Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart

Recent research has shown that the adaptive control charts are quicker than the traditional static charts in detecting process shifts. This paper develops the algorithm for the optimization designs of the adaptive np control charts for monitoring the process fraction non‐conforming p. It includes the variable sample size chart, the variable sampling interval chart, and the variable sample size and sampling interval chart. The performance of the adaptive np charts is measured by the average time to signal under the steady‐state mode, which allows the shift in p to occur at any time, even during the sampling inspection. By studying the performance of the adaptive np charts systematically, it is found that they do improve effectiveness significantly, especially for detecting small or moderate process shifts. Copyright © 2004 John Wiley & Sons, Ltd.     

An adaptive dimension reduction scheme for monitoring feedback‐controlled processes

Detecting dynamic mean shifts is particularly important in monitoring feedback‐controlled processes in which time‐varying shifts are usually observed. When multivariate control charts are being utilized, one way to improve performance is to reduce dimensions. However, it is difficult to identify and remove non‐informative variables statically in a process with dynamic shifts, as the contribution of each variable changes continuously over time. In this paper, we propose an adaptive dimension reduction scheme that aims to reduce dimensions of multivariate control charts through online variable evaluation and selection. The resulting chart is expected to keep only informative variables and hence maximize the sensitivity of control charts. Specifically, two sets of projection matrices are presented and dimension reduction is achieved via projecting process vectors into a low‐dimensional space. Although developed based on feedback‐controlled processes, the proposed scheme can be easily extended to monitor general multivariate applications. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Performance of Phase I Dispersion Control Charts for Process Monitoring

Control charts are usually implemented in two phases: the retrospective phase (phase I) and the monitoring phase (phase II). The performance of any phase II control chart structure depends on the preciseness of the control limits obtained from the phase I analysis. In statistical process control, the performance of phase I dispersion charts has mainly been investigated for normal or contaminated normal distributions of the quality characteristic of interest. Little work has been carried out to investigate the performance of a wide range of possible phase I dispersion charts for processes following non‐normal distributions. The current study deals with the proper choice of a control chart for the evaluation of process dispersion in phase I. We have analyzed the performance of a wide range of dispersion control charts, including two distribution‐free structures. The performance of the control charts is evaluated in terms of probability to signal, under normal and non‐normal process setups. These results will be useful for quality control practitioners in their selection of a phase I control chart. Copyright © 2014 John Wiley & Sons, Ltd.     

Increasing the Sensitivity of Cumulative Sum Charts for Location

The cumulative sum (CUSUM) chart is a very effective control charting procedure used for the quick detection of small‐sized and moderate‐sized changes. It can detect small process shifts missed by the Shewhart‐type control chart, which is sensitive mainly to large shifts. To further enhance the sensitivity of the CUSUM control chart at detecting very small process disturbances, this article presents CUSUM control charts based on well‐structured sampling procedures, double ranked set sampling, median‐double ranked set sampling, and double‐median ranked set sampling. These sampling techniques significantly improve the overall performance of the CUSUM chart over the entire process mean shift range, without increasing the false alarm rate. The newly developed control schemes do not only dominate most of the existing charts but are also easy to design and implement as illustrated through an application example of real datasets. The control schemes used for comparison in this study include the conventional CUSUM chart, a fast initial response CUSUM chart, a 2‐CUSUM chart, a 3‐CUSUM chart, a runs rules‐based CUSUM chart, the enhanced adaptive CUSUM chart, the CUSUM chart based on ranked set sampling (RSS), and the single CUSUM and combined Shewhart–CUSUM charts based on median RSS. Copyright © 2014 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.     

Guidelines for the application of adaptive control charting schemes

A comprehensive performance study and comparison of several adaptive statistical process control procedures is presented. These adaptive control chart procedures are modifications to standard Shewhart control charts that include changing the sampling interval, the sample size or both according to rules based on the value of the sample statistic. Adaptive control techniques are known to improve the performance of the standard Shewhart control charts. In this paper we develop a four-state adaptive sample size control chart and several variations of a three-state combined adaptive sample size and sampling interval control chart. We then compare these new schemes with the previously developed schemes, the two-state adaptive sampling interval, the two-state adaptive sample size and two-state combined adaptive sample size and sampling interval control chart, three-state adaptive sample size control chart and non-adaptive Shewhart control charts. These results show that the addition of the third and fourth states on the adaptive control chart schemes improve the control chart performance; however, the improvement is relatively modest.     

A new adaptive CUSUM control chart for detecting the multivariate process mean

We propose a new multivariate CUSUM control chart, which is based on self adaption of its reference value according to the information from current process readings, to quickly detect the multivariate process mean shifts. By specifying the minimum magnitude of the process mean shift in terms of its non‐centrality parameter, our proposed control chart can achieve an overall performance for detecting a particular range of shifts. This adaptive feature of our method is based on two EWMA operators to estimate the current process mean level and make the detection at each step be approximately optimal. Moreover, we compare our chart with the conventional multivariate CUSUM chart. The advantages of our control chart detection for range shifts over the existing charts are greatly improved. The Markovian chain method, through which the average run length can be computed, is also presented. Copyright © 2010 John Wiley & Sons, Ltd.     

New Synthetic EWMA and Synthetic CUSUM Control Charts for Monitoring the Process Mean

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are potentially powerful statistical process monitoring tools because of their excellent speed in detecting small to moderate persistent process shifts. Recently, synthetic EWMA (SynEWMA) and synthetic CUSUM (SynCUSUM) control charts have been proposed based on simple random sampling (SRS) by integrating the EWMA and CUSUM control charts with the conforming run length control chart, respectively. These synthetic control charts provide overall superior detection over a range of mean shift sizes. In this article, we propose new SynEWMA and SynCUSUM control charts based on ranked set sampling (RSS) and median RSS (MRSS) schemes, named SynEWMA‐RSS and SynEWMA‐MRSS charts, respectively, for monitoring the process mean. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed control charts. The run length performances of these control charts are compared with their existing powerful counterparts based on SRS, RSS and MRSS schemes. It turns out that the proposed charts perform uniformly better than the Shewhart, optimal synthetic, optimal EWMA, optimal CUSUM, near‐optimal SynEWMA, near‐optimal SynCUSUM control charts based on SRS, and combined Shewhart‐EWMA control charts based on RSS and MRSS schemes. A similar trend is observed when constructing the proposed control charts based on imperfect RSS schemes. An application to a real data is also provided to demonstrate the implementations of the proposed SynEWMA and SynCUSUM control charts. Copyright © 2014 John Wiley & Sons, Ltd.     

Enhancing the Performance of Exponentially Weighted Moving Average Charts: Discussion

Abbas et al. (Abbas N, Riaz M, Does RJMM. Enhancing the performance of EWMA charts. Quality and Reliability Engineering International 2011; 27(6):821–833) proposed the use of signaling schemes with exponentially weighted moving average charts (named as 2/2 and modified ? 2/3 schemes) for their improved design structures. A two‐sided control structure of these schemes is given in the paper. The computational results in some of the tables of that paper for modified ? 2/3 are mistakenly given for the one‐sided control structure. The corrected two‐sided results are provided here. It is noticed that the superiority of the proposed scheme over the classical exponentially weighted moving average chart remains but is less pronounced. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimization design of the CUSUM and EWMA charts for autocorrelated processes

The traditional control charts produce frequent false alarm signals in the presence of autocorrelation. The implementation of the modified chart scheme is a way of handling the problem of autocorrelation in control charts. In modified charts, the standard control limits of the traditional charts are adjusted to offset the influence because of the autocorrelation. The exponentially weighted moving average– and cumulative sum–modified charts are 2 widely used charts for monitoring autocorrelated data. These charts have design parameters in their formulation, and the choice of these parameters play significant roles in the detection of out‐of‐control situations. In reality, the magnitude of the mean shift is uncertain, and this leads to a difficulty in the choice of design parameters by the practitioner. The use of optimal parameters can enhance process performance in such situations. In this paper, we determine optimal design parameters for the charts using an exhaustive search procedure. In the optimization process, we determine the parameters that produce the smallest extra quadratic loss (EQL) value for each autocorrelation coefficient. This criterion measures the anticipated loss attributed to poor quality in the process. The loss in quality is lowered by minimizing the EQL and the combination of parameters in the chart that yields the smallest EQL has a better detection ability over the entire shift range. For the purpose of this work, we concentrate on autocorrelation that can be specifically modelled with autoregressive models. This article provides the practitioner with optimal parameters that can be used to enhance the overall effectiveness of the charts over an entire shift range.     

Optimum Multiple and Multivariate Poisson Statistical Control Charts

This paper deals with the simultaneous statistical process control of several Poisson variables. The practitioner of this type of monitoring may employ a multiple scheme, i.e. one chart for controlling each variable, or may use a multivariate scheme, based on monitoring all the variables with a single control chart. If the user employs the multivariate schemes, he or she can choose from, for example, three options: (i) a control chart based on the sum of the different Poisson variables; (ii) a control chart on the maximum value of the different Poisson variables; and (iii) in the case of only two variables, a chart that monitors the difference between them. In this paper, the previous control charts are studied when applied to the control of p = 2, 3 and 4 variables. In addition, the optimization of a set of univariate Poisson control charts (multiple scheme) is studied. The main purpose of this paper is to help the practitioner to select the most adequate scheme for her/his production process. Towards this goal, a friendly Windows© computer program has been developed. The program returns the best control limits for each control chart and makes a complete comparison of performance among all the previous schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance

This article compares the effectiveness and robustness of nine typical control charts for monitoring both process mean and variance, including the most effective optimal and adaptive sequential probability ratio test (SPRT) charts. The nine charts are categorized into three types (the type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and adaptive version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and adaptive charts are designed optimally in order to minimize an index average extra quadratic loss for the best overall performance. Moreover, the probability distributions of the mean shift δ_µ and standard deviation shift δ_σ are studied explicitly as the influential factors in a factorial experiment. The main findings obtained in this study include: (1) From an overall viewpoint, the SPRT‐type chart is more effective than the CUSUM‐type chart and type chart by 15 and 73%, respectively; (2) in general, the adaptive chart outperforms the optimal chart and basic chart by 16 and 97%, respectively; (3) the optimal CUSUM chart is the most effective fixed sample size and sampling interval chart and the optimal SPRT chart is the best choice among the adaptive charts; and (4) the optimal sample sizes of both the charts and the CUSUM charts are always equal to one. Furthermore, this article provides several design tables which contain the optimal parameter values and performance indices of 54 charts under different specifications. Copyright © 2011 John Wiley & Sons, Ltd.     

On the Performance of Phase‐I Bivariate Dispersion Charts to Non‐Normality

A phase‐I study is generally used when population parameters are unknown. The performance of any phase‐II chart depends on the preciseness of the control limits obtained from the phase‐I analysis. The performance of phase‐I bivariate dispersion charts has mainly been investigated for bivariate normal distribution. However, this assumption is seldom fulfilled in reality. The current work develops and studies the performance of phase‐I |S| and |G| charts for monitoring the process dispersion of bivariate non‐normal distributions. The necessary control charting constants are determined for the bivariate non‐normal distributions at nominal false alarm probability (FAP₀). The performance of these charts is evaluated and compared in a situation when samples are generated by bivariate logistic, bivariate Laplace, bivariate exponential, or bivariate t₅ distribution. The analysis shows that the proper consideration to underlying bivariate distribution in the construction of phase‐I bivariate dispersion charts is very important to give a real picture of in or out of control process status. Copyright © 2016 John Wiley & Sons, Ltd.     

A double sampling scheme for process variability monitoring

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries come from processes exhibiting nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. This paper thus proposes a standardized asymmetric exponentially weighted moving average (EWMA) variance chart with a double sampling scheme (SDS EWMA‐AV chart) for monitoring process variability. We further explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using the proposed SDS EWMA‐AV chart. The performance of the SDS EWMA‐AV chart and that of the single sampling EWMA variance (SS EWMA‐V) chart are then compared, with the former showing superior out‐of‐control detection performance versus the latter. We also compare the out‐of‐control variance detection performance of the proposed chart with those of nonparametric variance charts, the nonparametric Mood variance chart (NP‐M chart) with runs rules, and the nonparametric likelihood ratio‐based distribution‐free EWMA (NLE) chart and the combination of traditional EWMA (CEW) and the SS EWMA‐V control charts by considering cases in which the critical quality characteristic presents normal, double exponential, uniform, chi‐square, and exponential distributions. Comparison results show that the proposed chart always outperforms the NP‐M with runs rules, the NLE, CEW, and the SS EWMA‐V control charts. We hence recommend employing the SDS EWMA‐AV chart. Finally, a numerical example of a service system for a bank branch in Taiwan is used to illustrate the application of the proposed variability control chart.     

Model‐based control chart for autoregressive and correlated data

In recent years, statistical process control for autocorrelated processes has received a great deal of attention. This is due in part to the improvements in measurement and data collection that allow processes to be sampled at higher frequency rates and, hence, data autocorrelation. A method for monitoring autocorrelated processes based on regression adjustment is presented in this paper. The performance of the residual‐based control chart in terms of the average run length is compared to observation‐based control charts via Monte Carlo simulations. In general, the observation‐based control charts perform very poorly when data are correlated over time. Under the assumption that the model is correct, the residual‐based control charts are superior for all cases considered here. This suggests using a residual‐based control chart to detect the mean shift. This is recommended particularly for chemical processes where there are often cascade processes with several inputs but only a few outputs, and where many of the variables are highly autocorrelated. Copyright © 2002 John Wiley & Sons, Ltd.     

An efficient adaptive EWMA control chart for monitoring the process mean

In recent years, the memory‐type control charts—exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)—along with the adaptive and dual control‐charting structures have received considerable attention because of their excellent ability in providing an overall good detection over a range of mean‐shift sizes. These adaptive memory‐type control charts include the adaptive exponentially weighted moving average (AEWMA), dual CUSUM, and adaptive CUSUM charts. In this paper, we propose a new AEWMA chart for efficiently monitoring the process mean. The idea is to first design an unbiased estimator of the mean shift using the EWMA statistic and then adaptively update the smoothing constant of the EWMA chart. The run length profiles of the proposed AEWMA chart are computed using extensive Monte Carlo simulations. Based on a comprehensive comparative study, it turns out that the proposed AEWMA chart performs better than the existing AEWMA, adaptive CUSUM, dual CUSUM, and Shewhart‐CUSUM charts, in terms of offering more balanced protection against mean shifts of different sizes. An example is also used to explain the working of the existing and proposed control charts.     

An adaptive exponentially weighted moving average chart for the mean with variable sampling intervals

The AEWMA control chart is an adaptive EWMA (exponentially weighted moving average) type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. To improve the detection performance of the FSI (fixed sampling interval) AEWMA control chart 7 in terms of the ATS(average time to signal), this paper proposes a new VSI (variable sampling interval) AEWMA control chart. A Markov chain approach is used to calculate the ATS values of the new VSI AEWMA control chart, and comparative results show that the proposed control chart performs better than the standard FSI AEWMA control chart and than other VSI control charts over a wide range of shifts.     

On Proper Choice of Variability Control Chart for Normal and Non‐normal Processes

Control charts are an important statistical process control tool used to monitor changes in process location and variability. This study addresses issues regarding the proper choice of control chart for efficient monitoring of process variability. The choice of the best estimator to be used for variability charts has not been made clear in literature. We have analyzed the performance of eight control chart structures, based on different estimates of process standard deviation. The performance of control charts is investigated under the existence and violation of ideal assumptions of normality. Control chart constants and factors required for computing probability limits, considering normal and different non‐normal parent distributions, are provided for all variability charts. This study aims at providing guidance to quality practitioners in choosing the appropriate variability control chart for normal and non‐normal processes. Copyright © 2011 John Wiley & Sons, Ltd.     

A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA‐PRSS chart. The performance of the EWMA‐PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA‐PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA‐IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA‐IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA‐PRSS chart. Copyright © 2014 John Wiley & Sons, Ltd.     

A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated

The performance of control charts can be adversely affected when based on parameter estimates instead of known in‐control parameters. Several studies have shown that a large number of phase I observations may be needed to achieve the desired in‐control statistical performance. However, practitioners use different phase I samples and thus different parameter estimates to construct their control limits. As a consequence, there would be in‐control average run length (ARL) variation between different practitioners. This kind of variation is important to consider when studying the performance of control charts with estimated parameters. Most of the previous literature has relied primarily on the expected value of the ARL (AARL) metric in studying the performance of control charts with estimated parameters. Some recent studies, however, considered the standard deviation of the ARL metric to study the performance of control charts. In this paper, the standard deviation of the ARL metric is used to study the in‐control and out‐of‐control performance of the adaptive exponentially weighted moving average (AEWMA) control chart. The performance of the AEWMA chart is then compared with that of the Shewhart and EWMA control charts. The simulation results show that the AEWMA chart might represent a good solution for practitioners to achieve a reasonable amount of ARL variation from the desired in‐control ARL performance. In addition, we apply a bootstrap‐based design approach that provides protection against frequent false alarms without deteriorating too much the out‐of‐control performance. Copyright © 2014 John Wiley & Sons, Ltd.