An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

We evaluate the performance of the Crosier's cumulative sum (C‐CUSUM) control chart when the probability distribution parameters of the underlying quality characteristic are estimated from Phase I data. Because the average run length (ARL) under estimated parameters is a random variable, we study the estimation effect on the chart performance in terms of the expected value of the average run length (AARL) and the standard deviation of the average run length (SDARL). Previous evaluations of this control chart were conducted while assuming known process parameters. Using the Markov chain and simulation approaches, we evaluate the in‐control performance of the chart and provide some quantiles for its in‐control ARL distribution under estimated parameters. We also compare the performance of the C‐CUSUM chart to that of the ordinary CUSUM (O‐CUSUM) chart when the process parameters are unknown. Our results show that large number of Phase I samples are required to achieve a quite reasonable performance. Additionally, the performance of the C‐CUSUM chart is found to be superior to that of the O‐CUSUM chart. Finally, we recommend the use of a recently proposed bootstrap procedure in designing the C‐CUSUM chart to guarantee, at a certain probability, that the in‐control ARL will be of at least the desired value using the available amount of Phase I data. Copyright © 2015 John Wiley & Sons, Ltd.     

Bridging the gap between theory and practice in basic statistical process monitoring

ABSTRACT

Some issues are discussed relative to the gap between theory and practice in the area of statistical process monitoring (SPM). Among other issues, it is argued that the collection and use of baseline data in Phase I needs a greater emphasis. Also, the use of sample ranges in practice to estimate process standard deviations deserves reconsideration. A discussion is given on the role of modeling in SPM. Then some work on profile monitoring and the effect of estimation error on Phase II chart performance is summarized. Finally, some ways that researchers could influence practice more effectively are discussed along with how SPM research could become more useful to practitioners.     

Dynamic probability control limits for CUSUM charts for monitoring proportions with time-varying sample sizes

We consider the problem of monitoring a proportion with time-varying sample sizes. Control charts are generally designed by assuming a fixed sample size or a priori knowledge of a sample size probability distribution. Sometimes, it is not possible to know, or accurately estimate, a sample size distribution or the distribution may change over time. An improper assumption for the sample size distribution could lead to undesirable performance of the control chart. To handle this problem, we propose the use of dynamic probability control limits (DPCLs) which are determined successively as the sample sizes become known. The method is based on keeping the conditional probability of a false alarm at a predetermined level given that there has not been any earlier false alarm. The control limits dynamically change, and the in-control performance of the chart can be controlled at the desired level for any sequence of sample sizes. The simulation results support this result showing that there is no need for any assumption of a sample size distribution with the use of this proposed approach.     

一种恒虚警线谱检测算法研究

提出基于高低分辨率功率谱匹配度估计的线谱检测算法,该算法对信号分别进行高分辨率功率谱估计和多段低分辨率功率谱估计,然后以高分辨率功率谱估计为模板,用多段低分辨率功率谱估计进行校验的方式进行线谱检测。基于单频信号加高斯白噪声假设条件,理论上导出该检测方法的检测率和虚警率,并进行了仿真验证。与传统的线谱检测方法相比,该线谱检测算法不需要预知噪声功率谱,且具有恒虚警的特点。在车辆目标远距离声学检测应用中,该检测算法具有较好的检测性能。     

Estimating the Change Point of the Process Fraction Non‐conforming with a Monotonic Change Disturbance in SPC

Knowing when a process has changed would simplify the search for and identification of the special cause. In this paper, we propose a maximum‐likelihood estimator for the change point of the process fraction non‐conforming without requiring knowledge of the exact change type a priori. Instead, we assume the type of change present belongs to a family of monotonic changes. We compare the proposed change‐point estimator to the maximum‐likelihood estimator for the process change point derived under a simple step change assumption. We do this for a number of monotonic change types and following a signal from a binomial cumulative sum (CUSUM) control chart. We conclude that it is better to use the proposed change point estimator when the type of change present is only known to be monotonic. The results show that the proposed estimator provides process engineers with an accurate and useful estimate of the time of the process change regardless of the type of monotonic change that may be present. Copyright © 2006 John Wiley & Sons, Ltd.     

A head-to-head comparative study of the conditional performance of control charts based on estimated parameters

Implementation of the Shewhart, CUSUM, and EWMA charts requires estimates of the in-control process parameters. Many researchers have shown that estimation error strongly influences the performance of these charts. However, a given amount of estimation error may differ in effect across charts. Therefore, we perform a pairwise comparison of the effect of estimation error across these charts. We conclude that the Shewhart chart is more strongly affected by estimation error than the CUSUM and EWMA charts. Furthermore, we show that the general belief that the CUSUM and EWMA charts have similar performance no longer holds under estimated parameters.     

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.     

Transferring biological sequence analysis tools to break-point detection for on-line monitoring: A control chart based on the local score

The Lindley process defined for the queuing file domain is equivalent to the cumulative sum (CUSUM) process used for break-point detection in process control. The maximum of the Lindley process, called local score, is used to highlight atypical regions in biological sequences, and its distribution has been established by different manners. I propose here to use the local score and also a partial maximum of the Lindley process over the immediate past to create control charts. Stopping time corresponds to the first time where the statistic achieves a statistical significance less than a given threshold α in ]0,1[, the instantaneous first error rate. The local score p value is computed using existing theoretical results. I establish here the exact distribution of the partial maximum of the Lindley process. Performance of the control charts is evaluated by Monte Carlo estimation of the average run lengths for an in-control process (ARL₀) and for an out-of-control process (ARL₁). I also use the standard deviation of the run length (SdRL) and the extra quadratic loss (EQL). Comparison with the usual and recent control charts present in the literature shows that the local score control chart outperforms the others with a much larger ARL₀ and ARL₁ smaller or of the same order. Many interesting openings exist for the local score chart: not only Gaussian model but also any of them, Markovian dependance of the data, both location and dispersion monitoring at the same time can be considered.     

统计过程控制在微电脑控制器生产中的应用:案例研究

以某电子集团生产的某类型控制器的实际生产为例,采用因果分析法对其生产过程中造成质量缺陷的原因从5M1E(人、机、料、法、测、环)方面进行综合分析.通过对其测量系统进行监控,在其稳定可靠的情况下采集数据.运用SPC技术对波峰焊工序进行控制图监控,对失控原因进行分析并在线调整.有效地保证了控制器的质量,为其质量改善指明了方向.     

A CUSUM scheme with variable sample sizes and sampling intervals for monitoring the process mean and variance

The adaptive control feature and CUSUM chart are two monitoring schemes that are much more effective than the traditional static Shewhart chart in detecting process shifts in mean and variance. However, the designs and analyses of the adaptive CUSUM chart are mathematically intractable and the operation is very laborious. This article proposes a VSSI WLC scheme, which is a weighted‐loss‐function‐based CUSUM (WLC) scheme using variable sample sizes and sampling intervals (VSSI). This scheme detects the two‐sided mean shift and increasing standard deviation shift based on a single statistic WL (the weighted loss function). Most importantly, the VSSI WLC scheme is much easier to operate and design than a VSSI CCC scheme which comprises three individual CUSUM charts (two of them monitoring the increasing and decreasing mean shifts and one monitoring the increasing variance shift). Overall, the VSSI WLC scheme is much more effective than the static &S charts (by 72.36%), the VSSI &S charts (by 30.97%) and the static WLC scheme (by 50.94%) for detection. It is even more effective than the complicated VSSI CCC scheme for most cases. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating the time of step change with Poisson CUSUM and EWMA control charts

Knowing when a process has changed would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. Much of the literature on change point models and techniques for statistical process control applications consider processes well modelled by the normal distribution. However, the Poisson distribution is commonly used in industrial quality control applications for modelling attribute-based process quality characteristics (e.g., counts of non-conformities). Some commonly used control charts for monitoring Poisson distributed data are the Poisson cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts. In this paper, we study the effect of changes in the design of the control chart on the performances of the change point estimators offered by these procedures. In particular, we compare root mean square error performances of the change point estimators offered by the Poisson CUSUM and EWMA control charts relative to that achieved by a maximum likelihood estimator for the process change point. Results indicate that the relative performance achieved by each change point estimator is a function of the corresponding control chart design. Relative mean index plots are provided to enable users of these control charts to choose a control chart design and change point estimator combination that will yield robust change point estimation performance across a range of potential change magnitudes.     

A clustering approach to identify the time of a step change in Shewhart control charts

Control charts are the most popular statistical process control tools used to monitor process changes. When a control chart indicates an out‐of‐control signal it means that the process has changed. However, control chart signals do not indicate the real time of process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifying the real time of the change is known as the change‐point estimation problem. Most of the traditional methods of estimating the process change point are developed based on the assumption that the process follows a normal distribution with known parameters, which is seldom true. In this paper, we propose clustering techniques to estimate Shewhart control chart change points. The proposed approach does not depend on the true values of the parameters and even the distribution of the process variables. Accordingly, it is applicable to both phase‐I and phase‐II of normal and non‐normal processes. At the end, we discuss the performance of the proposed method in comparison with the traditional procedures through extensive simulation studies. Copyright © 2008 John Wiley & Sons, Ltd.     

Simultaneous Monitoring of Sample and Group Autocorrelations

Most statistical process control (SPC) methods for detecting the presence of special causes of variation when process observations are inherently autocorrelated are focused on studying changes in the mean or variance of a time series. It is seldom emphasized in the quality literature that the presence of special causes of variation is manifested not only by the changes in mean or variance of a time series but also by the changes in its stochastic behavior. An approach to detect this type of change can be based on the sample autocorrelation function (ACF) or the Ljung-Box-Pierce portmanteau statistic applied to the residuals of the chosen time series model. In this article, we discuss the reasons why the residual ACF and portmanteau statistic give different sensitivities in terms of testing model adequacy and, hence, of detecting changes in stochastic behavior of a process. The problem is shown to be related to the multivariate SPC problem of deciding whether to monitor the individual observations using separate control charts or Hotelling's T² statistic. Here, we present a graphical scheme for simultaneously monitoring the residual ACF and the portmanteau statistic.     

Phase I process monitoring: The case of the balanced one-way random effects model

Phase I is crucial for the success of the overall statistical process control (SPC) and monitoring regime. Shewhart-type charts are recommended in this phase because of their broader shift detection ability. In this paper, a Phase I Shewhart-type $\overline{X}$ chart is considered for the balanced random effects (also called a variance components) model. The proposed methodology takes proper account of the effects of parameter estimation and uses the false alarm probability (FAP) metric to design the chart. In the sequel, the corrected (adjusted) charting constants are calculated and tabulated. The constant can be found, on demand, from an accompanying R package. Motivations and illustrations with some real data are provided. Performance of the chart is examined in terms of in-control robustness and detection of nonhomogeneity (out-of-control). The proposed chart is shown to be easily adaptable to more general models, with more variance components and nested factors, and can accommodate various estimators of variance. Thus, it enables a broader Phase I process monitoring strategy, under normality, which can be applied within the ANOVA framework applicable for many DOE models. A summary and some recommendations are provided.     

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.     

Transition Monitoring and Adjustment for Dynamic Systems in a Process Improvement Environment

In manufacturing applications, we often encounter process transitions due to a changeover in the production or perhaps an unknown perturbation. The main process improvement goal is to shorten the transition time by monitoring the process in order to quickly identify the start and end of the transition period and by actively adjusting the process during the transition. To address these issues, we propose a transition monitoring and adjustment methodology. A polymer process is used to illustrate this methodology. Using simulation, we characterize the impact of the transition adjustment on the effectiveness of monitoring. We show that the adaptive monitoring procedure is robust to small transition adjustments, thus supporting a complimentary application of process monitoring and process adjustment to improve process transitions. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Control Charts for Monitoring Correlated Poisson Counts with an Excessive Number of Zeros

The zero‐inflated Poisson distribution serves as an appropriate model when there is an excessive number of zeros in the data. This phenomenon frequently occurs in count data from high‐quality processes. Usually, it is assumed that these counts exhibit serial independence, while a more realistic assumption is the existence of an autocorrelation structure between them. In this work, we study control charts for monitoring correlated Poisson counts with an excessive number of zeros. Zero‐inflation in the process is captured via appropriate integer‐valued time series models. Extensive numerical results are provided regarding the performance of the considered charts in the detection of changes in the mean of the process as well as the effects of zero‐inflation on them. Finally, a real‐data practical application is given. Copyright © 2016 John Wiley & Sons, Ltd.     

A Neural Network Method for Modelling the Parameters of a CUSUM Chart

The cumulative sum (CUSUM) chart is widely employed in quality control to monitor a process or to evaluate historic data. CUSUM charts are designed to exhibit acceptable average run lengths both when the process is in and out of control. This paper introduces a functional technique for generating the parameters h and k for such a chart that will have specified average run lengths. It employs the method of artificial neural networks to derive the appropriate coefficients. An EXCEL spreadsheet to assist computing the parameters is presented.