Adaptive CUSUM Research Articles

New adaptive CUSUM charts for process mean

In this article, we develop an unbiased estimator of the mean shift, and then use it to enhance the sensitivity of the existing adaptive CUSUM (ACUSUM) chart. Moreover, a new ACUSUM chart is proposed using the structure of the Crosier CUSUM chart and the new mean shift estimator. A comprehensive zero-state run length comparison is conducted between the proposed and existing ACUSUM charts in terms of the average run length measures, which shows that the former uniformly outperform the latter. A real dataset is also used to explain the implementation of existing and proposed ACUSUM charts.

Weighted adaptive multivariate CUSUM charts with variable sampling intervals

ABSTRACTThe adaptive multivariate CUSUM (AMCUSUM) chart has received considerable attention because of its superior sensitivity against a range of mean shift sizes than that of the conventional non-adaptive multivariate CUSUM (MCUSUM) chart. Recently, weighted AMCUSUM (WAMCUSUM) charts with a fixed sampling interval (FSI) have been proposed, called the WAMCUSUM-FSI charts, which provide more sensitivity than the AMCUSUM-FSI charts. In this paper, we extend this work and propose WAMCUSUM charts with variable sampling interval (VSI), named the WAMCUSUM-VSI charts, for efficiently monitoring the mean of a multivariate normally distributed process. The Monte Carlo simulation method is used to compute the average time to signal (ATS) and the adjusted ATS (AATS) profiles of the existing and proposed charts. It is found that the WAMCUSUM-VSI charts perform substantially and nearly uniformly better than the WAMCUSUM-FSI charts in terms of the ATS and AATS performance criterion. An example is given to explain the implementation of the WAMCUSUM charts with fixed and VSIs.

Optimal CUSUM and adaptive CUSUM charts with auxiliary information for process mean

ABSTRACTThe CUSUM chart is good enough to detect small-to-moderate shifts in the process parameter(s) as it can be optimally designed to detect a particular shift size. The adaptive CUSUM (ACUSUM) chart provides good detection over a range of shift sizes because of its ability to update the reference parameter using the estimated process shift. In this paper, we propose auxiliary-information-based (AIB) optimal CUSUM (OCUSUM) and ACUSUM charts, named AIB-OCUSUM and AIB-ACUSUM charts, using a difference estimator of the process mean. The performance comparisons between existing and proposed charts are made in terms of the average run length (ARL), extra quadratic loss and integral relative ARL measures. It is found that the AIB-OCUSUM and AIB-ACUSUM charts are more sensitive than the AIB-CUSUM and ACUSUM charts, respectively. Moreover, the AIB-ACUSUM chart surpasses the AIB-OCUSUM chart when detecting a range of mean shift sizes. Illustrative examples are given to support the theory.

An adaptive multivariate EWMA chart

Abstract The adaptive multivariate EWMA (AMEWMA) and adaptive multivariate CUSUM (AMCUSUM) charts are recently proposed as they provide an overall good detection over a range of mean shift sizes than their non-adaptive conventional counterparts. In this paper, we propose an adaptive MEWMA (AMEWMA) chart for monitoring the infrequent changes in the mean of a multivariate normally distributed process. The idea is to consider an unbiased estimator of the mean shift using an MEWMA statistic, and then use it to adaptively update the smoothing constant of the MEWMA chart. By using Monte Carlo simulations, the run length characteristics of the AMEWMA chart are computed. The AMEWMA chart is comprehensively compared with the existing AMEWMA and AMCUSUM charts in terms of the average run length when detecting mean shifts in different ranges. It is found that the proposed chart is able to perform uniformly and substantially better than the existing charts. Both real and simulated datasets are considered to support the theory.

Estimation of Change-point and Post-change Parameters after Adaptive Sequential CUSUM Test in an Exponential Family

In this paper, we consider an adaptive sequential CUSUM procedure in an exponential family where the change-point and post-change parameters are estimated adaptively. It is shown that the adaptive CUSUM procedure is efficient at the first order. The conditional biases of the estimation for the change-point and post-change parameter are studied. Comparison with the classical CUSUM procedure in the normal case is made. Nile river flow and average global temperature data sets are used for demonstration.

Real-Time Detection of False Data Injection in Smart Grid Networks: An Adaptive CUSUM Method and Analysis

A smart grid is delay sensitive and requires the techniques that can identify and react on the abnormal changes (i.e., system fault, attacker, shortcut, etc.) in a timely manner. In this paper, we propose a real-time detection scheme against false data injection attack in smart grid networks. Unlike the classical detection test, the proposed algorithm is able to tackle the unknown parameters with low complexity and process multiple measurements at once, leading to a shorter decision time and a better detection accuracy. The objective is to detect the adversary as quickly as possible while satisfying certain detection error constraints. A Markov-chain-based analytical model is constructed to systematically analyze the proposed scheme. With the analytical model, we are able to configure the system parameters for guaranteed performance in terms of false alarm rate, average detection delay, and missed detection ratio under a detection delay constraint. The simulations are conducted with MATPOWER 4.0 package for different IEEE test systems.

An adaptive CUSUM chart for monitoring poisson rates with increasing population sizes

The CUSUM control chart is an effective tool for monitoring both variable and count data. However, it often requires the assumption of known process parameters. To get away from this assumption, the adaptive CUSUM (ACUSUM) procedure has been suggested, with primary focus on the monitoring of variable data. This paper extends the idea of ACUSUM control charts from the monitoring of variable data to the monitoring of count data based on an inhomogeneous Poisson model. The study is motivated by a real example of male thyroid cancer data in New Mexico. The comparison results show that the ACUSUM method generally performs better than the traditional Poisson CUSUM charts and other variations for monitoring a wide range of shifts in the Poisson mean. [Received 11 January 2014; Revised 15 July 2014; Accepted 25 August 2014]

Adaptive CUSUM charts for monitoring linear drifts in Poisson rates

There has been relatively less attention paid to the monitoring of linear drifts in Poisson rates. Although the conventional CUSUM charts can be used for monitoring linear drifts in Poisson rates, they often rely on the assumption of a known parameter. To get rid of this assumption, this paper develops adaptive CUSUM (ACUSUM) charts for monitoring drifts in Poisson rates. The basic idea is to first estimate the current Poisson mean level and then to dynamically update the likelihood ratio in the CUSUM chart based on the estimated mean. Three different mean estimators based on the exponentially weighted moving average (EWMA) schemes are discussed. The comparison results are shown to favor the ACUSUM chart, especially at small drifts.

Adaptive nonparametric CUSUM scheme for detecting unknown shifts in location

In this paper, we provide a sequential rank-based adaptive nonparametric cumulative sum control chart for detecting a range of shifts in the location parameter. This chart is a self-starting scheme, and thus can be used to monitor processes at the start-up stages rather than having to wait for the accumulation of sufficiently large calibration samples. It does not require any prior knowledge of the underlying distribution. The choice of the chart parameters is studied and a simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also efficiently detects various magnitudes of shifts. An illustrative example is also given to introduce the implementation of this proposed control chart.

Category-Specific Comparison of Univariate Alerting Methods for Biosurveillance Decision Support

We compared detection performance of univariate alerting methods on real and simulated events in different types of biosurveillance data. Both kinds of detection performance analysis showed the method based on Holt-Winters exponential smoothing superior on non-sparse time series with day-of-week effects. The adaptive CUSUM and Shewhart methods proved optimal on sparse data and data without weekly patterns.

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.

A new adaptive CUSUM control chart for detecting the multivariate process mean

AbstractWe propose a new multivariate CUSUM control chart, which is based on self adaption of its reference value according to the information from current process readings, to quickly detect the multivariate process mean shifts. By specifying the minimum magnitude of the process mean shift in terms of its non‐centrality parameter, our proposed control chart can achieve an overall performance for detecting a particular range of shifts. This adaptive feature of our method is based on two EWMA operators to estimate the current process mean level and make the detection at each step be approximately optimal. Moreover, we compare our chart with the conventional multivariate CUSUM chart. The advantages of our control chart detection for range shifts over the existing charts are greatly improved. The Markovian chain method, through which the average run length can be computed, is also presented. Copyright © 2010 John Wiley & Sons, Ltd.

An Adaptive CUSUM Procedure for Signaling Process Variance Changes of Unknown Sizes

Similar to the CUSUM location chart, the traditional CUSUM dispersion chart can be designed to optimize the detection of specified variance changes. However, this optimality property requires that the magnitude of the out-of-control variance is known exactly a priori. To get away from this requirement, this paper suggests an adaptive CUSUM procedure for signaling changes in the process variance of unknown sizes. The basic idea is to first estimate the current process variance and then dynamically adjust the CUSUM chart to match the variance estimate. A two-dimensional Markov chain model is developed to analyze the chart performance. The comparison results with the traditional CUSUM dispersion chart and other competitive procedures favor the proposed one.

Cusum of Q chart with variable sampling intervals for monitoring the process mean

Recently, adaptive control charts (that is, with variable sample sizes and/or sampling intervals) for univariate or multivariate quality characteristics have received considerable attention in Phase II analysis in the literature. Due to insufficient samples to obtain good knowledge of the parameters in the start-up process, adding adaptive features to self-starting control charts remains an open problem. In this paper, we propose an adaptive Cusum of Q chart with variable sampling intervals for monitoring the process mean of normally distributed variables. A Fortran program is available to assist in the design of the control chart with different parameters. The effect of the control chart parameters on the performance is studied in detail. The control chart is further enhanced by finding adaptive reference values. Due to the powerful properties of the proposed control chart, the Monte Carlo simulation results show that it provides quite satisfactory performance in various cases. The proposed control chart is applied to a real-life data example to illustrate its implementation.

An enhanced adaptive CUSUM control chart

Adaptive CUSUM charts, referred to as ACUSUM charts, have attracted considerable attention from the research community. By adjusting the reference parameter k dynamically, an ACUSUM chart may achieve a better performance over a range of mean shifts than conventional CUSUM charts that are designed for maximal detection effectiveness at a particular level of process shift. This article studies a new feature of the ACUSUM chart related to an additional charting parameter w, i.e., the exponential of the sample mean shift in (x t – μ 0) w . The ACUSUM chart can be enhanced by adapting this parameter w according to the on-line estimated value of the mean shift, in conjunction with the reference parameter k. The testing cases reveal that this new adaptive CUSUM chart not only outperforms the earlier ACUSUM chart to a substantial degree, but also works as well as the most effective combined schemes consisting of a few CUSUM and/or charts. Furthermore, this enhanced ACUSUM chart is easier to design and implement in a computerized environment compared with those combined schemes. In addition, a general-purpose optimization algorithm is proposed to assist the designs of various CUSUM charts. This paper demonstrates that this algorithm can significantly improve the performance of many CUSUM charts over the entire process shift range. Moreover, a systematic performance comparison of eight CUSUM charts is presented. The findings from this comparison are useful aids for SPC practitioners to select an appropriate CUSUM chart for real applications. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplementary resource: Appendix]

Adaptive CUSUM control chart with variable sampling intervals

The standard cumulative sum chart (CUSUM) is widely used for detecting small and moderate process mean shifts, and its optimal detection ability for any pre-specified mean shift has been demonstrated by its equivalence to continuous sequential tests. In real practice, the assumption of knowing the true mean shift in prior cannot be always met. So it is desirable to design a procedure that is efficient for detecting a range of future expected but unknown mean shifts. Adaptive CUSUM control chart, which can continuously adjust itself by a one-step forecasting operator, has been proposed to detect efficiently and robustly for a range of mean shifts in the early literature. Moreover, in terms of sampling time to signal, control chart with the VSI (variable sampling intervals) feature can detect the process changes more quickly than the traditional FSI (fixed sample intervals) chart. In this paper, a new CUSUM control chart which is based on both adaptive and VSI features is discussed. Also, a two-dimensional Markov chain model is developed to evaluate its run-time performance.

Adaptive CUSUM of the Q chart

The CUSUM of the Q chart, as a self-starting approach, was previously proposed for detecting process shifts when the in-control process parameters are unknown. Motivated by the recent development of the adaptive chart, this paper proposes a new self-starting approach that integrates the CUSUM of the Q chart with the feature of adaptively varying the reference value, to better detect a range of shifts with unknown process parameters. The choice of the chart parameters and the masking effect are also studied. Simulation results show that our proposed chart offers balanced protection against shifts of different magnitude, and has performance comparable to the dynamic change-point control scheme. A real example from industrial manufacturing is used to demonstrate its implementation.

A Retrospective on Volume 23 of Quality and Reliability Engineering International

Through the first 23 years of its existence, Quality and Reliability Engineering International has established itself as a key journal in the field, providing valuable information on new developments on many aspects of the subject to professionals all over the world with research articles, applications, and case study papers and timely reviews of new books. The recently completed Volume 23 (2007) continues that tradition. It is appropriate to look back over that volume and identify some important themes for the volume, highlight some of the significant papers that contribute to those themes, and discuss the future—what we hope to see going forward. Six sigma was an important topic for the journal last year. The papers by Tang et al.1 and Ung et al.2 identified some potentially useful additions to the usual six sigma tool kit as it is typically practiced through the DMAIC process and showed how six sigma principles can be applied to the critical issue of port security. Six sigma, which celebrated its 20th birthday in 2007, will continue to grow as the primary framework for quality and business improvement. The journal will continue to be a forum for both research and applications of six sigma. Applications grow in fields outside traditional manufacturing, and applications in finance, marketing, health care, distribution and logistics, public service, and government operations will continue to expand. We hope to see papers on these new applications and new tools to support those applications in future issues of the journal. Statistical process control continues to be an important area of research and applications. The journal published many noteworthy papers in this area, including the work by Wu et al.3 on adaptive Cusum schemes for monitoring the mean and variance, use of cuscores by Nembhard and Changpetch4, Nembhard and Valverde-Ventura5, and Nembhard and Chen6, and the important works on monitoring profiles by Mahmoud et al.7 and Williams et al.8. Other interesting and useful papers include work on change points by Perry et al.9, control charting dependent attribute data by Shepherd et al.10, and multivariate quality control by Guh11 and Bersimis et al.12. Another major technique for process and product quality improvement, designed experiments, continued to attract important papers to the journal. These include new work on blocking in two-level factorial designs by Kulahci13, split-plots (see Liang et al.14 and Naes et al.15), and Plackett–Burman designs by Kulahci and Bisgaard16. Many industrial experiments involve both factors that are easy to change and hard to change. Consequently, complete randomization of the treatment combinations is expensive, time consuming, or (frequently) impossible. Split-plot designs were originally developed in the agricultural sciences as a solution to this problem. The last few years have seen considerable research devoted to the deployment of these designs in the industrial setting. This journal continues to lead the way in publishing innovative research on this topic. Issue number 6 was a special issue devoted to quality management, applications, and development. Two highlights of this issue were the papers by Kenett17, Godfrey and Kenett18, and Bisgaard19 on the contributions, impact, and legacy of Joseph M. Juran. Juran is one of the foremost thinkers in the filed of management, not just quality management. Managerial breakthrough, a project-oriented approach to improvement, and system-wide approach to the integrated organizational use of quality tools are only some of the ideas he pioneered. Six sigma and the DMAIC process borrow heavily from the philosophy and methods of Juran. Quality and reliability engineers are knowledge workers, in the truest sense of that phrase. They accumulate, generate, and deploy knowledge with the express objective of improving products, processes, services, and society. Journals that facilitate the generation and widespread adoption of new methods perform a valuable service to the profession and to society in general. Quality and Reliability Engineering International will continue to play that vital role.

Monitoring the quality of GPS station coordinates in real time

This paper evaluates various statistical process control algorithms for monitoring the quality of GPS station coordinates in real-time kinematic applications. Real-time detection of small but persistent shifts in GPS coordinates is critical for applications requiring automatic and reliable results in deformation monitoring. Examples include monitoring of dams, high-rise buildings, bridges, tectonic movements, landslides and so on. The conventional cumulative sums (Cusums), the robustified and self-starting Cusums, the adaptive Cusum and the exponential weighted moving average are some of the control charts applied to real-time-kinematic (RTK) data in field experiments. All control charts have been evaluated for their effectiveness in detecting an actual but intentional deformation shift of at least 0.5 standard deviations from a target mean. The observations used in testing these control charts had initially been assumed to be independent and follow a normal distribution, but later, their serial correlation was taken into consideration. These results show that the self-starting but robustified Cusums as well as the exponentially weighted moving average charts are suitable and efficient tools in monitoring quality in the RTK data. All presented control charts are implemented as modules in a software package being developed by the Technical University of Crete.

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

AbstractThe 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 $\delta_{\mu}$ and increasing standard deviation shift $\delta_{\sigma}$ 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 $\bar{X}$&S charts (by 72.36%), the VSSI $\bar {X}$&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.