Performance Of Control Charts Research Articles

Auxiliary Information Based Mixed EWMA–CUSUM Mean Control Chart with Measurement Error

Measurement error is a usually met distortion factor in real-world applications that influences the outcome of a process. The performance of the control charts can be affected in the presence of measurement error which also leads to erroneous conclusions regarding the average run length. In this paper, we proposed regression estimator-based mixed exponentially weighted moving average-cumulative sum (MxEMCUS) control chart to monitor the process mean and investigate the effect of measurement error on shift detection ability of the proposed control chart. The performance of MxEMCUS control chart is evaluated in the cases of mean shift with and without measurement error. The linear covariate model is used to evaluate the control chart in the presence of measurement error. The case of multiple measurements and linear increasing variance is also investigated in the presence of measurement error. The average run length and standard deviation of run length are used as the performance measuring tool. Based on simulation results, it is concluded that in the presence of measurement error, proposed chart has better performance as compared to other existing charts. An example with real data set is given to demonstrate the implementation of MxEMCUS control chart.

A Comparative Analysis of Bootstrap Multivariate Exponentially-Weighted Moving Average (BMEWMA) Control Limits

In the manufacturing and service industries, multivariate statistical quality control charts are mostly used to determine whether a process is performing as intended or if there are some special causes resulting in the variation of an overall statistics. Normally, control charts are obtained under the assumption that the variable under study follows some form of parametric distribution. When this assumption is violated, the performance of such control chart often gives false alarm signals. To address this problem, the Multivariate Exponential Weighted Moving Average (MEWMA) control limits have been proposed in existing literature. This article focuses on reviewing this existing method with a view to developing a novel approach based on the use of bootstrap. Results from a performance study shows that the proposed method enables the setting of control limits that can enhance the easy detection of out of control signals.

A robust alternate to the HEWMA control chart under non-normality

ABSTRACT In practice, a hybrid exponentially weighted moving average (HEWMA) control chart for monitoring the process mean based on the normality assumption. The performance of control chart is seriously affected if quality characteristics depart from normality or have the presence of outliers. For such situations, a new robust-HEWMA control chart is proposed for the scenario in which quality characteristics being monitored follow symmetric not necessarily normal as well as skewed phenomena. The generalized least-squares (GLS) algorithm based on order statistics is integrated to determine the control limits for non-normal process. Consequently, the process mean is unbiased and has the minimum variance in spite of non-normality. Moreover, for the long-tailed symmetric and skewed processes, the GLS estimators through their systematic coefficients structures provide robust estimates. To utilize this advantage, we have investigated the impact of data contamination and the estimators used in Phase I on the performance of proposed robust HEWMA control chart in the Phase II. Finally, we provide two real-life examples along with the simulation studies to show the implantation of our proposed chart.

Exponentially weighted moving average control chart using auxiliary variable with measurement error

Control chart is one of the important industrial tools used for monitoring the stability of manufacturing processes. Measurement error plays an important role in quality control process and adversely affects the shift detection ability of control charts. In this article, we examined the effect of measurement error on auxiliary variable based exponentially weighted moving average (EWMA-Z) control chart by using three different techniques (i) covariate method (ii) multiple measurements (iii) linearly increasing variance. The performance of EWMA-Z control chart is measured through ARL and SDRL by using Monte-Carlo simulation method. An example is provided with real data set for the implementation of EWMA-Z control chart in the presence of measurement error.

Guaranteed in-control control chart performance with cautious parameter learning

Parameter estimation has a large impact on control chart performance. Recently, widened control limits have been suggested to guarantee an acceptable in-control behavior. However, the consequence is a reduced ability to detect a real change in the process. In order to overcome this undesired effect, we explore an alternative design based on a delayed updating of parameter estimates. We consider an application to the Shewhart X, EWMA, and CUSUM control charts for the process mean. This approach is simple to implement, reduces the variation of the in-control average run lengths, and significantly improves the out-of-control performance.

Estimation Mean by the Bayesian Approach on the Exponentially Weighted Moving Average Control Chart

A control chart is one of the primary techniques of statistical quality control. Exponentially Weighted Moving Average (EWMA) control chart is one of the control charts used to detect a small shift in the mean process. In the quality control process, the control chart is often constructed by ignoring parameter uncertainty. This can affect the long-term performance of the control chart in a controlled or out-of-control state, so parameter estimation is necessary. The parameter estimation method used in this paper is the Bayesian approach. The Bayesian approach is used to develop an EWMA control chart in monitoring a process. The performance of the EWMA control chart with the Bayesian approach has been evaluated using Average Run Length (ARL). Based on the comparison of the ARL value from the EWMA control chart with the Bayesian approach and the Classical EWMA control chart, it shows that the EWMA control chart with the Bayesian approach is more sensitive in detecting the shift in the mean process.

Applying a change-point control chart based on likelihood ratio to supply chain network monitoring

In this paper, a supply chain network system is viewed as a serial-parallel multistage process; and the application of a change point control chart based on likelihood ratio is explored to monitor this system. Firstly, state-space modeling is used to characterize complexity of the supply chain network system. Then, a change point control chart based on likelihood ratio is built to trigger potential tardy orders in the system. A case study is illustrated to indicate that the change point control charts can effectively signal process mean shift, and accurately estimate the change point and the out-of-control stage in term of power of detection and the accuracy of estimation of change point. We also investigate the effect of misspecified parameters of state space equations on the performance of the change point control chart. The results show that the performance of the change point control chart is relatively stable.

SAX Breakpoints for Random Forest Based Real-Time Contrast Control Chart

In the manufacturing process, process monitoring is very important. Real-time contrast (RTC) control chart outperforms existing monitoring methods. However, the performance of RTC control chart depends on the classifier. The existing RTC charts use random forest (RF), support vector machine (SVM), or kernel linear discriminant analysis (KLDA) as a classifier. RF classifier can find cause of faults but the performance is lower than others. Therefore, we suggest the data representation method to improve the RF based RTC control chart. Symbolic aggregate approximation (SAX) is famous method to improve the performance of classification and clustering. We convert the input data by using SAX. We change the parameters of SAX such as alphabet size and breakpoints to improve the performance. Experiment shows that represented data is efficient method to improve the performance of RTC control chart.

Proposal of Methodology for Practical Application of Nonparametric Control Charts

Abstract This paper deals with the methodology for practical application of nonparametric control charts. This topic is very important for two reasons: firstly nonparametric control charts are very effective instruments for the realization of the statistical process monitoring phase I due to their robustness against various deviations from the data assumptions that must be met when applying model-based control charts. Secondly nonparametric control charts have very weak SW support and also they are not taught in the frame of training courses not even of the university study programmes. For that reason the practitioners do not know them and do not use them. The paper offers the proposal how to practically apply these control charts which is based on the complex simulation study of various nonparametric control charts performance when various data assumptions have not been met. The study has covered these nonparametric control charts: Shewhart sign control chart, nonparametric EWMA and nonparametric CUSUM control charts, nonparametric progressive mean control chart, control chart based on Mood statistics and robust median absolute deviation control chart. All charts have been studied in condition of not normally distributed data, autocorrelated data and data with nonconstant distribution parameters. The simulations were realized for statistically stable (IC – in control) and also statistically unstable (OC – out of control) processes. For the evaluation of the control charts performance median run length, 0.05-quantile, and 0.95-quantile were used.

Rethinking control chart design and evaluation

We discuss some practical issues involving the control of the number of false alarms in process monitoring. This topic is of growing importance as the number of variables being monitored and the frequency of measurement increase. An alternative formulation for evaluating and comparing the performance of control charts is given based on defining in-control, indifference and out-of-control regions of the parameter space. Methods are designed so that only changes of practical importance are to be detected quickly. This generalization of the existing framework makes control charting much more useful in practice, especially when many variables are being monitored. It also justifies to a greater extent the use of cumulative sum (CUSUM) methods.

Improving wind turbine power curve monitoring with standardisation

Against the background of increasing cost pressure, condition monitoring is becoming increasingly relevant to the wind energy industry. The present study examines the role of wind turbulence and the non-constant variance of residuals in power curve monitoring. Power curve monitoring methods are classified and compared by means of Monte Carlo simulations. It is found that adjusting for the non-constant variance of residuals using standardisation may considerably improve the performance of control charts, no matter what method is used to generate them. Additionally, turbulence is found to be an important factor, and including it may further increase the performance of control charts.

On the performance of CUSUM control charts for monitoring the coefficient of variation with measurement errors

In this paper, we investigate the effect of the measurement error on the performance of the cumulative sum (CUSUM) control charts monitoring the coefficient of variation. The measurement errors are supposed to follow a linear covariate error model. The obtained results show that the precision error ratio and the accuracy error have negative impact on the chart performance. Moreover, in order to overcome the difficulty in predetermining a specific value for the process shift size, we suggest to optimize the parameters of the charts according to the random shift size in a given interval. The robustness of the proposed method is studied. An example is given to illustrate the use of the CUSUM charts on a real quality control problem from sintering process.

Nonparametric control of the conditional performance in statistical process monitoring

Because the in-control distribution and parameters are generally unknown, control limits have to be estimated using a Phase I reference sample. Because different practitioners obtain different samples, their control limit estimates will vary and, consequently, also their control chart performance. We propose the use of nonparametric tolerance intervals in statistical process monitoring to guarantee a minimum control chart performance with a prespecified probability. We evaluate the performance of the proposed limits for various distributions and sample sizes. Note that this nonparametric set-up includes control charts for location and dispersion. Moreover, we compare the performance with other existing methods involving data transformations and a bootstrap procedure. It turns out that the use of nonparametric tolerance intervals performs very well in statistical process monitoring, especially when moderately large sample sizes are available in Phase I.

On the performance of VSI Shewhart control chart for monitoring the coefficient of variation in the presence of measurement errors

In this paper, we propose a variable sampling interval Shewhart control chart to monitor the coefficient of variation (CV) squared, denoted by VSI SH-γ2. The new model overcomes the ARL-biased (average run length) property of the control chart monitoring the CV in a previous study by designing two one-sided charts rather than one two-sided chart. Moreover, the effect of measurement error on the performance of the VSI SH-γ2 control chart is investigated. The incorrect formula for the distribution of the CV in the presence of measurement error in a former study is fixed. Numerical simulations show that the precision errors and accuracy errors do have negative influences on the VSI SH-γ2 chart. An appropriate strategy based on the obtained results is suggested to reduce these negative effects.

Conditional analysis of Phase II exponential chart for monitoring times to an event

ABSTRACTIt is now well known that the error in estimating parameter(s) adversely affects the performance of control charts. The charts with estimated control limits are usually assessed by some of characteristics of unconditional run length (URL) distribution. However, it is now under criticism because the unconditional analysis based on URL does not give the full impression of the chart’s performance conditioning on a given Phase I sample. In recent years, the focus has been shifted from unconditional performance analysis to conditional analysis which is carried out in terms of conditional run length (CRL) and its associated characteristics and provides deep understanding of conditional performance of the chart given a Phase I sample. In this article, Phase II exponential charts are considered to monitor times to an event and their performance are examined conditional on given Phase I sample by considering several indicators based on conditional average run length (CARL) distribution. In this respect, the exact expressions of the distribution functions of for the estimated exponential control charts are derived and several statistical constants are computed which could be helpful in evaluating and designing the chart.

Conditional design of the CUSUM median chart for the process position when process parameters are unknown

ABSTRACTIn practice, different practitioners will use different Phase I samples to estimate the process parameters, which will lead to different Phase II control chart's performance. Researches refer to this variability as between-practitioners-variability of control charts. Since between-practitioners-variability is important in the design of the CUSUM median chart with estimated process parameters, the standard deviation of average run length (SDARL) will be used to study its properties. It is shown that the CUSUM median chart requires a larger amount of Phase I samples to sufficiently reduce the variation in the in-control ARL of the CUSUM median chart. Considering the limitation of the amount of the Phase I samples, a bootstrap approach is also used here to adjust the control limits of the CUSUM median chart. Comparisons are made for the CUSUM and Shewhart median charts with estimated parameters when using the adjusted- and unadjusted control limits and some conclusions are made.

Control Charts for Monitoring Process Capability Index Using Median Absolute Deviation for Some Popular Distributions

A control chart monitoring the process capability index (PCI) using median absolute deviation (MAD) is proposed to analyze the industrial process performance. Extensive simulation studies were carried out to evaluate the performance of MAD-based PCI control charts under the low, moderate, and high asymmetric conditions when the process characteristic follows Weibull, log-normal, and gamma distributions. The performance of the proposed control charts was evaluated based on the average run lengths. The practical implementation of the proposed charts was also illustrated with industrial data.

The SPRT control chart for process dispersion

AbstractThis paper investigates the statistical performance of a sequential probability ratio test control chart for monitoring the dispersion of a normally distributed process. The expressions for statistical performance measures of the chart are derived using a Markov chain approach. It is shown through numerical comparisons that the overall statistical performance of this chart is superior to that of the existing competitor charts for dispersion. An example illustrating an application of the chart in practice is provided.

Performance of the hotelling T2 control chart for compositional data in the presence of measurement errors

ABSTRACTIn statistical process monitoring, the presence of measurement errors is known to impact the performance of control charts. This paper makes an attempt to investigate the performance of the Hotelling CoDa (Compositional Data) control chart in the presence of measurement errors. A linearly covariate measurement error model for CoDa is introduced to study the influence of the measurement device parameters ( and b) and the number of independent observations m on the performance of the Hotelling CoDa control chart in the in- and out-of-control cases. A realistic illustrative example based on the production of muesli is used to illustrate the estimation of the measurement device parameters and the in-control process parameters, as well as to demonstrate the ability of this control chart to efficiently detect changes in the muesli composition.

A new auxiliary information based cumulative sum median control chart for location monitoring

Control charts are commonly used tools in statistical process control for the detection of shifts in process parameters. Shewhart-type charts are efficient for large shift values, whereas cumulative sum (CUSUM) charts are effective in detecting medium and small shifts. Control chart use commonly assumes that data are free of outliers and parameters are known or correctly estimated based on an in-control process. In practice, these assumptions are not often true because some processes occasionally have outliers. Monitoring the location parameter is usually based on mean charts, which are seriously affected by violations of these assumptions. In this paper we propose several CUSUM median control charts based on auxiliary variables, and offer comparisons with their corresponding mean control charts. To monitor the location parameter, we examined the performance of mean and median control charts in the presence and absence of outliers. Both symmetric and non-symmetric processes were studied to examine the properties of the proposed control charts to monitor the location parameter using CUSUM control charts. We used different run length measures to study in-control and out-of-control performances of CUSUM charts. Results revealed that our proposed control charts perform much better than the traditional charts in the presence of outliers. A real application of our study was provided using data on concrete compressive strength as it relates to the quality of cement manufacturing.