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.     

Space–time surveillance of count data subject to linear trends

This paper proposes a new space–time cumulative sum (CUSUM) approach for detecting changes in spatially distributed Poisson count data subject to linear drifts. We develop expressions for the likelihood ratio test monitoring statistics and the change point estimators. The effectiveness of the proposed monitoring approach in detecting and identifying trend-type shifts is studied by simulation under various shift scenarios in regional counts. It is shown that designing the space–time monitoring approach specifically for linear trends can enhance the change point estimation accuracy significantly. A case study for male thyroid cancer outbreak detection is presented to illustrate the application of the proposed methodology in public health surveillance.     

New control charts for monitoring the Weibull percentiles under complete data and Type‐II censoring

In this paper, we propose 3 new control charts for monitoring the lower Weibull percentiles under complete data and Type‐II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA‐SEV‐Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM‐SEV‐Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA‐YP and CUSUM‐YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA‐YP and CUSUM‐YP control charts perform better than the EWMA‐SEV‐Q and CUSUM‐SEV‐Q control charts in terms of average run length. In Type‐II censoring, the EWMA‐SEV‐Q chart is slightly better than the CUSUM‐SEV‐Q chart in terms of average run length. Two numerical examples are used to illustrate the applications of the proposed control charts.     

New CUSUM and Shewhart-CUSUM charts for monitoring the process mean

The CUmulative SUM (CUSUM) charts have sensitive nature against small and moderate shifts that occur in the process parameter(s). In this article, we propose the CUSUM and combined Shewhart-CUSUM charts for monitoring the process mean using the best linear unbiased estimator of the location parameter based on ordered double-ranked set sampling (RSS) scheme, where the CUSUM chart refers to the Crosier's CUSUM chart. The run-length characteristics of the proposed CUSUM charts are computed with the Monte Carlo simulations. The run-length profiles of the proposed CUSUM charts are compared with those of the CUSUM charts based on simple random sampling, RSS, and ordered RSS schemes. It is found that the proposed CUSUM charts uniformly outperform their existing counterparts when detecting all different kinds of shifts in the process mean. A real data set is also considered to explain the implementation of the proposed CUSUM charts.     

Process monitoring with ICA‐based signal extraction technique and CART approach

In order to reduce the variation in a manufacturing process, traditional statistical process control (SPC) techniques are the most frequently used tools in monitoring engineering process control (EPC)‐controlled processes for detecting assignable cause process variation. Even though application of SPC with EPC can successfully detect time points when abnormalities occur during process, their combination can also cause an increased occurrence of false alarms when autocorrelation is present in the process. In this paper, we propose an independent component analysis‐based signal extraction technique with classification and regression tree approach to identify disturbance levels in the correlated process parameters. For comparison, traditional cumulative sum (CUSUM) chart was constructed to evaluate the identifying capability of the proposed approach. The experimental results show that the proposed method outperforms CUSUM control chart in most instances. Copyright © 2008 John Wiley & Sons, Ltd.     

Monitoring Bernoulli processes considering measurement errors and learning effect

This paper presents the effect of measurement errors and learning on monitoring processes with individual Bernoulli observations. A cumulative sum control chart is considered to evaluate the possible impacts of measurement errors and learning. We propose a time‐dependent learning effect model along with measurement errors and incorporate them into the Bernoulli CUSUM control chart statistic. The performance of the Bernoulli CUSUM control chart is then merely assessed by comparing the average number of observations to signal (ANOS) under two proposed conditions with the condition of no possible errors. Thus, the ANOS values are obtained under different proportions of non‐conforming items, once considering errors due to measurement by inspectors, and once considering both errors and learning effect together. The experimental results show that the efficiency of the control chart to detect assignable causes deteriorates in the presence of measurement errors and enhances when learning affects operators' performance. The proposed approach has a potential to be used in monitoring high‐quality Bernoulli processes as well as disease diagnosis, and other health care applications with Bernoulli observations.     

Detection of linear trends in process mean

In this paper, we develop a process control approach to detect linear trends in the process mean. A statistic based on the deviation between the target mean and the expected mean of the process is used in the development of the new approach. The statistic is shown to have a chi-square distribution. The approach is described and its performance is compared with cumulative sum (CUSUM), exponentially weighted moving average (EWMA), Shewhart, and generalized likelihood ratio (GLR) charts in detecting linear trends in the process mean. The results indicate that proposed approach is effective in detecting small to large trends. We also investigate the run length properties of the proposed approach under linear trends and compare its values with simulation results. Finally, we analyse the performance of the proposed approach in detecting the time when a drift occurs in the process and compare it with CUSUM and EWMA estimators. The results show that the proposed approach is more effective in detecting drift time for moderate and large trends.     

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.     

New GWMA‐CUSUM control chart for monitoring the process dispersion

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely accepted because of their fantastic speed in identifying small‐to‐moderate unusual variations in the process parameter(s). Recently, a new CUSUM chart has been proposed that uses the EWMA statistic, called the CS‐EWMA chart, for monitoring the process variability. On similar lines, in order to further improve the detection ability of the CS‐EWMA chart, we propose a CUSUM chart using the generally weighted moving average (GWMA) statistic, named the GWMA‐CUSUM chart, for monitoring the process dispersion. Monte Carlo simulations are used to compute the run length profiles of the GWMA‐CUSUM chart. On the basis of the run length comparisons, it turns out that the GWMA‐CUSUM chart outperforms the CUSUM and CS‐EWMA charts when identifying small variations in the process variability. A simulated dataset is also used to explain the working and implementation of the CS‐EWMA and GWMA‐CUSUM charts.     

Two CUSUM schemes for simultaneous monitoring of parameters of a shifted exponential time to events

Two‐parameter (shifted) exponential distribution is widely applied in many areas such as reliability modeling and analysis where time to failure is protected by a guaranty period that induces an origin parameter in the exponential model. Despite a large volume of works on inferential aspects of two‐parameter exponential distribution, only few studies are done from the perspective of process monitoring. In the modern production process, where items come with a warranty, we often encounter shifted‐exponential time between events from consumers' perspective, and therefore, in this paper, we propose two CUSUM schemes for joint monitoring of the origin and scale parameters based on the Maximum Likelihood estimators. We study the in‐control behavior of the proposed procedures via Markov chain approach as well as applying Monte Carlo. We provide detailed implementation strategies of the two schemes along with the follow‐up procedures to identify the source of shifts when an out‐of‐control signal is obtained. We examine the performance properties of CUSUM schemes and find that the two proposed schemes offer performance advantages over the Shewhart‐type schemes especially for monitoring small to moderate shifts. Further, we provide some guidance for choosing the appropriate schemes and study the effect of reference parameter k of the CUSUM schemes. We also investigate the optimal design of reference values both in known and unknown shift cases. Finally, two examples are given to illustrate the implementation of the proposed approach.     

A New Rank‐based Multivariate CUSUM Approach for Monitoring the Process Mean

In many cases, data do not follow a specific probability distribution in practice. As a result, a variety of distribution‐free control charts have been developed to monitor changes in the processes. An existing rank‐based multivariate cumulative sum (CUSUM) procedure based on the antirank vector does not quickly detect the large shift levels of the process mean. In this paper, we explore and develop an improved version of the existing rank‐based multivariate CUSUM procedure in order to overcome the difficulty. The numerical experiments show that the proposed approach dramatically outperforms the existing rank‐based multivariate CUSUM procedure in terms of the out‐of‐control average run length. In addition, the proposed approach particularly resolves the critical problem of the original approach, which occurs in the simultaneous shifts whose components are all the same but not 0. We believe that the proposed approach can be utilized for monitoring real data. Copyright © 2015 John Wiley & Sons, Ltd.     

Phase II monitoring of survival times with categorical covariates

Monitoring surgical outcomes is of paramount importance especially by accounting for health conditions of the patients prior to surgery. However, the problem arises as the effect of some covariates is pronounced but cannot be measured. In this paper, in order to deal with the effect of measured and unmeasured (categorical) covariates simultaneously, a class of survival analysis regression models called accelerated failure time (AFT) model and discrete frailty models is integrated and some Phase II risk-adjusted control schemes are devised to monitor the patients' lifetime. Three monitoring procedures including the cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and probability limits-based control charts are developed in the presence and absence of censored observations. The performance analysis reveals that the proposed AFT frailty-based CUSUM control chart outweighs the competing counterparts in detecting shifts under various scenarios. Subsequently, two CUSUM control charts have been constructed corresponding to the cases of neglecting both the unmeasured and measured covariates and ignoring just the unmeasured covariate. The results clearly indicate that the detection ability for both of the mentioned CUSUM control charts declines, and including the unmeasured and measured covariates is critical while monitoring surgical outcomes. Finally, a real case study in a cardiac surgical center in the United Kingdom has been provided to investigate the application of the proposed AFT frailty-based CUSUM control scheme.     

Improving the Performance of Combined Shewhart–Cumulative Sum Control Charts

For an improved monitoring of process parameters, it is generally desirable to have efficient designs of control charting structures. The addition of Shewhart control limits to the cumulative sum (CUSUM) control chart is a simple monitoring scheme sensitive to wide range of mean shifts. To improve the detection ability of the combined Shewhart–CUSUM control chart to off‐target processes, we developed the scheme using ranked set sampling instead of the traditional simple random sampling. We investigated the run length properties of the Shewhart–CUSUM with ranked set samples and compared their performance with certain established control charts. It is revealed that the proposed schemes offer better protection against different types of mean shifts than the existing counterparts including classical Shewhart, classical CUSUM, classical combined Shewhart–CUSUM, adaptive CUSUM, double CUSUM, three simultaneous CUSUM, combined Shewhart‐weighted CUSUM, runs rules‐based CUSUM and the mixed exponentially weighted moving average‐CUSUM. Applications on real data sets are also given to demonstrate the implementation simplicity of the proposed schemes Copyright © 2012 John Wiley & Sons, Ltd.     

A general approach to modeling CUSUM charts for a proportion

This paper considers two CUmulative SUM (CUSUM) charts for monitoring a process when items from the process are inspected and classified into one of two categories, namely defective or non-defective. The purpose of this type of process monitoring is to detect changes in the proportion p of items in the first category. The first CUSUM chart considered is based on the binomial variables resulting from counting the total number of defective items in samples of n items. A point is plotted on this binomial CUSUM chart after n items have been inspected. The second CUSUM chart considered is based on the Bernoulli observations corresponding to the inspection of the individual items in the samples. A point is plotted on this Bernoulli CUSUM chart after each individual inspection, without waiting until the end of a sample. The main objective of the paper is to evaluate the statistical properties of these two CUSUM charts under a general model for process sampling and for the occurrence of special causes that change the value of p. This model applies to situations in which there are inspection periods when n items are inspected and non-inspection periods when no inspection is done. This model assumes that there is a positive time between individual inspection results, and that a change in p can occur anywhere within an inspection period or a non-inspection period. This includes the possibility that a shift can occur during the time that a sample of n items is being taken. This model is more general and often more realistic than the simpler model usually used to evaluate properties of control charts. Under our model, it is shown that there is little difference between the binomial CUSUM chart and the Bernoulli CUSUM chart, in terms of the expected time required to detect small and moderate shifts in p, but the Bernoulli CUSUM chart is better for detecting large shifts in p. It is shown that it is best to choose a relatively small sample size when applying the CUSUM charts. As expected, the CUSUM charts are substantially faster than the traditional Shewhart p-chart for detecting small shifts in p. But, surprisingly, the CUSUM charts are also better than the p-chart for detecting large shifts in p.     

A magnitude‐robust control chart for monitoring and estimating step changes for normal process means

Statistical process control charts are intended to assist operators of a usually stable system in monitoring whether a change has occurred in the process. When a change does occur, the control chart should detect it quickly. If the operator can also be provided information that aids in the search for the special cause, then critical off‐line time can be saved. We investigate a process‐monitoring tool that not only provides speedy detection regardless of the magnitude of the process shift, but also supplies useful change point statistics. A likelihood ratio approach can be used to develop a control chart for permanent step change shifts of a normal process mean. The average run length performance for this chart is compared to that of several cumulative sum (CUSUM) charts. Our performance comparisons show that this chart performs better than any one CUSUM chart over an entire range of potential shift magnitudes. The likelihood ratio approach also provides point and interval estimates for the time and magnitude of the process shift. These crucial change‐point diagnostics can greatly enhance special cause investigation. Copyright © 2002 John Wiley & Sons, Ltd.     

A distribution-free CUSUM chart for joint monitoring of location and scale based on the combination of Wilcoxon and Mood statistics

We propose a distribution-free cumulative sum (CUSUM) chart for joint monitoring of location and scale based on a Lepage-type statistic that combines the Wilcoxon rank sum and the Mood statistics. Monte Carlo simulations were used to obtain control limits and examine the in-control and out-of-control performance of the new chart. A direct comparison of the new chart was made with the original CUSUM Lepage based on Wilcoxon rank sum and Ansari-Bradley statistics. The result is a more powerful chart in most of the considered scenarios and thus a more useful CUSUM chart. An example using real data illustrates how the proposed control chart can be implemented.     

A Copula Markov CUSUM Chart for Monitoring the Bivariate Auto‐correlated Binary Observations

Although in the statistical process control (SPC) literature, there are considerable number of researches related to the multivariates variables control charting (focusing on the variable quality characteristics), fewer investigations could be found regarding the multivariate attributes control charts (relying on the attribute quality characteristics). More specifically considering the multivariate attributes control charting, it would be more interesting to monitor the auto‐correlated data, since the real‐world processes usually include the data based on an auto‐correlation structure. Ignoring the auto‐correlation structure in developing a multivariate control chart increases the type I and type II errors simultaneously and consequently reduces the performance of the chart. The most important difficulty with developing multivariate attributes control charts is the absence of the joint distribution for the quality characteristics. This deficiency can be dispelled through the use of the copula approach for developing the joint distribution. In this paper, we use the Markov approach for modeling the auto‐correlated data. Then, the copula approach is used to make the joint distribution of two auto‐correlated binary data series. Finally, based on this joint distribution, we develop a cumulative sum (CUSUM) chart. Hence, the proposed chart is entitled the copula Markov CUSUM chart. The proposed control chart is compared with the most recent and effective existing one in the literature. Based on the average number of observations to signal (ANOS) measure, it is considered that the developed control chart performs better than the other one. In addition, a real case study related to two correlated diseases such as the Type 2 Diabetes Mellitus and the Obesity, in which each has an auto‐correlated structure, is investigated to verify the applicability of the control chart. Copyright © 2012 John Wiley & Sons, Ltd.     

Directionally sensitive weighted adaptive multivariate CUSUM mean charts

In many service and manufacturing industries, process monitoring involves multivariate data, instead of univariate data. In these situations, multivariate charts are employed for process monitoring. Very often when the mean vector shifts to an out-of-control situation, the exact shift size is unknown; hence, multivariate charts for monitoring a range of the mean shift sizes in the mean vector are adopted. In this paper, directionally sensitive weighted adaptive multivariate CUSUM charts are developed for monitoring a range of the mean shift sizes. Directionally sensitive charts are useful in situations where the aim lies in monitoring either an increasing or a decreasing shift in the mean vector of the quality characteristics of interest. The Monte Carlo simulation is used to compute the run length characteristics in comparing the sensitivities of the proposed and existing multivariate CUSUM charts. In general, the directionally sensitive and weighted adaptive features enhance the sensitivities of the proposed multivariate CUSUM charts in comparison with the existing multivariate CUSUM charts without the adaptive feature or those that are directionally invariant. It is also found that the variable sampling interval feature enhances the sensitivities of the proposed and existing charts as compared to their fixed sampling interval counterparts. The implementation of the proposed charts in detecting upward and downward shifts in the in-control process mean vector is demonstrated using two different datasets.     

Conditional mean- and median-based cumulative sum control charts for Weibull data

This article deals with the monitoring of censored data using the cumulative sum (CUSUM) control charts for Weibull lifetimes under type-I censoring. To develop an efficient CUSUM structure for censored data, we use the conditional expected value (CEV) and conditional median (CM) approaches. In particular, we focus on the detection of shifts in the mean of Weibull lifetimes assuming censored data. In addition to fixed/known parameter values, the effect of estimation is assessed on the detection power of control charts. The performance of the proposed charts is evaluated by the average run length (ARL). Furthermore, the ARL performance of CUSUM charts is compared with CEV- and CM-based exponentially weighted moving average (EWMA) control charts. Besides an extensive simulation study, the significance of the current work is illustrated by a data set on the response time of a thermostat experiment.