A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

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 control scheme integrating the T chart and TCUSUM chart

This article proposes an integrated scheme (T&TCUSUM chart) which combines a Shewhart T chart and a TCUSUM chart (a CUSUM‐type T chart) to monitor the time interval T between the occurrences of an event or the time between events. The performance studies show that the T&TCUSUM chart can effectively improve the overall performance over the entire T shift range. On average, it is more effective than the T chart by 26.66% and the TCUSUM chart by 14.12%. Moreover, the T&TCUSUM chart performs more consistently than other charts for the detection of either small or large T shifts, because it has the strength of both the T chart (more sensitive to large shifts) and the TCUSUM chart (more sensitive to small shifts). The implementation of the new chart is almost as easy as the operation of a TCUSUM chart. Copyright © 2010 John Wiley & Sons, Ltd.     

Novel design of composite generally weighted moving average and cumulative sum charts

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts are popular statistical tools to improve the performance of the Shewhart chart in detecting small process shifts. In this study, we propose the mixed generally weighted moving average (GWMA)‐CUSUM chart and its reverse‐order CUSUM‐GWMA chart to enhance detection ability compared with existing counterparts. The simulation revealed that the mixed GWMA‐CUSUM and mixed CUSUM‐GWMA charts have the sensitivity to detect small process shifts and efficient structures compared with the mixed EWMA‐CUSUM and mixed CUSUM‐EWMA charts, respectively. Moreover, the mixed GWMA‐CUSUM chart with a large design parameter has robust performance, regardless of the high tail t distribution or right skewness gamma distribution.     

A New Combined Shewhart–Cumulative Sum S Chart for Monitoring Process Standard Deviation

The combined application of a Shewhart chart and cumulative sum (CUSUM) control chart is an effective tool for the detection of all sizes of process shifts as the scheme combines the advantages of a CUSUM at detecting small to moderate shifts and Shewhart for the quick detection of very large shifts. This article proposes new combined Shewhart–CUSUM S charts based on the extreme variations of ranked set sampling technique, for efficient monitoring of changes in the process dispersion. Using Monte Carlo simulations, the combined scheme is designed to minimize the average extra quadratic loss over the entire process shift domain. The results show that the combined Shewhart–CUSUM S charts uniformly outperform several other procedures for detecting increases and decreases in the process variability. Moreover, the proposed scheme can detect changes that are small enough to escape the Shewhart S chart or fairly large to escape detection by the CUSUM S chart. Numerical example is given to illustrate the practical application of the proposed scheme using real industrial data. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal design of one-sided exponential cumulative sum charts with known and estimated parameters based on the median run length

As a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high-quality processes. Considering both known and estimated parameter cases, the one-sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run length (RL ) distribution of the one-sided exponential CUSUM charts is skewed and it also changes with the mean shift size and the number of Phase I samples used to estimate the process parameter, the median run length (MRL ) is employed as a good alternative performance measure for the charts. The optimal design procedures based on MRL of the one-sided exponential CUSUM charts with known and estimated parameters are discussed. By comparing the MRL performance of the chart with known parameters with the one of the chart with estimated parameters, we investigate the effect of estimated process parameters on the properties of the chart. Finally, an application is illustrated to show the implementation of the chart.     

Multivariate statistical process control charts based on the approximate sequential χ2 test

Similar to the univariate CUSUM chart, a multivariate CUSUM (MCUSUM) chart can be designed to detect a particular size of the mean shift optimally based on the scheme of a sequential likelihood ratio test for the noncentrality parameter. However, in multivariate case, the probability ratio of a sequential test is intractable mathematically and the test statistic based on the ratio does not have a closed form expression which makes it impractical for real application. We drive an approximate log-likelihood ratio and propose a multivariate statistical process control chart based on a sequential χ² test to detect a change in the noncentrality parameter. The statistical properties of the proposed test statistic are explored. The average runs length (ARL) performance of the proposed charts is compared with other MCUSUM charts for process mean monitoring. The experimental results reveal that the proposed charts achieve superior, both zero-state and steady-state, ARL performance over a wide range of mean shifts, especially when the dimension of measurements is large.     

Using FIR to Improve CUSUM Charts for Monitoring Process Dispersion

Statistical process control deals with monitoring process to detect disturbances in the process. These disturbances may be from the process mean or variance. In this study, we propose some charts that are efficient for detecting early shifts in dispersion parameter, by applying the Fast Initial Response feature. Performance measures such as average run length, standard deviation of the run length, extra quadratic loss, relative average run length, and performance comparison index are used to compare the proposed charts with their existing counterparts, including the Shewhart R chart and the Shewhart S chart with and without warning lines. Others include the CUSUM R chart, the CUSUM S chart, the EWMA of ln S², the CUSUM of ln S², the P_σ CUSUM, the χ CUSUM, and the Change Point (CP) CUSUM charts. The proposed charts do not only detect early shifts in the process dispersion faster, but also have better overall performance than their existing counterparts. Copyright © 2016 John Wiley & Sons, Ltd.     

CUSUM charts for monitoring a zero‐inflated poisson process

A zero‐inflated Poisson (ZIP) process is different from a standard Poisson process in that it results in a greater number of zeros. It can be used to model defect counts in manufacturing processes with occasional occurrences of non‐conforming products. ZIP models have been developed assuming that random shocks occur independently with probability p, and the number of non‐conformities in a product subject to a random shock follows a Poisson distribution with parameter λ. In our paper, a control charting procedure using a combination of two cumulative sum (CUSUM) charts is proposed for monitoring increases in the two parameters of the ZIP process. Furthermore, we consider a single CUSUM chart for detecting simultaneous increases in the two parameters. Simulation results show that a ZIP‐Shewhart chart is insensitive to shifts in p and smaller shifts in λ in terms of the average number of observations to signal. Comparisons between the combined CUSUM method and the single CUSUM chart show that the latter's performance is worse when there are only increases in p, but better when there are only increases in λ or when both parameters increase. The combined CUSUM method, however, is much better than the single CUSUM chart when one parameter increases while the other decreases. Finally, we present a case study from the light‐emitting diode packaging industry. Copyright © 2011 John Wiley & Sons, Ltd.     

Memory‐Type Control Charts for Monitoring the Process Dispersion

Control charts have been broadly used for monitoring the process mean and dispersion. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are memory control charts as they utilize the past information in setting up the control structure. This makes CUSUM and EWMA‐type charts good at detecting small disturbances in the process. This article proposes two new memory control charts for monitoring process dispersion, named as floating T ? S² and floating U ? S² control charts, respectively. The average run length (ARL) performance of the proposed charts is evaluated through a simulation study and is also compared with the CUSUM and EWMA charts for process dispersion. It is found that the proposed charts are better in detecting both positive as well as negative shifts. An additional comparison shows that the floating U ? S² chart has slightly smaller ARLs for larger shifts, while for smaller shifts, the floating T ? S² chart has better performance. An example is also provided which shows the application of the proposed charts on simulated datasets. Copyright © 2013 John Wiley & Sons, Ltd.     

Monitoring of zero-inflated Poisson processes with EWMA and DEWMA control charts

The zero-inflated Poisson (ZIP) distribution is an extension of the ordinary Poisson distribution and is used to model count data with an excessive number of zeros. In ZIP models, it is assumed that random shocks occur with probability p, and upon the occurrence of random shock, the number of nonconformities in a product follows the Poisson distribution with parameter λ. In this article, we study in more detail the exponentially weighted moving average control chart based on the ZIP distribution (regarded as ZIP-EWMA) and we also propose a double EWMA chart with an upper time-varying control limit to monitor ZIP processes (regarded as ZIP-DEWMA chart). The two charts are studied to detect upward shifts not only in each parameter individually but also in both parameters simultaneously. The steady-state performance and the performance with estimated parameters are also investigated. The performance of the two charts has been evaluated in terms of the average and standard deviation of the run length, and compared with Shewhart-type and CUSUM schemes for ZIP distribution, it is shown that the proposed chart is very effective especially in detecting shifts in p when λ remains in control (IC) and in both parameters simultaneously. Finally, one real example is given to display the application of the ZIP charts on practitioners.     

Probabilities on Algebraic Structures

Time-between-events (TBE) charts or T charts have attracted increasing research interest in statistical process control (SPC). These charts monitor TBE or the time interval T between the events. Currently, almost all studies on T charts are focused on applications under 100% inspection. However, due to limitations in resources and working conditions, sampling inspection has to be adopted for many SPC applications, especially when testing is destructive and/or expensive. The operational characteristics of T charts under sampling inspection could be quite different from those under 100% inspection. Specifically, some highly efficient techniques or methods, such as sequential analysis, may be adopted for sampling inspection. This article studies four T charts for sampling inspection: (1) a Shewhart T chart; (2) a CUSUM T chart and its variable sample size version; (3) a SA T chart (the T chart using sequential analysis); and (4) a curtailed SA T chart. It is the first time that sequential analysis and curtailment technique are adopted for TBE control charts. It is found that these SA-type charts, especially the curtailed chart, are significantly more effective than the Shewhart T chart, CUSUM T chart, and any other charts in current literature. This article has supplementary material online.     

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.     

Binomial CUSUM chart with curtailment

The binomial cumulative sum (CUSUM) chart has been widely used to monitor the fraction nonconforming (p) of a process. It is a powerful procedure for detecting small and moderate p shifts. This article proposes a binomial CUSUM control chart using curtailment technique (Curt_CUSUM chart in short). The new chart is able to improve the overall detection effectiveness while holding the false alarm rate at a specified level. The results of the comparative studies show that, on average, the Curt_CUSUM chart is more effective than the CUSUM chart without curtailment by 30%, in terms of Average Number of Defectives, under different circumstances. The Curt_CUSUM chart can be applied to a 100% inspection as well as a general random sampling inspection.     

Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals

Recent research has shown that adaptive control charts and the CUmulative SUM (CUSUM) schemes are quicker in detecting process shifts than traditional static Shewhart charts. This article proposes a weighted loss function CUSUM (WLC) scheme with Variable Sampling Intervals (VSI). It simultaneously monitors both mean shifts and an increasing variance shift by manipulating a single CUSUM chart. Most importantly, this VSI WLC scheme is much easier to operate and design than a VSI CCC scheme which comprises of three CUSUM charts (two of them monitoring the increasing and decreasing mean shifts and one monitoring the increasing variance shift). In terms of detection efficiency, the VSI WLC scheme is a much more powerful tool than the static X&S chart, the VSI X&S chart and the static WLC scheme. It is even more powerful than the VSI CCC scheme for many different combinations of mean and increasing variance shifts.     

A comparative study of the CRL‐type control charts

The CRL (Conforming Run Length) type control charts have attracted increasing interest recently for attribute Statistical Process Control (SPC). The two most promising charts of this type are identified as the CRL‐CUSUM chart and the SCRL (Sum of CRLs) chart. This article compares the operating characteristics of these two charts in a comprehensive manner. The general findings reveal that the CRL‐CUSUM chart excels the SCRL chart in detecting downward (decreasing) fraction nonconforming (p) shifts and large‐scale upward (increasing) p shifts. However, the SCRL chart is superior to the CRL‐CUSUM chart in detecting the small and moderate scale upward p shifts, especially when the normal p value is small. The information acquired in this study will provide Quality Assurance (QA) engineers with useful guidance for selecting and applying the CRL‐type control charts. Copyright © 2000 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.     

CUSUM control charts with variable sampling interval for monitoring the ratio of two normal variables

In many industrial manufacturing processes, the ratio between two normal random variables plays a key role in ensuring quality of products. Thus,  monitoring this ratio is an important task that is well worth considering. In this paper, we combine a variable sampling interval (VSI) strategy with a cumulative sum (CUSUM) scheme to create a new type of control chart for purpose of tracking the ratio between two normal variables. The average time to signal (ATS) and the expected average time to signal (EATS) criteria are used to evaluate the performance of the new VSI CUSUM RZ control chart. The  numerical results show that the proposed control chart has much more attractive performance in comparison with the standard CUSUM-RZ control chart and the VSI EWMA-RZ control chart.     

A CUSUM chart for detecting the intensity ratio of negative events

This paper developed a single cumulative sum (CUSUM) scheme, called the UCUSUM chart, for simultaneously detecting the size N and time interval T of an event. The new chart used the information of size and frequency of the event and the UCUSUM chart is carried out using the only one statistic U, which contains both T and N; on the other hand, the UCUSUM chart could allocate the detection power to the T shifts and the N shifts. The results present that the UCUSUM chart is significantly powerful compared to other charts which are in the current research with either the time interval T or with the size N. The UCUSUM chart could be applied in many areas including industries and non-industries and the performance of the new chart shows it is much effective in example.     

An Adaptive CUSUM Chart with Single Sample Size for Monitoring Process Mean and Variance

This article proposes an adaptive absolute cumulative sum chart (called the adaptive ACUSUM chart) for statistical process control. The new development includes the variable sampling interval (VSI), variable sample size (VSS) and VSS and interval (VSSI) versions, all of which are highly effective for monitoring the mean and variance of a variable x by inspecting the absolute sample shift (where μ₀ is the in‐control mean or target value of x). While the adaptive ACUSUM chart is a straightforward extension of the ABS CUSUM chart developed by Wu, et al., it is much more effective than all other adaptive CUSUM charts. Noteworthily, the superiority of VSI ACUSUM chart over the best adaptive CUSUM chart in literature is about 35% from an overall viewpoint. Moreover, the design and implementation of the adaptive ACUSUM chart are much simpler than that of all other adaptive CUSUM schemes. All these desirable features of the adaptive ACUSUM chart may be attributable to the use of a single sample size (n = 1). Another quite interesting finding is that the simpler VSI ACUSUM chart works equally well as the more complicated VSSI ACUSUM chart. Copyright © 2012 John Wiley & Sons, Ltd.