Adaptive CUSUM Research Articles

Adaptive EWMA and CUSUM charts with dynamic probability control limits

The utilization of dynamic probability control limits (DPCLs) can prove advantageous in the development of control charts, particularly in scenarios where sample sizes, areas of opportunity, or any other covariate values exhibit temporal fluctuations. In this study, we design the DPCLs-based two adaptive EWMA (AE) and adaptive CUSUM (AC) charts for monitoring the mean of a normally distributed process. We use Monte Carlo simulations to estimate the conditional false alarm rates, zero-state and steady-state (SS) average run-length profiles of the adaptive charts. It is found that the proposed AE and AC charts outperform the existing AE chart in terms of relative mean index. An example is given to demonstrate the implementation of the proposed charts.

A distribution-free adaptive CUSUM-sign chart for monitoring shifts in the location of unknown industrial process

In most of the manufacturing industry, the distributional assumption of the online working processes is customarily unknown or hard to meet. In such situations, parametric charting mechanisms generally designed under normality assumptions of the model yield more false alarms and invalid out-of-control (OOC) comparisons. The nonparametric (distribution-free) charts are a better choice for practitioners in such cases as their in-control (IC) run length (RL) profiles remain the same. The study intends to develop a new distribution-free adaptive CUSUM sign (NPACUSUM-SN; named hereafter) chart for monitoring the process location. The proposed NPACUSUM-SN chart estimates the unknown process mean shift using an unbiased function and updates adaptively the reference parameter of the CUSUM statistic. The IC robustness of the conventional adaptive CUSUM and the proposed NPACUSUM-SN charts under the symmetric, skewed, and contaminated normal (CN) distributions have been computed using Monte Carlo simulations. The OOC RL profiles of the proposed study have been assessed for the initial state and the shift delay (steady state) in the processes. The proposed NPACUSUM-SN chart shows more resistance against non-normality and effective behaviour as compared to its conventional competitor. The proposed NPACUSUM-SN chart provides uniformly efficient RL characteristics as compared to its counterparts. Implementation of the proposal is made by using a manufacturing industry dataset along with an artificial dataset.

A novel adaptive CUSUM system for efficient process mean monitoring: An application in piston ring manufacturing process

The adaptive versions of charting tools are well-established statistical monitoring techniques for detecting unknown changes in the process over a range of shifts. A re-weighted adaptive CUSUM mean (RACUSUM) charting scheme has been proposed in this study for monitoring the range of shifts. The proposed RACUSUM statistic estimates the unknown changes in the ongoing process using an EWMA statistic by plugging in an unbiased shift estimator and choosing a suitable smoothing constant according to the estimated shift to update the slack value of the CUSUM statistic. By employing Monte Carlo simulation using the zero- and steady-state processes, the proposal’s run-length (RL) profiles have been calculated. The proposed RACUSUM chart shows more sensitive behavior under the shift delay process than in the case of zero-state. A comparative analysis between the proposal and competitors has been presented using average RL, extra quadratic loss (EQL), and the relative mean index (RMI) as metrics for 1-sided and 2-sided charting schemes. The robustness of the proposed 2-sided RACUSUM chart against non-normality has also been reported. The proposal’s applicability has been demonstrated using two cases, one from the artificial and the other from a dataset of piston ring manufacturing industrial process.

Parametric and nonparametric versions of adaptive CUSUM charts for monitoring the location of individual measurements

Control charts are customarily developed under the assumption of normal quality characteristics to be monitored. However, in many real dataset applications, the normality assumption is not easy to hold. The in-control (IC) robustness of the charting schemes has significant importance for the valid out-of-control (OOC) performance. This article intends to investigate the IC robustness of the unbiased-function-based adaptive cumulative sum (ACUSUM) chart and nonparametric ACUSUM (NPACUSUM) chart against the non-normal process distributions including symmetrical, skewed, and contaminated normal distributions. The OOC run length profiles of the ACUSUM and the proposed NPACUSUM charts for the individual measurements against the non-normal distributions are also a part of this study. The run length profiles of the proposed charting schemes have been computed using the Monte Carlo simulation method. The artificial datasets have been taken from some symmetric and skewed distributions to implement the proposals. An electrical engineering dataset has also been taken for the implementation of the proposal on a real dataset.

Anomaly Detection Method for Rocket Engines Based on Convex Optimized Information Fusion.

The power system, as a core component of a launch vehicle, has a crucial impact on the reliability and safety of a rocket launch. Due to the limited measurement information inside the engine, it is often challenging to realize fast and accurate anomaly detection. For this reason, this paper introduces the rocket flight state data to expand the information source for anomaly detection. However, engine measurement and rocket flight state information have different data distribution characteristics. To find the optimal data fusion scheme for anomaly detection, a data set information fusion algorithm based on convex optimization is proposed, which solves the optimal fusion parameter using the convex quadratic programming problem and then adopts the adaptive CUSUM algorithm to realize the fast and accurate anomaly detection of engine faults. Numerical simulation tests show that the algorithm proposed in this paper has a higher detection accuracy and lower detection time than the traditional algorithm.

Weighted adaptive CUSUM mean chart with variable sample size and sampling interval

The classical CUSUM (C) chart is designed by assuming that the size of the shift in the process, in which a quick detection is important, is known a priori. However, this assumption is often violated in practice, as the actual shift size is rarely known even though it may vary within a certain interval. The adaptive C (AC) chart gives better protection against process shifts in a certain interval than the classical C chart. In this paper, we propose a new weighted AC (WAC) chart with the variable sample size and sampling interval (VSSI) feature, which encompasses the fixed sampling rate (FSR), variable sample size (VSS) and variable sampling interval (VSI) based WAC charts. The Monte Carlo simulations are adopted in the run-length computations of the considered charts, where the newly developed (VSS and VSSI based) charts outperform the existing (FSR and VSI) WAC charts when detecting small shifts in the process mean. An illustrative example shows the implementation of the existing and proposed WAC charts.

A maximum dual CUSUM chart for joint monitoring of process mean and variance

ABSTRACT A dual chart provides more sensitivity than the conventional chart when it is known that a shift size varies within a given interval. In this paper, we propose a maximum dual CUSUM (MDC) chart for monitoring the joint shifts (that lie in different intervals) in the mean and variance of a normally distributed process. The Monte Carlo simulation method is used to estimate the zero-state and steady-state run-length properties of the MDC chart, which include the average run-length (ARL), expected weighted run-length (EWRL) and expected relative ARL (ERARL). Based on detailed run-length comparisons in terms of the EWRL and ERARL, it is found that the MDC chart outperforms the maximum adaptive EWMA (MAE) and maximum weighted adaptive CUSUM (MWAC) charts when detecting a range of the joint shift sizes. Moreover, the diagnostic abilities of the MDC chart are also studied. Real and simulated datasets are considered to demonstrate the implementation of the MAE, MWAC and MDC charts.

New EWMA charts for process variance

AbstractThe EWMA chart is effective in detecting small shifts in the process mean or process variance. Numerous EWMA charts for the process variance have been suggested in the literature. In this article, new one‐sided and two‐sided EWMA charts are developed for monitoring the variance of a normal process. In developing these new EWMA charts, first, new unbiased estimators of the process variance are developed, followed by incorporating the developed estimators into the new EWMA charts' statistics. The Monte Carlo simulation method is adopted to evaluate the zero‐state and steady‐state run‐length performances of the proposed EWMA variance charts, in comparison with that of three existing EWMA variance charts and the weighted adaptive CUSUM variance chart. The findings reveal that the proposed charts generally perform better than the existing charts. An example of application is given to show the implementation of the proposed and existing charts in detecting increases or decreases in the process variance.

Adaptive resources allocation CUSUM for binomial count data monitoring with application to COVID-19 hotspot detection

In this paper, we present an efficient statistical method (denoted as ‘Adaptive Resources Allocation CUSUM’) to robustly and efficiently detect the hotspot with limited sampling resources. Our main idea is to combine the multi-arm bandit (MAB) and change-point detection methods to balance the exploration and exploitation of resource allocation for hotspot detection. Further, a Bayesian weighted update is used to update the posterior distribution of the infection rate. Then, the upper confidence bound (UCB) is used for resource allocation and planning. Finally, CUSUM monitoring statistics to detect the change point as well as the change location. For performance evaluation, we compare the performance of the proposed method with several benchmark methods in the literature and showed the proposed algorithm is able to achieve a lower detection delay and higher detection precision. Finally, this method is applied to hotspot detection in a real case study of county-level daily positive COVID-19 cases in Washington State WA) and demonstrates the effectiveness with very limited distributed samples.

New weighted adaptive CUSUM charts for monitoring the generalized variance of a bivariate normal process

In modern and high volume manufacturing environments, it is vital to early detect a small sustained shift in a short period of time as it may have a serious impact on a manufacturing process. Adaptive memory-type control charts have the ability to swiftly detect a range of the shift sizes, and one such control chart is a weighted adaptive CUSUM (abbreviated as C) chart. In this paper, using a simple likelihood ratio test-statistic, we propose two types of the C charts (with and without the normalizing transformation) using three different shift estimators for monitoring the generalized variance (GV) of a bivariate normally distributed production process. In addition, the sensitivities of these control charts are also enhanced with the variable sampling interval feature. Monte Carlo simulations are used to compute the zero-state and steady-state run-length characteristics of the proposed charts. Based on detailed run-length comparisons, it is observed that the proposed charts may uniformly and substantially outperform the existing charts when detecting different kinds of shifts in the GV. A real dataset is also selected to illustrate the implementation of the newly proposed charts.

Adaptive CUSUM chart with cautious parameter learning

AbstractThe classic CUSUM chart assumes that the in‐control (IC) mean and variance are known. In practice, these parameters are usually estimated from an IC Phase I sample. Recently, Capizzi and Masarotto proposed a cautious parameter learning scheme to incorporate Phase II IC observations in the estimation of the IC mean and variance to reduce the variation of conditional average run lengths (ARLs). In this paper, we develop a new cautious parameter learning scheme that can distinguish IC observations from out‐of‐control (OC) observations in the Phase II sample more effectively than Capizzi and Masarotto's scheme. As a result, our cautious parameter learning scheme can provide better estimation of the IC mean and variance. Combining the new cautious parameter learning scheme with an adaptive CUSUM chart, our proposed monitoring procedure is easy to implement, and is shown to have less variability in conditional ARLs and better overall performance for detecting different mean shifts than existing methods.

Adaptive CUSUM control charts for efficient monitoring of process dispersion

AbstractAn adaptive cumulative sum (ACUSUM) control chart is an advance form of the classical CUSUM control chart to identify different sizes of shift in the process parameters (location and/or dispersion). In the continuation of the ACUSUM control chart, this study also proposed ACUSUM control charts to enhance the performance of the process dispersion for a broad range of shift. The proposed ACUSUM control charts methodologies are based on the dispersion CUSUM statistic, score (Huber and Bi‐square) functions, generalized likelihood ratio test, and nonlinear optimization technique. The use of dispersion CUSUM statistic helps to distinguish a specific shift as the classical CUSUM statistic does, the score functions, the nonlinear optimization technique and generalized likelihood ratio test enhance the ability of the proposed ACUSUM control charts to distinguish a shift of different size. For the assessment of control charts, run length (RL) measure is used, and it is generated by developing an algorithm in MATLAB through Monte Carlo simulation method. Further, average of RL is utilized to carry out comparative analysis of control charts for a single shift, while for a certain range of shift (comprehensive analysis), extra quadratic loss (EQL), relative average run length (ARL), and performance comparison index (PCI) measures are used. Findings based on numerical results and visual presentations reveal the superiority of the proposed control charts against some existing control charts. Moreover, for real‐world point of assessment, the proposed control chart is implemented with numerical data to show the worth over other control charts.

New weighted adaptive CUSUM dispersion charts

AbstractThe conventional CUSUM chart is usually designed for a known shift size against which the protection is required. In practice, the shift sizes are rarely known, but they may vary within a given interval. Given a range of the shift size, the weighted adaptive CUSUM (WAC) chart provides better protection than the CUSUM chart. In this paper, we propose two types of the WAC chart for monitoring different kinds of shifts in the variance of a normal process, named WAC‐I and WAC‐II charts, based on the CUSUM and Crosier CUSUM charts, respectively. Monte Carlo simulations are used to compute the run length characteristics of the proposed one‐sided and two‐sided charts. The proposed charts are compared with existing adaptive and non‐adaptive charts in terms of the average run length. It is found that the proposed charts perform uniformly and substantially better than the existing charts. A real dataset is considered to support the theory.

Adaptive CUSUM Location Control Charts Based on Score Functions: An Application in Semiconductor Wafer Field

Adaptive CUSUM Location Control Charts Based on Score Functions: An Application in Semiconductor Wafer Field

Directionally sensitive weighted adaptive multivariate CUSUM mean charts

AbstractIn 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.

Enhanced adaptive multivariate EWMA and CUSUM charts for process mean

The multivariate charts are mostly used to simultaneously monitor several quality characteristics in manufacturing processes. In this study, we enhance the sensitivities of the recently proposed adaptive multivariate EWMA (AME) and weighted adaptive multivariate CUSUM (WAMC) charts with an auxiliary-information-based (AIB) estimator, namely the AIB-AME and AIB-WAMC charts, for monitoring different kinds of shifts in the mean of a multivariate normally distributed process. In addition, the variable sampling interval (VSI) feature is also incorporated into the proposed charts. The run length properties of these control charts are computed using Monte Carlo simulations. It is found that the AIB-AME and AIB-WAMC charts are uniformly and substantially more sensitive than the AME and WAMC charts, respectively. The same trend is observed when these control charts have the VSI feature incorporated into them. Real datasets are used to demonstrate the implementation of the proposed charts.

Memory‐type control charts with multiple auxiliary information for process mean

AbstractMemory‐type auxiliary‐information‐based (AIB) control charts are very effective in detecting small‐to‐moderate shifts in the process mean. In this study, we first develop a unique uniformly minimum variance unbiased estimator of the process mean that requires information on the study variable as well as on several correlated auxiliary variables. Then, based on this estimator, adaptive and nonadaptive CUSUM and EWMA charts are developed with either fixed or variable sampling interval for monitoring the process mean, namely, the multiple AIB (MAIB) charts. The proposed charts encompass existing charts with or without the auxiliary information. The run length characteristics of the proposed charts are computed with the Monte Carlo simulations when sampling from a multivariate normal distribution. Based on the run length comparisons, it is found that the MAIB charts are uniformly and substantially more sensitive than the AIB charts when monitoring the process mean. Real datasets are also considered to explain the implementation of the MAIB charts.

Maximum weighted adaptive CUSUM charts for simultaneous monitoring of process mean and variance

ABSTRACT In this paper, we propose maximum weighted adaptive Crosier CUSUM (MaxWACCUSUM) charts with three different unbiased estimators of the process mean and variance shifts for joint monitoring of the mean and variance of a normal process. The MaxWACCUSUM charts provide an overall good performance for detecting a range of joint mean and dispersion shift sizes. The run length characteristics of the proposed charts are computed using the Monte Carlo simulation method. A detailed comparative study is conducted to compare the run length performances of the proposed and existing charts. It is found that the MaxWACCUSUM charts are more sensitive than the maximum EWMA, double EWMA and CUSUM charts when detecting a range of joint shift sizes. Real datasets are considered to support the theory.

Nonparametric adaptive CUSUM chart for detecting arbitrary distributional changes

Nonparametric control charts that can detect arbitrary distributional changes are highly desirable due to their flexibility to adapt to different distributional assumptions and changes. However, most of the nonparametric control charts in the literature either can only detect location changes, or involve intensive computation. In this article, we propose a new nonparametric adaptive CUSUM chart. The proposed control chart can detect arbitrary distributional changes and is computationally efficient. Its self-starting nature makes the proposed control chart applicable to situations where no sufficiently large reference data are available. The proposed control chart also has a built-in post-signal diagnostics function that can identify what kind of distributional changes have occurred after an alarm. Our simulation study and real data analysis show that the proposed control chart performs well across a broad range of settings, and compares favorably with existing nonparametric control charts.

Enhanced adaptive CUSUM charts for process mean

ABSTRACTA statistical quality control chart is an important tool of the statistical process control, which is widely used to control and monitor a production process. The CUSUM chart is designed to detect a specific shift, provided that the shift size is known in advance. In practice, however, shift sizes are rarely known. It is then customary to use an adaptive CUSUM chart, which can effectively detect a range of shift sizes. In this paper, we enhance the sensitivities of the improved adaptive CUSUM mean charts using an auxiliary-information-based (AIB) mean estimator. The run length performances of the proposed charts are compared with those of the AIB adaptive and non-adaptive CUSUM charts in terms of the average run length (ARL), extra quadratic loss, and integral relative ARL. These run length comparisons reveal that the proposed charts are more sensitive than the existing charts when detecting different kinds of shift in the process mean. An example is given to demonstrate the implementation of existing and proposed charts.