A double exponentially weighted moving average control chart for monitoring COM‐Poisson attributes

The Conway‐Maxwell‐Poisson (COM‐Poisson) distribution is a two‐parameter generalization of the Poisson distribution, which can be used for overdispersed or underdispersed count data and also contains the geometric and Bernoulli distributions as special cases. This article presents a double exponentially weighted moving average control chart with steady‐state control limits to monitor COM‐Poisson attributes (regarded as CMP‐DEWMA chart). The performance of the proposed control chart has been evaluated in terms of the average, the median, and the standard deviation of the run‐length distribution. The CMP‐DEWMA control chart is studied not only to detect shifts in each parameter individually but also in both parameters simultaneously. The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the CMP‐DEWMA chart is more effective than the EWMA chart at detecting downward shifts of the process mean. Finally, a real data set is presented to demonstrate the application of the proposed chart.     

Poisson progressive mean control chart

In real life applications, many process‐monitoring problems in statistical process control are based on attribute data resulting from quality characteristics that cannot be measured on numerical or quantitative scales. For the monitoring of such data, a new attribute control chart has been proposed in this study, namely, the Poisson progressive Mean (PPM) control chart. The performance of the PPM chart is compared with the existing charts used for the monitoring of Poisson processes such as the Shewhart c‐chart, Poisson Exponentially Weighted Moving Average chart, Poisson double Exponentially Weighted Moving Average chart and the Poisson Cumulative Sum charts. The average run length comparison indicated the superior performance of the PPM chart in terms of shift detection ability. This study will help quality practitioners to choose an efficient attribute control chart.     

A Flexible and Generalized Exponentially Weighted Moving Average Control Chart for Count Data

The Conway–Maxwell–Poisson distribution can be used to model under‐dispersed or over‐dispersed count data. This study proposes a flexible and generalized attribute exponentially weighted moving average (EWMA), namely GEWMA, control chart for monitoring count data. The proposed EWMA chart is based on the Conway–Maxwell–Poisson distribution. The performance of the proposed chart is evaluated in terms of run length (RL) characteristics such as average RL, median RL, and standard deviation of the RL distribution. The average RL of the proposed GEWMA chart is compared with Sellers chart. The sensitivity of the standard Poisson EWMA (PEWMA) chart is also studied and compared with the proposed GEWMA chart for under‐dispersed or over‐dispersed data. It has been observed that the PEWMA chart is very sensitive for under‐dispersed or over‐dispersed data while the proposed GEWMA is very robust. Finally, the generalization of the proposed chart to the Bernoulli EWMA, PEWMA, and geometric EWMA charts is also studied using someone simulated data sets. Copyright © 2013 John Wiley & Sons, Ltd.     

A Two‐Sided Cumulative Sum Chart for First‐Order Integer‐Valued Autoregressive Processes of Poisson Counts

Count data processes are often encountered in manufacturing and service industries. To describe the autocorrelation structure of such processes, a Poisson integer‐valued autoregressive model of order 1, namely, Poisson INAR(1) model, might be used. In this study, we propose a two‐sided cumulative sum control chart for monitoring Poisson INAR(1) processes with the aim of detecting changes in the process mean in both positive and negative directions. A trivariate Markov chain approach is developed for exact evaluation of the ARL performance of the chart in addition to a computationally efficient approximation based on bivariate Markov chains. The design of the chart for an ARL‐unbiased performance and the analyses of the out‐of‐control performances are discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

The Use of Probability Limits of COM–Poisson Charts and their Applications

The conventional c and u charts are based on the Poisson distribution assumption for the monitoring of count data. In practice, this assumption is not often satisfied, which requires a generalized control chart to monitor both over‐dispersed as well as under‐dispersed count data. The Conway–Maxwell–Poisson (COM–Poisson) distribution is a general count distribution that relaxes the equi‐dispersion assumption of the Poisson distribution and in fact encompasses the special cases of the Poisson, geometric, and Bernoulli distributions. In this study, the exact k‐sigma limits and true probability limits for COM–Poisson distribution chart have been proposed. The comparison between the 3‐sigma limits, the exact k‐sigma limits, and the true probability limits has been investigated, and it was found that the probability limits are more efficient than the 3‐sigma and the k‐sigma limits in terms of (i) low probability of false alarm, (ii) existence of lower control limits, and (iii) high discriminatory power of detecting a shift in the parameter (particularly downward shift). Finally, a real data set has been presented to illustrate the application of the probability limits in practice. Copyright © 2012 John Wiley & Sons, Ltd.     

Design of a t‐chart using generalized multiple dependent state sampling

In this article, a new t‐chart based on generalized multiple dependent state (GMDS) sampling is proposed for efficient monitoring of a process by assuming that the time between events follows the exponential distribution. The proposed t‐chart has two pair of control limits and utilizes the past sample information with the current sample information. The control chart coefficients are estimated by considering different values of the in‐control average run lengths. The proposed t‐chart is compared with the existing chart by using the out‐of‐control average run length and extra quadratic loss function. The comparison reveals that the proposed charting strategy has better shift detection ability in process mean. An illustrative example is given for the practical implementation of the proposed chart.     

Improved CUSUM monitoring of Markov counting process with frequent zeros

There has been a growing interest in monitoring processes featuring serial dependence and zero inflation. The phenomenon of excessive zeros often occurs in count time series because of the advancement of quality in manufacturing process. In this study, we propose three control charts, such as the cumulative sum chart with delay rule (CUSUM‐DR), conforming run length (CRL)‐CUSUM chart, and combined Shewhart CRL‐CUSUM chart, to enhance the performance of monitoring Markov counting processes with excessive zeros. Numerical experiments are conducted based on integer‐valued autoregressive time series models, for example, zero‐inflated Poisson INAR and INARCH, to evaluate the performance of the proposed charts designed for the detection of mean increase. A real example is also illustrated to demonstrate the usability of our proposed charts.     

Optimal one- and two-sided adaptive EWMA scheme for monitoring Poisson count data

The Poisson distribution assumption often arises in several industrial applications for modeling defects or nonconformities. In this work, we investigate the one- and two-sided performance of a new adaptive EWMA (exponentially weighted moving average)-type chart for monitoring Poisson count data. An appropriate discrete-state Markov chain technique is provided to compute the exact ARL (average run length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed.     

A generally weighted moving average control chart for zero-inflated Poisson processes

Zero-inflated Poisson (ZIP) model is very useful in high-yield processes where an excessive number of zero observations exist. This model can be viewed as an extension of the standard Poisson distribution. In this paper, a one-sided generally weighted moving average (GWMA) control chart is proposed for monitoring upward shifts in the two parameters of a ZIP process (regarded as ZIP-GWMA chart). The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the ZIP-GWMA performs better than the existing control charts under shifts in both parameters. Moreover, an illustrative example is presented to display the application of the proposed chart on practitioners.     

Multiple Attribute Control Charts with False Discovery Rate Control

The statistical cumulative sum (CUSUM) chart is a powerful tool for monitoring the attribute quality variable in manufacturing industry. In this article, we studied the multiplicity problem caused by simultaneously monitoring more than one attribute quality variable. Multiple binomial and Poisson CUSUM charts incorporating a multiple hypothesis testing technique known as false discovery rate control were proposed. The procedures for establishing the new control schemes were presented, and the performance of the new methods was evaluated using Monte Carlo simulation. The approximation methods for obtaining the p‐values of the CUSUM statistics for conducting the new control schemes were also provided and evaluated. The new methods were also illustrated with a real example. Copyright © 2011 John Wiley & Sons, Ltd.     

Attribute Control Charts with Optimal Limits

A new attribute control chart is presented to monitor processes that generate count data. The economic objective of the chart is to minimize the total cost of its errors, a linear function of errors Type I and II. The proposed chart can be applied to Poisson, geometric, and negative binomial assumptions. Control limits are calculated optimally, because they are based on exact probability distributions and used to detect defined directional shifts in a process. Some numerical results are provided, and expected costs of the new chart are compared with those of a one‐sided c‐chart. Other effects such as changing the cost structure are shown graphically. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

A New Chart for Monitoring Service Process Mean

Control charts are demonstrated effective in monitoring not only manufacturing processes but also service processes. In service processes, many data came from a process with nonnormal distribution or unknown distribution. Hence, the commonly used Shewhart variable control charts are not suitable because they could not be properly constructed. In this article, we proposed a new mean chart on the basis of a simple statistic to monitor the shifts of the process mean. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed chart. Furthermore, an arcsine transformed exponentially weighted moving average chart was proposed because the average run lengths of this modified chart are more intuitive and reasonable than those of the mean chart. We would recommend the arcsine transformed exponentially weighted moving average chart if we were concerned with the proper values of the average run length. A numerical example of service times with skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the proposed charts. Copyright © 2011 John Wiley & Sons, Ltd.     

Monitoring Process Variability for Stationary Process Data

Processes that arise naturally, for example, from manufacturing or the environment, often exhibit complicated autocorrelation structures. When monitoring such a process for changes in variance, accounting for that structure is critical. While charts for monitoring the variance of processes of independent observations and some specific autocorrelated processes have been proposed in the past, the chart presented in this article can handle a general stationary process. The performance of the proposed chart was examined through simulations for the first‐order autoregressive and first‐order autoregressive‐moving average processes and demonstrated with examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Surveillance of Nonhomogeneous Poisson Processes

The use of varying sample size monitoring techniques for Poisson count data has drawn a great deal of attention in recent years. Specifically, these methods have been used in public health surveillance, manufacturing, and safety monitoring. A number of approaches have been proposed, from the traditional Shewhart charts to cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) methods. It is convenient to use techniques based on statistics that are invariant to the units of measurement since in most cases these units are arbitrarily selected. A few of the methods reviewed in our expository article are not inherently invariant, but most are easily modified to be invariant. Most importantly, if methods are invariant to the choice of units of measurement, they can be applied in situations where the in-control Poisson mean varies over time, even if there is no associated varying sample size. Several examples are discussed to highlight the promising uses of invariant Poisson control charting methods in this much broader set of applications, which includes risk-adjusted monitoring in healthcare, public health surveillance, and monitoring of continuous time nonhomogeneous Poisson processes. A new chart design method based on extensive online simulation is highlighted.     

A Distribution‐free Control Chart for the Joint Monitoring of Location and Scale

Traditional statistical process control for variables data often involves the use of a separate mean and a standard deviation chart. Several proposals have been published recently, where a single (combination) chart that is simpler and may have performance advantages, is used. The assumption of normality is crucial for the validity of these charts. In this article, a single distribution‐free Shewhart‐type chart is proposed for monitoring the location and the scale parameters of a continuous distribution when both of these parameters are unknown. The plotting statistic combines two popular nonparametric test statistics: the Wilcoxon rank sum test for location and the Ansari–Bradley test for scale. Being nonparametric, all in‐control properties of the proposed chart remain the same and known for all continuous distributions. Control limits are tabulated for implementation in practice. The in‐control and the out‐of‐control performance properties of the chart are investigated in simulation studies in terms of the mean, the standard deviation, the median, and some percentiles of the run length distribution. The influence of the reference sample size is examined. A numerical example is given for illustration. Summary and conclusions are offered. Copyright © 2011 John Wiley & Sons, Ltd.     

Monitoring of Time‐Between‐Events with a Generalized Group Runs Control Chart

Control charting methods for time between events (TBE) is important in both manufacturing and nonmanufacturing fields. With the aim to enhance the speed for detecting shifts in the mean TBE, this paper proposes a generalized group runs TBE chart to monitor the mean TBE of a homogenous Poisson failure process. The proposed chart combines a TBE subchart and a generalized group conforming run length subchart. The zero‐state and steady‐state performances of the proposed chart were evaluated by applying a Markov chain method. Overall, it is found that the proposed chart outperforms the existing TBE charts, such as the T, T_r, EWMA‐T, Synth‐T_r, and GR‐T_r charts. Copyright © 2015 John Wiley & Sons, Ltd.     

A new non‐parametric CUSUM mean chart

Not all data in practice came from a process with normal distribution. When the process distribution is non‐normal or unknown, the commonly used Shewhart control charts are not suitable. In this paper, a new non‐parametric CUSUM Mean Chart is proposed to monitor the possible small mean shifts in the process. The sampling properties of the new monitoring statistics are examined and the average run lengths of the proposed chart are examined. Two numerical examples are used to illustrate the proposed chart and compare with the two existing charts, assuming normality and Beta distribution, respectively. The CUSUM Mean Chart showed better detection ability than those two charts in monitoring and detecting small process mean shifts. Copyright © 2010 John Wiley & Sons, Ltd.     

A New Cumulative Sum Quality Control Scheme for Monitoring the Process Mean

A control chart is a powerful statistical process monitoring tool that is frequently used in many industrial and service organizations to monitor in‐control and out‐of‐control performances of the manufacturing processes. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been recognized as potentially powerful tool in quality and management control. These control charts are sensitive to both small and moderate changes in the process. In this paper, we propose a new CUSUM (NCUSUM) quality control scheme for efficiently monitoring the process mean. It is shown that the classical CUSUM control chart is a special case of the proposed controlling scheme. The NCUSUM control chart is compared with some of the recently proposed control charts by using characteristics of the distribution of run length, i.e. average run length, median run length and standard deviation of run length. It is worth mentioning that the NCUSUM control chart detects the random shifts in the process mean substantially quicker than the classical CUSUM, fast initial response‐based CUSUM, adaptive CUSUM with EWMA‐based shift, adaptive EWMA and Shewhart–CUSUM control charts. An illustrative example is given to exemplify the implementation of the proposed quality control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

A New Statistical High‐Quality Process Monitoring Method: The Counted Number Between Omega‐Event Control Charts

Control chart techniques for high‐quality process have attracted great attention in modern precision manufacturing. Traditional control charts are no longer applicable because of high false alarm rate. To solve this problem, in this article a new statistical process monitoring method, the counted number between omega‐event statistical process control charts, abbreviated as CBΩ charts, is proposed. The phrase omega event denotes that one observation falls into some certain interval and the CBΩ chart is to monitor the number of consecutive parts between successive r omega events. On the basis of CBΩ charts, a dual‐CBΩ monitoring scheme is developed. This scheme sets up two CBΩ charts with symmetrical omega events, (μ + ?σ, + ∞) and (? ∞, μ ? ?σ), respectively. The performance of CBΩ charts and dual‐CBΩ monitoring is investigated. Dual‐CBΩ monitoring has shown its capability in detecting both mean and variance shift and convenience in implementation compared with other traditional charts. Dual‐CBΩ monitoring can reduce false alarm rate greatly without introducing an unacceptable loss of sensitivity in detecting out‐of‐control signals in high‐quality process control. Copyright © 2011 John Wiley & Sons, Ltd.