A double generally weighted moving average exceedance control chart

Since the inception of control charts by W. A. Shewhart in the 1920s, they have been increasingly applied in various fields. The recent literature witnessed the development of a number of nonparametric (distribution‐free) charts as they provide a robust and efficient alternative when there is a lack of knowledge about the underlying process distribution. In order to monitor the process location, information regarding the in‐control (IC) process median is typically required. However, in practice, this information might not be available due to various reasons. To this end, a generalized type of nonparametric time‐weighted control chart labeled as the double generally weighted moving average (DGWMA) based on the exceedance statistic (EX) is proposed. The DGWMA‐EX chart includes many of the well‐known existing time‐weighted control charts as special or limiting cases for detecting a shift in the unknown location parameter of a continuous distribution. The DGWMA‐EX chart combines the better shift detection properties of a DGWMA chart with the robust IC performance of a nonparametric chart, by using all the information from the start until the most recent sample to decide if a process is IC or out‐of‐control. An extensive simulation study reveals that the proposed DGWMA‐EX chart, in many cases, outperforms its counterparts.     

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 triple exponentially weighted moving average control chart for monitoring time between events

Time between events (TBE) charts are used in high-yield processes where the rate of occurrences is very low. In the current article, we propose a triple exponentially weighted moving average control chart to monitor TBE (regarded as triple exponentially weighted moving average TEWMA-TBE chart) modeled by a gamma distribution. One- and two-sided schemes of the proposed chart are designed and compared with the double EWMA DEWMA-TBE and EWMA-TBE charts. It is shown that the lower- and two-sided TEWMA-TBE charts outperform its competitors, especially for small to moderate downward shifts, while the upper-sided TEWMA-TBE chart has very good detection ability for small shifts. We also study the robustness of the proposed chart when the true distribution is a Weibull or a lognormal and it is found that the TEWMA-TBE chart has better robustness properties than its competitors, especially for small shifts. Two illustrative examples from airplane accidents and earthquakes are also provided to display the application of the proposed chart.     

Monitoring reliability for a gamma distribution with a double progressive mean control chart

Control charting technique for time between events (TBE) is very important in high-yield processes for monitoring reliability. For a regularly maintained system, the interfailure times can be modeled by a gamma distribution. This article proposes a new control chart based on the double progressive mean statistic for monitoring the time between k (≥1 ) failures of a maintained gamma distributed system (referred as DPM-TBE chart). The performance of the proposed scheme is measured in terms of the average run-length (ARL) for the case when the scale parameter is known as well as when it is unknown and is estimated from an in-control (IC) reference sample. A comparison study with other TBE charts shows that the DPM-TBE chart is more effective. In addition, the proposed chart is shown to be very robust for large shifts when the true distribution of time between failures is a Weibull or a lognormal. Finally, an illustrative example is given to demonstrate the implementation of the proposed chart.     

Exponential cumulative sums chart for detecting shifts in time-between-events

Time-between-events (TBE) charts use the time interval T between events to monitor process shifts (or failure rates λ). This paper presents a two-sided TBE cumulative sums (CUSUM) chart called a weighted CUSUM(WCUSUM)chart for detecting either a deterioration (decrease in T) or an improvement (increase in T) in the condition of a process. A new kind of WCUSUM chart that has an additional charting power parameter w is proposed here. A WCUSUM chart’s efficiency can be improved by using the parameter w, based on an estimated value of the mean shift. In addition, a methodology and optimal design are presented for minimising the average loss. Construction of the WCUSUM chart is illustrated by considering a random shift δ in λ (including both increasing and decreasing shifts) in the design.     

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.     

Properties of the exponential EWMA chart with parameter estimation

Count rates may reach very low levels in production processes with low defect levels. In such settings, conventional control charts for counts may become ineffective since the occurrence of many samples with zero defects would cause control statistic to be consistently zero. Consequently, the exponentially weighted moving average (EWMA) control chart to monitor the time between successive events (TBE) or counts has been introduced as an effective approach for monitoring processes with low defect levels. When the counts occur according to a Poisson distribution, the TBE observations are distributed as exponential. Although the assumption of exponential distribution is a reasonable choice as a model of TBE observations, its parameter, i.e. the mean (also the standard deviation), is rarely known in practice and its estimate is used in place of the unknown parameter when constructing the exponential EWMA chart. In this article, we investigate the effects of parameter estimation on the performance measures (average run length, standard deviation, and percentiles of the run length distribution) of the exponential EWMA control chart. A comprehensive analysis of the conditional performance measures of the chart shows that the effect of estimation can be serious, especially if small samples are used. An investigation of the marginal performance measures, which are calculated by averaging the conditional performance measures over the distribution of the parameter estimator, allows us to provide explicit sample size recommendations in constructing these charts to reach a satisfactory performance in both the in‐control and the out‐of‐control situation. Copyright © 2009 John Wiley & Sons, Ltd.     

A New Control Technique with Quality Characteristic Shifting with Time

In this paper, a new quality control technique is discussed, in which the quality characteristic shifts with time. A trends semi‐circle control chart is proposed to control this type of processes effectively. An optimization model is suggested to determine the optimal interval of adjustment. We also discuss the average run length of the proposed control chart and the extension to the EWMA chart. An example is used to illustrate its application in a production process. Copyright © 2015 John Wiley & Sons, Ltd.     

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

Exponentially weighted moving average (EWMA) control charts have been widely recognized as a potentially powerful process monitoring tool of the statistical process control because of their excellent speed in detecting small to moderate shifts in the process parameters. Recently, new EWMA and synthetic control charts have been proposed based on the best linear unbiased estimator of the scale parameter using ordered ranked set sampling (ORSS) scheme, named EWMA‐ORSS and synthetic‐ORSS charts, respectively. In this paper, we extend the work and propose a new synthetic EWMA (SynEWMA) control chart for monitoring the process dispersion using ORSS, named SynEWMA‐ORSS chart. The SynEWMA‐ORSS chart is an integration of the EWMA‐ORSS chart and the conforming run length chart. Extensive Monte Carlo simulations are used to estimate the run length performances of the proposed control chart. A comprehensive comparison of the run length performances of the proposed and the existing powerful control charts reveals that the SynEWMA‐ORSS chart outperforms the synthetic‐R, synthetic‐S, synthetic‐D, synthetic‐ORSS, CUSUM‐R, CUSUM‐S, CUSUM‐ln S², EWMA‐ln S² and EWMA‐ORSS charts when detecting small shifts in the process dispersion. A similar trend is observed when the proposed control chart is constructed under imperfect rankings. An application to a real data is also provided to demonstrate the implementation and application of the proposed control chart. Copyright © 2014 John Wiley & Sons, Ltd.     

An Efficient Shewhart‐Type Control Chart to Monitor Moderate Size Shifts in the Process Mean in Phase II

According to Shewhart, control charts are not very sensitive to small and moderate size process shifts that is why those are less likely to be effective in Phase II. So to monitor small or moderate size process shifts in Phase II, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are considered as alternate of Shewhart control charts. In this paper, a Shewhart‐type control chart is proposed by using difference‐in‐difference estimator in order to detect moderate size shifts in process mean in Phase II. The performance of the proposed control chart is studied for known and unknown cases separately through a detailed simulation study. For the unknown case, instead of using reference samples of small sizes, large size reference sample(s) is used as we can see in some of nonparametric control chart articles. In an illustrative example, the proposed control charts are constructed for both known and unknown cases along with Shewhart ‐chart, classical EWMA, and CUSUM control charts. In this application, the proposed chart is found comprehensively better than not only Shewhart ‐chart but also EWMA and CUSUM control charts. By comparing average run length, the proposed control chart is found always better than Shewhart ‐chart and in general better than classical EWMA and CUSUM control charts when we have relatively higher values of correlation coefficients and detection of the moderate shifts in the process mean is concerned. Copyright © 2015 John Wiley & Sons, Ltd.     

A synthetic double sampling control chart for process mean using auxiliary information

A control chart is a simple yet powerful tool that is extensively adopted to monitor shifts in the process mean. In recent years, auxiliary‐information–based (AIB) control charts have received considerable attention as these control charts outperform their counterparts in monitoring changes in the process parameter(s). In this article, we integrate the conforming run length chart with the existing AIB double sampling (AIB DS) chart to propose an AIB synthetic DS chart for the process mean. The AIB synthetic DS chart also encompasses the existing synthetic DS chart. A detailed discussion on the construction, optimization, and evaluation of the run length profiles is provided for the proposed control chart. It is found that the optimal AIB synthetic DS chart significantly outperforms the existing AIB Shewhart, optimal AIB synthetic, and AIB DS charts in detecting various shifts in the process mean. An illustrative example is given to demonstrate the implementation of the existing and proposed AIB control charts.     

A New EWMA Chart Based on Weighted Loss Function for Monitoring the Process Mean and Variance

With the weighted loss function, a new single Exponential Weighted Moving Average (EWMA) chart (WLE chart hereafter for short) is proposed to detect both mean and variance shifts simultaneously. It includes the EWMA control chart based on the semicircle statistic and weighted‐loss‐function control chart as special cases. Numerical studies show that the WLE chart is superior to the weighted‐loss‐function Cumulative Sum (CUSUM) chart when the mean and standard deviation shifts are both small, and offers at least comparable detection ability with the WLC chart in other cases. Compared with the Shiryaev–Roberts chart, the WLE chart has a better or comparable performance except for small and moderate mean shifts. Furthermore, an equivalent form of the WLE chart is developed to diagnose the source and direction of a process change. Copyright © 2014 John Wiley & Sons, Ltd.     

A sum of squares triple exponentially weighted moving average control chart

Control charts are widely known quality tools used to detect and control industrial process deviations in statistical process control. In the current paper, we propose a new single memory-type control chart, called the sum of squares triple exponentially weighted moving average control chart (referred as SS-TEWMA chart), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed SS-TEWMA control chart is compared with that of the sum of squares EWMA, sum of squares double EWMA, sum of squares generally weighted moving average, and sum of squares double generally weighted moving average, control charts, through Monte Carlo simulations. The comparisons indicate that the proposed chart is more efficient, than the competing ones, in detecting small shifts in the process mean and/or variability for most of the considered scenarios, while it has comparable performance for some others in identifying large shifts in the process mean and small to large shifts in the process variability. Finally, two illustrative examples are provided to explain the application of the SS-TEWMA control chart.     

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.     

A new risk-adjusted EWMA control chart based on survival time for monitoring surgical outcome quality

Monitoring surgical outcome quality by risk-adjusted control charts has attracted wide attention. The hidden medical errors may cause increasing of adverse events such as infection, rehospitalization, and even death. Quickly and timely detecting abnormal changes of surgical performance helps reduce the probability of adverse events and improve health care quality. Most existing monitoring schemes focus on the binary surgical outcomes. However, continuous survival times of patients should be considered for more accurate monitoring. In this paper, a new exponentially weighted moving average (EWMA) control chart is proposed for monitoring continuous surgical outcomes. To describe surgical performance, a patient's actual survival time and predicted mortality are combined in an illustrative and interpretable way. Performance of the proposed chart is evaluated with different chart parameters under different shifts by a simulation study. We compare our chart with the risk-adjusted survival time cumulative sum chart, and the simulation results demonstrate that the proposed monitoring scheme has better efficiency. The implementation of the proposed chart is illustrated by a real example. Besides an analysis of the entire dataset, the surgical performance of each surgeon is monitored, because each of them has patients with different risk levels.     

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.     

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.     

Design of EWMA and CUSUM control charts subject to random shift sizes and quality impacts

Statistical process control charts are important tools for detecting process shifts. To ensure accurate, responsive fault detection, control chart design is critical. In the literature, control charts are typically designed by minimizing the control chart's responding time, i.e., average run length (ARL), to an anticipated shift size under a tolerable false alarm rate. However, process shifts, originating from various variation sources, often come with different sizes and result in different degrees of quality impacts. In this paper, we propose a new performance measure for EWMA and CUSUM control chart design to take into consideration the variable shift sizes and corresponding quality impacts. Unlike economic designs of control charts that suffer from a complex cost structure and intensive numerical computation, the proposed design methodology does not involve any cost estimation and the design procedure is as simple as looking up tables. Given the Gaussian random shifts and quadratic quality loss function, we show that the proposed design has a significant reduction in the quality impact as compared to conventional ARL-based designs. Guidelines and useful worksheets for practical implementation of the proposed designs are then suggested to practitioners with different knowledge levels of the process excursions.     

A Synthetic median control chart for monitoring the process mean with measurement errors

Recent studies show that the Shewhart median chart is widely used for detecting shifts in a process, but it is often rather inefficient in detecting small or moderate process shifts. In order to overcome this problem, a Synthetic chart can be used. This chart outperforms the Shewhart‐type chart because it uses the information about the time interval between two consecutive nonconforming samples. In this paper, we propose and study the Phase II Synthetic median control chart. A Markov chain methodology is used to evaluate the statistical performance of the proposed chart. Moreover, its performance is investigated in the presence of measurement errors, which are modelled by a linear covariate error model. We provide the results of an extensive numerical analysis with several tables and figures in order to show the statistical performance of the investigated chart, for both cases of measurement errors and no measurement errors. Finally, an example illustrates the use of the Synthetic median chart.