Geometric Charts with Estimated Control Limits

The geometric control chart has been shown to be more effective than p and np‐charts for monitoring the proportion of nonconforming items, especially for high‐quality Bernoulli processes. When implementing a geometric control chart, the in‐control proportion nonconforming is typically unknown and must be estimated. In this article, we used the standard deviation of the average run length (SDARL) and the standard deviation of the average number of inspected items to signal, SDARL*, to show that much larger phase I sample sizes are needed in practice than implied by previous research. The SDARL (or SDARL*) was used because practitioners would estimate the control limits based on different phase I samples. Thus, there would be practitioner‐to‐practitioner variability in the in‐control ARL (or ARL*). In addition, we recommend a Bayes estimator for the in‐control proportion nonconforming to take advantage of practitioners' knowledge and to avoid estimation problems when no nonconforming items are observed in the phase I sample. If the in‐control proportion nonconforming is low, then the required phase I sample size may be prohibitively large. In this case, we recommend an approach to identify a more informative continuous variable to monitor. Copyright © 2012 John Wiley & Sons, Ltd.     

Exponential CUSUM Charts with Estimated Control Limits

Exponential CUSUM charts are used in monitoring the occurrence rate of rare events because the interarrival times of events for homogeneous Poisson processes are independent and identically distributed exponential random variables. In these applications, it is assumed that the exponential parameter, i.e. the mean, is known or has been accurately estimated. However, in practice, the in‐control mean is typically unknown and must be estimated to construct the limits for the exponential CUSUM chart. In this article, we investigate the effect of parameter estimation on the run length properties of one‐sided lower exponential CUSUM charts. In addition, analyzing conditional performance measures shows that the effect of estimation error can be significant, affecting both the in‐control average run length and the quick detection of process deterioration. We also provide recommendations regarding phase I sample sizes. This sample size must be quite large for the in‐control chart performance to be close to that for the known parameter case. Finally, we provide an industrial example to highlight the practical implications of estimation error, and to offer advice to practitioners when constructing/analyzing a phase I sample. Copyright © 2013 John Wiley & Sons, Ltd.     

Linking EWMA p Charts and the Risk Adjustment Control Charts

This paper develops an adaptive exponentially weighted moving average (EWMA) chart that can be used as either a p chart for monitoring significant departures from in‐control non‐homogenous probabilities of failure or success or a risk‐adjusted control chart for success or failure of an event. An example of a risk adjustment process is monitoring the performance of a particular surgery over time where we need to adjust for the temporal changes in patient case mix. If the magnitude of this shift is known in advance, as would be the case in some hypothesis testing applications, then the paper offers a way of selecting the appropriate exponential weights to be efficient at detecting such a variable shift. The adaptive EWMA p chart is tested using extensive simulations. Processes for its efficient design are offered. The example application offers practitioners a means of evaluating a trial in real time rather than the traditional approach of evaluating the trial at the end of the study period. This is helpful in deciding how long the trial should run as well as potentially adapting the design over time as more is understood about the trial uncertainties. This may be particularly useful in evaluating expensive trials. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust CUSUM charts for monitoring the process mean and variance

This paper considers the problem of obtaining robust control charts for detecting changes in the mean µ and standard deviation σ of process observations that have a continuous distribution. The standard control charts for monitoring µ and σ are based on the assumption that the process distribution is normal. However, the process distribution may not be normal in many situations, and using these control charts can lead to very misleading conclusions. Although some control charts for µ can be tuned to be robust to non‐normal distributions, the most critical problem with non‐robustness is with the control chart for σ. This paper investigates the performance of two CUSUM chart combinations that can be made to be robust to non‐normality. One combination consists of the standard CUSUM chart for µ and a CUSUM chart of absolute deviations from target for σ, where these CUSUM charts are tuned to detect relatively small parameter shifts. The other combination is based on using winsorized observations in the standard CUSUM chart for µ and a CUSUM chart of squared deviations from target for σ. Guidance is given for selecting the design parameters and control limits of these robust CUSUM chart combinations. When the observations are actually normal, using one of these robust CUSUM chart combination will result in some reduction in the ability to detect moderate and large changes in µ and σ, compared with using a CUSUM chart combination that is designed specifically for the normal distribution. Copyright © 2009 John Wiley & Sons, Ltd.     

New Corrections for Old Control Charts

When using standard control charts, typically several parameters need to be estimated. For the usual sample sizes, this is known to affect the performance of the chart. Here we present simple corrections to solve this problem. As a basis, we use existing factors which are widely used for the traditional charts. The advantage of the new proposals is that a clear link is made to the actual performance characteristics of the chart.     

A Comparison of Normal Approximation Rules for Attribute Control Charts

Control charts, known for more than 80 years, have been important tools for business and industrial manufactures. Among many different types of control charts, the attribute control chart (np‐chart or p‐chart) is one of the most popular methods to monitor the number of observed defects in products, such as semiconductor chips, automobile engines, and loan applications. The attribute control chart requires that the sample size n is sufficiently large and the defect rate p is not too small so that the normal approximation to the binomial works well. Some rules for the required values for n and p are available in the textbooks of quality control and mathematical statistics. However, these rules are considerably different, and hence, it is less clear which rule is most appropriate in practical applications. In this paper, we perform a comparison of five frequently used rules for n and p required for the normal approximation to the binomial. With this result, we also refine the existing rules to develop a new rule that has a reliable performance. Datasets are analyzed for illustration. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive ―X Control Charts with Sampling at Fixed Times

The idea of a variable sampling interval with sampling at fixed times (VSIFT) has been presented by Reynolds. This paper extends this idea to the other two adaptive ―X charts: the variable sampling rate with sampling at fixed times (VSRFT) ―X chart and the variable parameters with sampling at fixed times (VPFT) ―X chart. The VSIFT, VSRFT and VPFT ―X charts are inclusively called the adaptive with sampling at fixed times (AFT) ―X charts in this paper. The control scheme and the design issue are described and discussed for each of the AFT ―X charts. A comparative study shows that the AFT ―X charts have almost the same detection ability as the traditional adaptive ―X charts. However, from the practical viewpoint, the AFT ―X charts are considered to be more convenient to administer than the traditional adaptive ―X charts. Overall, this paper advances the application of ‘sampling at fixed times’ to the adaptive ―X control charts. Copyright © 2004 John Wiley & Sons, Ltd.     

On the Performance of Control Charts for Simultaneous Monitoring of Location and Dispersion Parameters

A single control chart is very famous to control assignable causes that shift the process because of variations in parameters (e.g., location and dispersion). Simultaneous monitoring of processes is another popular approach used for the bilateral processes. In this study, we have proposed the mixed control charts for simultaneously monitoring of process location and dispersion parameters. We have used the idea of mixed exponential weighted moving average and cumulative sum charts and designed the charting structures for simultaneous monitoring. The proposals are compared with several existing counterparts. The comparisons reveal numerous advantages of the proposed charts over the other existing scheme. The practical application of the proposed charts is also highlighted using an illustrative example based on a real dataset. Copyright © 2016 John Wiley & Sons, Ltd.     

Monitoring Two Dependent Process Steps Using Special Variable Sample Sizes and Sampling Intervals Cause‐Selecting Control Charts

Cause‐selecting control charts are effective statistical process control tools for monitoring multistage processes. In this article, an adaptive statistical process control scheme to monitor a process with two dependent steps is proposed. Two different policies based on a combination of two different sample sizes and sampling intervals are utilized. Adjusted average time to signal measure, calculated through Markov chain approach, is applied to evaluate performance of the proposed control scheme. Numerical results indicate that the proposed scheme has improved performance over the fixed sample sizes at fixed sampling intervals scheme. Finally, the optimal parameters of the proposed scheme with two different policies are recommended, and comparisons between the minimum adjusted average time to signal of the proposed charts and variable sample sizes and sampling intervals cause‐selecting control charts with three different sample sizes and sampling intervals are performed. It is shown that performance of the proposed scheme with four variable parameters is similar and even somewhat better than that of the scheme with six variable parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Type II Errors of Demerit Control Charts

Complex products may present more than one type of defect. A demerit control chart is a useful tool for monitoring different types of defects in a single chart while taking into account different levels of severity. Traditionally, control limits have been established based on standard deviations from the centerline assuming normality. These limits were improved upon by approaches to finding the exact distribution of the demerit statistic and establishing probability-based limits. With respect to Type I error, probability-based limits have been shown to outperform traditional limits. Now, again with exact distributions, we consider Type II errors as well when establishing control limits for different shifts, means and weights.     

An Overview of Control Charts for High‐quality Processes

Major difficulties in the study of high‐quality processes with traditional process monitoring techniques are a high false alarm rate and a negative lower control limit. The purpose of time‐between‐events control charts is to overcome existing problems in the high‐quality process monitoring setup. Time‐between‐events charts detect an out‐of‐control situation without great loss of sensitivity as compared with existing charts. High‐quality control charts gained much attention over the last decade because of the technological revolution. This article is dedicated to providing an overview of recent research and presenting it in a unifying framework. To summarize results and draw a precise conclusion from the statistical point of view, cross‐tabulations are also given in this article. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparisons of Some Exponentially Weighted Moving Average Control Charts for Monitoring the Process Mean and Variance

An exponentially weighted moving average (EWMA) control chart for monitoring the process mean μ may be slow to detect large shifts in μ when the EWMA tuning parameter λ is small. An additional problem, sometimes called the inertia problem, is that the EWMA statistic may be in a disadvantageous position on the wrong side of the target when a shift in μ occurs, which may significantly delay detection of a shift in μ. Options for improving the performance of the EWMA chart include using the EWMA chart in combination with a Shewhart chart or in combination with an EWMA chart based on squared deviations from target. The EWMA chart based on squared deviations from target is designed to detect increases in the process standard deviation σ, but it is also very effective for detecting large shifts inμ. Capizzi and Masarotto recently proposed the option of an adaptive EWMA control chart in which λ is a function of the data. With the adaptive feature, the EWMA chart behaves like a standard EWMA chart when the current observation is close to the previous EWMA statistic, and like a Shewhart chart otherwise. Here we extend the use of the adaptive feature to EWMA charts based on squared deviations from target, and also consider an alternate way of defining the adaptive feature. We discuss performance measures that we believe are appropriate for assessing the effects of inertia, and compare the performance of various charts and combinations of charts. Standard practice is to simultaneously monitor both μ and σ, so we consider control chart performance when the objective is to detect small or large changes in μ or increases in σ. We find that combinations of EWMA control charts that include a chart based on squared deviations from target give good overall performance whether or not these charts have the adaptive feature.     

Comparison of Multivariate Control Charts for Process Dispersion

In this article we compare four multivariate control charts for process dispersion in the retrospective analysis of a historical data set. Among the schemes compared, a new control chart based on a robust estimation of the variance-covariance matrix proved to be very effective in detecting changes in the process dispersion matrix.     

Control Charts monitoring Product's Loss to Society

Taguchi introduced a new philosophy in quality control that accounts for the economic loss associated to process variation measured by deviations from the target value of a product quality characteristic. The Taguchi loss function has been considered in the design of control charts only for the computation of costs associated with nonconformities. This paper considers sample statistics based on the Taguchi loss function as a means to implement Shewhart control charts monitoring both the deviation from the target and dispersion of normally distributed quality characteristics. The aim of this proposed control chart is to perform on‐line quality control of a process by monitoring its quality loss cost performance over time. To compute the quality loss performance, we consider a nominal‐the‐best quality characteristic. The statistical performance of the proposed control charts has been evaluated and compared with that of widely used control charts. Implementing target costing philosophy by means of one of the proposed charts is also discussed. An example illustrates the Taguchi control chart in a practical implementation. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance Measures for ―X Charts with Asymmetric Control Limits

Theoretical and empirical justification is given for using asymmetric control limits for certain types of production processes. The following are also discussed: the sensitivity of the performance measures to the process and control parameters, the advantages and disadvantages of using asymmetric control limits, and the construction of tradeoff curves to characterize performance. The justification is given in terms of a collection of quantitative performance measures for ―X charts with asymmetric control limits. The performance measures quantify the false‐alarm frequency, the sensitivity to out‐of‐control conditions, and the resources required for sampling. Copyright © 2005 John Wiley & Sons, Ltd.     

Single Variables Control Charts: an Overview

Control charts are widely used in industries to monitor a process for quality improvement. When dealing with variables data, we usually employ two control charts to monitor the process location and spread. We give an overview of the control charts proposed in the last decade or so in an effort to use only one chart to simultaneously monitor both process location and spread. Two approaches have been advocated for using one control chart for process monitoring. One approach plots two quality characteristics in the same chart while the other uses one plotting variable to represent the process location and spread. Copyright © 2006 John Wiley & Sons, Ltd.     

CUSUM charts for detecting special causes in integrated process control

This paper investigates control charts for detecting special causes in an ARIMA(0, 1, 1) process that is being adjusted automatically after each observation using a minimum mean‐squared error adjustment policy. It is assumed that the adjustment mechanism is designed to compensate for the inherent variation due to the ARIMA(0, 1, 1) process, but it is desirable to detect and eliminate special causes that occur occasionally and produce additional process variation. It is assumed that these special causes can change the process mean, the process variance, the moving average parameter, or the effect of the adjustment mechanism. Expressions are derived for the process deviation from target for all of these process parameter changes. Numerical results are presented for sustained shifts, transient shifts, and sustained drifts in the process parameters. The objective is to find control charts or combinations of control charts that will be effective for detecting special causes that result in any of these types of parameter changes in any or all of the parameters. CUSUM charts designed for detecting specific parameter changes are considered. It is shown that combinations of CUSUM charts that include a CUSUM chart designed to detect mean shifts and a CUSUM chart of squared deviations from target give good overall performance in detecting a wide range of process changes. Copyright © 2009 John Wiley & Sons, Ltd.     

Fault Diagnosis in Multivariate Control Charts Using Artificial Neural Networks

Most multivariate quality control procedures evaluate the in‐control or out‐of‐control condition based upon an overall statistic, like Hotelling's T². Although T² is optimal for finding a general shift in mean vectors, it is not optimal for shifts that occur for some subset of variables. This introduces a persistent problem in multivariate control charts, namely the interpretation of a signal that often discourages practitioners in applying them. In this paper, we propose an artificial neural network based model to diagnose faults in out‐of‐control conditions and to help identify aberrant variables when Shewhart‐type multivariate control charts based on Hotelling's T² are used. The results of the model implementation on two numerical examples and one case of real world data are encouraging. Copyright © 2005 John Wiley & Sons, Ltd.     

与控制点方法论相结合的V-mask累积和控制图

V-mask累积和控制图虽然能够有效地监控过程中发生的微小偏移,但是因为它需要存储大量统计量且计算时间较长,所以在计算机中实施起来比较困难.为了解决这一问题,介绍了将控制点方法论应用于V-mask累积和控制图这一方法,并通过实例来进一步说明.结果表明,与控制点方法论结合的控制图减少了存储量,缩短了计算时间,而且将在顾客满意度控制中得到广泛应用.     

Effective Control Charts for Monitoring Multivariate Process Dispersion

When monitoring process dispersion, it is common to pay more attention to dispersion increases than to decreases for practical reasons. Nonetheless, it is also important to detect dispersion decreases for two reasons: (i) it deserves further investigations as to why the process has improved; and (ii) if the process has changed, the settings of the control chart would need to be adjusted for effective future monitoring. In this paper, we first propose an effective control chart for detecting multivariate dispersion decreases in phase II process monitoring, which is constructed using the same approach as that of the one‐sided likelihood‐ratio‐test‐based multivariate chart proposed recently in the literature for detecting dispersion increases. We then discuss a combined charting scheme by combining these two one‐sided charts for detecting either dispersion increases or decreases. Comparative simulation studies show that the proposed combined control charting scheme outperforms several existing two‐sided control charts in terms of the average run length when the process dispersion indeed increases or decreases. Two real‐life examples are presented to demonstrate the applicability of the proposed charts. Copyright © 2011 John Wiley & Sons, Ltd.