGR CV) chart is proposed for monitoring the process CV. The run length performance of the SSMGR CV chart is compared to those of the existing CV charts in terms of the average and standard deviation of the run length criteria. The SSMGR CV chart is found to outperform the existing CV charts. In addition, the run length performance of the SSMGR CV chart is also evaluated in the presence of measurement errors, as these errors are not only unavoidable in practice but they also affect the sensitivity of a control chart in detecting an out‐of‐control situation. The results obtained show that the accuracy and precision errors affect the performance of the SSMGR CV chart in detecting an out‐of‐control situation.

Enhanced EWMA charts for monitoring the process coefficient of variation

AbstractThe coefficient of variation (CV) is an important quality characteristic when the process variance is a function of the process mean for a production process. In this paper, we develop an auxiliary information–based (AIB) estimator for estimating the squared CV, along with its approximated mean and variance. This estimator is then used to devise new one‐sided EWMA charts for monitoring the increases or decreases in the squared CV of a normal process, named the AIB‐EWMA CV charts. In addition, the sensitivities of these control charts are also enhanced with the fast initial response feature. The Monte Carlo simulation method is used to compute the run length characteristics of the proposed CV charts. Based on detailed run length comparisons, it is found that the proposed AIB‐EWMA CV charts are uniformly and substantially better than the existing EWMA CV charts when detecting different kinds of upward/downward shifts in the squared CV. The proposed charts are also applied to a real dataset to support the proposed theory.

Economic and economic-statistical designs of variable sample size and sampling interval coefficient of variation chart

In the literature, the variable sample size and sampling interval (VSSI) coefficient of variation (CV) chart was shown to have a better statistical performance than the Shewhart (SH) CV chart which uses fixed sample size and sampling interval. The VSSI CV chart adopts more frequent sampling and larger sample size when the process quality deteriorates for quicker detection of a process shift as there is a higher tendency for the said shift to occur. This paper investigates the economic and economic-statistical performances of the VSSI CV chart as the previous study only analyzes the chart’s statistical performance. By minimizing the cost via economic and economic-statistical designs, the VSSI CV chart can be implemented more economically. Statistical constraints are added in the economic-statistical design of the VSSI CV chart which makes it different from the economic design of the aforementioned chart. Numerical examples are given to illustrate the economic and economic-statistical performances of the VSSI CV chart, where a comparison with the SH CV chart is made. A study of misspecification of the shift size is also conducted to study the effect of wrongly specifying the shift size.

Monitoring coefficient of variation using one-sided run rules control charts in the presence of measurement errors

ABSTRACT We investigate, in this paper, the effect of the measurement error (ME) on the performance of Run Rules control charts monitoring the coefficient of variation (CV) squared. The previous Run Rules CV chart in the literature is improved slightly by monitoring the CV squared using two one-sided Run Rules charts instead of monitoring the CV itself using a two-sided chart. The numerical results show that this improvement gives better performance in detecting process shifts. Moreover, we will show through simulation that the precision and accuracy errors do have a negative effect on the performance of the proposed Run Rules charts. We also find out that taking multiple measurements per item is not an effective way to reduce these negative effects. The proposed Run Rules control charts can be applied in the anomaly detection area.

The efficiency of run rules schemes for the multivariate coefficient of variation in short runs process

In real industries, multivariate process monitoring is crucial as there are many instances that involve at least two quality variables to be monitored simultaneously. The short runs process is commonly seen in production after the industry moved toward flexible manufacturing. Monitoring the coefficient of variation (CV) is useful in a wide variety of scientific areas. In a view of the importance in monitoring the CV and the fact that most real-life data in process monitoring are multivariate in nature, this paper proposes to monitor the multivariate CV in short runs process by means of run rules (RR) control charts. A Markov chain model is established for designing the proposed charts. The statistical performances of the RR multivariate CV (MCV) and Shewhart MCV (SH MCV) charts are compared in terms of the truncated average run length and the expected truncated average run length. The results show that the proposed charts surpass the SH MCV chart for detecting small and moderate multivariate CV shifts. The implementation of the RR MCV chart in the short runs process is illustrated with an example using a real dataset.

A Re-Evaluation of the Run Rules Control Charts for Monitoring the Coefficient of Variation

An efficient process monitoring system is important for achieving sustainable manufacturing. The control charting technique is one of the most effective techniques to monitor process quality. In certain processes where the process mean and variance are not independent of one another, the coefficient of variation (CV), which measures the ratio of the standard deviation to the mean should be monitored. Castagliola et al. (2013a) proposed the two-sided run rules (RR) control charts for monitoring the CV and it is found that the RR CV charts revealed the problem of ARL-biased performances, especially when the monitored sample size is small, for detecting downward CV shifts. This paper alters the RR CV chart by suggesting the two one-sided run rules (ORR) CV charts achieve the unbiased ARL performances. Additionally, this paper also investigates the ORR CV charts in terms of the expected average run length (EARL) criterion, which is not discussed in Castagliola et al. (2013a). A Markov chain model is established for designing the proposed charts. The statistical performances of the ORR CV, RR CV and Shewhart CV (SH CV) charts are compared in terms of the average run length (ARL) and EARL criteria. The results show that the proposed charts surpass the RR CV and SH CV charts for detecting small and moderate upward and downward CV shifts. The implementation of the ORR CV charts is illustrated with an example using a real dataset.