Monitoring the Coefficient of Variation Using the Side Sensitive Group Runs Chart

Many quality characteristics have means and standard deviations that are not independent. Instead, the standard deviations of these quality characteristics are proportional to their corresponding means. Thus, monitoring the coefficient of variation (CV), for these quality characteristics, using a control chart has gained remarkable attention in recent years. This paper presents a side sensitive group runs chart for the CV (called the SSGR CV chart). The implementation and optimization procedures of the proposed chart are presented. Two optimization procedures are developed, i.e. (i) by minimizing the average run length (ARL) when the shift size is deterministic and (ii) by minimizing the expected average run length (EARL) when the shift size is unknown. An application of the SSGR CV chart using a real dataset is also demonstrated. Additionally, the SSGR CV chart is compared with the Shewhart CV, runs rules CV, synthetic CV and exponentially weighted moving average CV charts by means of ARLs and standard deviation of the run lengths. The performance comparison is also conducted using EARLs when the shift size is unknown. In general, the SSGR CV chart surpasses the other charts under comparison, for most upward and downward CV shifts. Copyright © 2015 John Wiley & Sons, Ltd.     

Monitoring the Coefficient of Variation Using a Variable Sampling Interval Control Chart

The coefficient of variation (CV) is a quality characteristic that has several applications in applied statistics and is receiving increasing attention in quality control. Few papers have proposed control charts that monitor this normalized measure of dispersion. In this paper, an adaptive Shewhart control chart implementing a variable sampling interval (VSI) strategy is proposed to monitor the CV. Tables are provided for the statistical properties of the VSI CV chart, and a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV. An example illustrates the use of these charts on real data gathered from a casting process. Copyright © 2012 John Wiley & Sons, Ltd.     

A Synthetic Control Chart for Monitoring Process Variability

The control chart based on Downton's estimator (D chart) has recently been introduced in the literature for monitoring the process variability. The D chart is found to be equally efficient to the S chart in terms of detecting shifts in process variability. In this paper, salient features of D chart and the conforming run length chart are combined to produce synthetic D chart. The average run length performance of the synthetic D chart is investigated using simulation study and is compared with the originally proposed D chart and some other procedures proposed in the literature. It is found that it has an improved performance in comparison with the traditional control charts for process variability. Copyright © 2013 John Wiley & Sons, Ltd.     

Variable Selection‐based Multivariate Cumulative Sum Control Chart

High‐dimensional applications pose a significant challenge to the capability of conventional statistical process control techniques in detecting abnormal changes in process parameters. These techniques fail to recognize out‐of‐control signals and locate the root causes of faults especially when small shifts occur in high‐dimensional variables under the sparsity assumption of process mean changes. In this paper, we propose a variable selection‐based multivariate cumulative sum (VS‐MCUSUM) chart for enhancing sensitivity to out‐of‐control conditions in high‐dimensional processes. While other existing charts with variable selection techniques tend to show weak performances in detecting small shifts in process parameters due to the misidentification of the ‘faulty’ parameters, the proposed chart performs well for small process shifts in identifying the parameters. The performance of the VS‐MCUSUM chart under different combinations of design parameters is compared with the conventional MCUSUM and the VS‐multivariate exponentially weighted moving average control charts. Finally, a case study is presented as a real‐life example to illustrate the operational procedures of the proposed chart. Both the simulation and numerical studies show the superior performance of the proposed chart in detecting mean shift in multivariate processes. Copyright © 2016 John Wiley & Sons, Ltd.     

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean: Discussion

A new hybrid exponentially weighted moving average (HEWMA) control chart has been proposed in the literature for efficiently monitoring the process mean. In that paper, the computed variance of the HEWMA statistic was, unfortunately, not correct! In this discussion, the correct variance of the HEWMA statistic is given, and the run length characteristics of the HEWMA control chart are studied and explored. It is noticed that not only the superiority of the HEWMA control chart remains over the existing (considered before) charts but also the new results based on the corrected control limits are more profound and reflective. Copyright © 2016 John Wiley & Sons, Ltd.     

A Synthetic Control Chart for Monitoring the Ratio of Two Normal Variables

Very recently, monitoring the ratio of two normal random variables by means of control charts has been investigated in statistical process control literature. The industrial implementation of these control charts involves monitoring of processes where the correct proportion of two ingredients or elements within a product should be maintained under statistical control, monitoring of quality characteristics measuring the performance of a product as the ratio before and after some specific operation, for example, a chemical reaction following the introduction of an additive in a product, and monitoring of a chemical or physical property of a product, which is itself defined and computed as a ratio. This paper presents a Phase II synthetic control chart with each subgroup consisting of n > 1 sample units. Several tables are generated and commented to show the statistical performance of the investigated chart for known and random shift sizes affecting the in‐control ratio. A performance comparison with another control chart already proposed in literature shows the advantages associated to the implementation of the synthetic control chart. An illustrative example from the food industry is given for illustration. Copyright © 2015 John Wiley & Sons, Ltd.     

The Performance of Variable Sample Size Chart with Measurement Errors

The variable sample size (VSS) chart has been investigated by several researchers under the assumption of no measurement error. However, in practice, measurement errors may exist in quality control applications. In this paper, the overall performance of the VSS chart is investigated when measurement errors exist using a linearly covariate error model, and a methodology is proposed for choosing optimal parameters by considering measurement errors. It is shown that the overall performance of the VSS chart is significantly affected by the presence of measurement errors. The effect of taking multiple measurements for each item in a subgroup on the performance of VSS chart is also investigated in this paper. An example is provided to illustrate the application of the VSS chart with measurement errors. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of Autocorrelation on Performance of the MCUSUM Control Chart

Control charts are designed to detect assignable causes of variation that may occur in production processes. When traditional control charts are used there is the implicit assumption that observations are independently and identically distributed over time. It is also assumed that the probability distribution representing the observations has a known functional form and is constant over time. However, in practice, observations generated by continuous as well as discrete production processes are often serially correlated. Autocorrelation not only violates the independence assumption of traditional control charts but also can affect the performance of control charts adversely. This point has received considerable attention in the past few decades. In this paper, we investigate the performance of the multivariate cumulative sum (MCUSUM) control chart in the presence of autocorrelation. Using an average run length (ARL) criterion, it is shown that autocorrelation can deteriorate the performance of MCUSUM control charts. A solution based on a time series model is presented that improves ARL properties of MCUSUM control charts. Copyright © 2005 John Wiley & Sons, Ltd.     

A Bivariate Semiparametric Control Chart Based on Order Statistics

In this article, a new bivariate semiparametric Shewhart‐type control chart is presented. The proposed chart is based on the bivariate statistic (X_(r), Y_(s)), where X_(r) and Y_(s) are the order statistics of the respective X and Y test samples. It is created by considering a straightforward generalization of the well‐known univariate median control chart and can be easily applied because it calls for the computation of two single order statistics. The false alarm rate and the in‐control run length are not affected by the marginal distributions of the monitored characteristics. However, its performance is typically affected by the dependence structure of the bivariate observations under study; therefore, the suggested chart may be characterized as a semiparametric control chart. An explicit expression for the operating characteristic function of the new control chart is obtained. Moreover, exact formulae are provided for the calculation of the alarm rate given that the characteristics under study follow specific bivariate distributions. In addition, tables and graphs are given for the implementation of the chart for some typical average run length values and false alarm rates. The performance of the suggested chart is compared with that of the traditional χ² chart as well as to the nonparametric SN² and SR² charts that are based on the multivariate form of the sign test and the Wilcoxon signed‐rank test, respectively. Finally, in order to demonstrate the applicability of our chart, a case study regarding a real‐world problem related to winery production is presented. Copyright © 2016 John Wiley & Sons, Ltd.     

A Statistical Control Chart for Stationary Process Data

In the statistical process control environment, a primary method to deal with autocorrelated data is the use of a residual chart. Although this methodology has the advantage that it can be applied to any autocorrelated data, it needs some modeling effort in practice. In addition, the detection capability of the residual chart is not always great. This article proposes a statistical control chart for stationary process data. It is simple to implement, and no modeling effort is required. Comparisons are made among the proposed chart, the residual chart, and other charts. When the process autocorrelation is not very strong and the mean changes are not large, the new chart performs better than the residual chart and the other charts.     

A Statistical Control Chart for Monitoring High‐dimensional Poisson Data Streams

Multivariate count data are popular in the quality monitoring of manufacturing and service industries. However, seldom effort has been paid on high‐dimensional Poisson data and two‐sided mean shift situation. In this article, a hybrid control chart for independent multivariate Poisson data is proposed. The new chart was constructed based on the test of goodness of fit, and the monitoring procedure of the chart was shown. The performance of the proposed chart was evaluated using Monte Carlo simulation. Numerical experiments show that the new chart is very powerful and sensitive at detecting both positive and negative mean shifts. Meanwhile, it is more robust than other existing multiple Poisson charts for both independent and correlated variables. Besides, a new standardization method for Poisson data was developed in this article. A real example was also shown to illustrate the detailed steps of the new chart. Copyright © 2016 John Wiley & Sons, Ltd.     

A progressive approach for the detection of the coefficient of variation

A progressive average chart usually triggers initial out-of-control (OC) signals more simply and quickly than other memory-type charts . In this paper, two progressive average control procedures are proposed for monitoring the coefficient of variation (CV) of a normally distributed process variable, namely, the progressive CV (PCV) and progressive resetting CV (PRCV) control charts , respectively. The implementation of the proposed charts is presented, and the necessary design parameters are provided. Through extensive numerical simulations, it is shown that the proposed PCV and PRCV charts outperform several existing control charts to detect the initial OC signals, especially for the small and moderate CV shifts, under each combination of the shift size, the sample size, and the in-control target value of the CV. In addition, the application of the proposed control charts is illustrated by a detection example for a spinning process.     

基于游程检验的多元非参控制图

本文提出了一个新的基于游程检验的多元非参控制图。首先,运用Kruskal算法的思想,将观测值排列成最短汉密尔顿路径;其次,基于最短汉密尔顿路径中的游程数设计带有滑动窗口的EWMA结构控制图,记为HAMEWMA控制图。通过蒙特卡洛随机方法对HAMEWMA控制图在不同条件(维度的高低,均值漂移的程度,受控数据量大小以及观测数据遵循的分布)下的控制效果进行研究,并与其他多元非参控制图(DFEWMA、SREWMA、SSEWMA、RTC)进行比较。结果表明：当均值漂移较大时,HAMEWMA控制图有更优秀的监控性能;当数据分布为非正态时,HAMEWMA控制图同样表现良好甚至优于数据分布为正态时;HAMEWMA控制图更适用于高维度的监控环境。     

A New Bivariate Control Chart to Monitor the Multivariate Process Mean and Variance Simultaneously

In this article a new control chart which enables a simultaneous monitoring of both the process mean and process variance of a multivariate data will be proposed. A thorough discussion in identifying whether the process mean or variability shifts is also given. Simulation studies will be performed to study the performance of the new chart by means of its average run length (ARL) profiles. Numerous examples are also given to show how the new chart is put to work in real situations.     

Design Strategies for the Multivariate Exponentially Weighted Moving Average Control Chart

The multivariate exponentially weighted moving average (MEWMA) control chart has received significant attention from researchers and practitioners because of its desirable properties. There are several different approaches to the design of MEWMA control charts: statistical design; economic–statistical design; and robust design. In this paper a review and comparison of these design strategies is provided.Copyright © 2004 John Wiley & Sons, Ltd.     

Design of a Phase II Control Chart for Monitoring the Ratio of two Normal Variables

In many industrial scenarios, on‐line monitoring of quality characteristics computed as the ratio of two normal random variables can be required. Potential industrial applications can include monitoring of processes where the correct proportion of a property between two ingredients or elements within a product should be maintained under statistical control; implementation of quality control procedures where the performance of a product is measured as a ratio before and after some specific operation, for example a chemical reaction following the introduction of an additive in a product and monitoring of a chemical or physical property of a product, which is itself defined and computed as a ratio. This paper considers Phase II Shewhart control charts with each subgroup consisting of n > 1 sample units. From one subgroup to another, the size of each sample unit, upon which a single measurement is made, can be changed. An approximation based on the normal distribution is used to efficiently handle the ratio distribution. Several tables are generated and commented to show the statistical performance of the investigated chart for known and random shift sizes affecting the in‐control ratio. An illustrative example from the food industry is given for illustration. Copyright © 2014 John Wiley & Sons, Ltd.     

EWMA Control Chart Performance with Estimated Parameters under Non‐normality

Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non‐normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non‐normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non‐normality using skewed and heavy‐tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non‐normal observations. Copyright © 2015 John Wiley & Sons, Ltd.     

Sum of Squares Control Charts for Monitoring of Multivariate Multiple Linear Regression Profiles in Phase II

In this paper, we propose four control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression profiles in Phase II. The proposed control charts include sum of squares exponential weighted moving average (SS‐EWMA) and sum of squares cumulative sum (SS‐CUSUM) for monitoring regression parameters and corresponding covariance matrix and SS‐EWMARe and SS‐CUSUMRe control charts for monitoring mean vector and covariance matrix of residual. Proposed methods are able to identify the out‐of‐control parameter responsible for shift. The performance of the proposed control charts is compared with existing method through Monte‐Carlo simulations. Moreover, the diagnostic performance of the proposed control charts is evaluated through simulation studies. The results show better performance of the proposed control charts rather than competing control chart. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry. Copyright © 2016 John Wiley & Sons, Ltd.     

A EWMA Control Chart for Exponential Distributed Quality Based on Moving Average Statistics

We propose an exponentially weighted moving average (EWMA) control chart for monitoring exponential distributed quality characteristics. The proposed control chart first transforms the sample data to approximate normal variables, then calculates the moving average (MA) statistic for each subgroup, and finally constructs the EWMA statistic based on the current and the previous MA statistics. The upper and the lower control limits are derived using the mean and the variance of EWMA statistics. The in‐control and the out‐of‐control average run lengths are derived and tabularized according to process shift parameters and smoothing constants. It is shown that the proposed control chart outperforms the MA control chart for all shift parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

A side-sensitive synthetic coefficient of variation chart

Control charts for monitoring the coefficient of variation (γ) are useful for processes with an inconsistent mean (μ) and a standard deviation (σ) which changes with μ, by monitoring the consistency in the ratio σ over μ. The synthetic-γ chart is one of the charts proposed to monitor γ, and its attractiveness lie in waiting until a second point to fall outside the control limits before a decision is made. However, existing synthetic-γ charts do not differentiate between the points falling outside the upper control limit (UCL) and lower control limit (LCL). Hence, this paper proposes a side-sensitive synthetic-γ chart, where successive nonconforming samples must either fall above the UCL or below the LCL. Formulae to compute the average run length (ARL), the standard deviation of the run length (SDRL) and expected average run length (EARL) are derived using the Markov chain approach, and the algorithms to obtain the optimal charting parameters are proposed. Subsequently, the optimal charting parameters, ARL, SDRL and EARL values for various numerical examples are shown. Comparisons show that the side-sensitive synthetic-γ chart consistently outperforms the existing synthetic-γ chart, especially for small shifts. The proposed chart also consistently outperforms the Shewhart-γ chart, while showing comparable or better performance than the Exponentially Weighted Moving Average (EWMA) chart for most shift sizes, except for very small shifts. Finally, this paper shows the implementation of the proposed chart on an industrial example.