Shifts In Process Mean Research Articles

A study on the run length properties of the side sensitive group runs double sampling (SSGRDS) control chart

The side sensitive group runs double sampling (SSGRDS) chart incorporates the control charting concepts of the side sensitive group runs (SSGR) and double sampling (DS) charts. The SSGRDS chart which combines the efficiency of its basic charts is an effective approach to increase the speed of mean shift detection. The performance of the SSGRDS chart, based on the average number of observations to signal (ANOS), median number of observations to signal (MNOS) and percentiles of the number of observations to signal (PNOS) is investigated in this paper. Based on the results obtained, it is found that the SSGRDS chart becomes more sensitive in detecting mean shifts with an increase in the size of the process mean shift. With the use of MNOS and PNOS to measure the performance of the SSGRDS chart, the entire run length distribution is considered and this leads to a more complete understanding of the performance of the chart. The findings in this paper will provide a clearer picture on the run length properties of the SSGRDS chart which will facilitate practitioners in using the chart.

A new double exponentially weighted moving average control chart using repetitive sampling

PurposeThe purpose of this paper is to propose a double exponentially weighted moving average control chart using repetitive sampling (RS-DEWMA) for a normally distributed process variable to improve the efficiency of detecting small process mean shift.Design/methodology/approachThe algorithm for the implementation of the proposed chart is developed and the formulae for the in-control and out-of-control average run lengths (ARLs) are derived. Tables of ARLs are presented for various process mean shift. The performance of the proposed chart is investigated in terms of the average run-length for small process mean shift and compared with the existing DEWMA control chart. Numerical examples are given as illustration of the design and implementation of the proposed chart.FindingsThe proposed control chart is more efficient than the existing DEWMA control chart in the detection of small process mean shifts as it consistently gives smaller ARL values and quickly detects the process shift. However, the performance of the proposed chart relatively deteriorates for large smoothing constants.Practical implicationsThe application of repetitive sampling in the control chart literature is gaining wide acceptability. The design and implementation of the RS-DEWMA control chart offers a new approach in the detection of small process mean shift by process control personnel.Originality/valueThis paper fills a gap in the literature by examining the performance of the repetitive sampling DEWMA control chart. The use of repetitive sampling technique in the control chart is discussed in the literature, however, its use based on the DEWMA statistic has not been considered in this context.

Capability index-based control chart for monitoring process mean using repetitive sampling

ABSTRACTA new process capability index (PCI) control chart for monitoring the process mean using repetitive sampling is presented. The design of the proposed control chart is based on an unbiased estimator of the process standard deviation for a normally distributed quality characteristic. The formulae for the in-control and out-of-control average run length and the standard deviation of the run length (SDRL) are derived. Tables of in-control and out-of-control average run length (ARL) and SDRL for various shifts, δ are presented. The proposed control chart outperforms existing control chart in detecting relatively small process mean shifts in terms of ARLs and SDRLs. Numerical example is presented to demonstrate the application of the proposed chart.

Distribution‐free mixed cumulative sum‐exponentially weighted moving average control charts for detecting mean shifts

AbstractIn this paper, we propose distribution‐free mixed cumulative sum‐exponentially weighted moving average (CUSUM‐EWMA) and exponentially weighted moving average‐cumulative sum (EWMA‐CUSUM) control charts based on the Wilcoxon rank‐sum test for detecting process mean shifts without any distributional assumption of the underlying quality process. The performances of the proposed charts are measured through the average run‐length, relative mean index, average extra quadratic loss, and average ratio of the average run‐length and performance comparison index. It is found that the proposed charts perform better than its counterparts considered in this paper under non‐normal distributions and outperform the classical mixed CUSUM‐EWMA and EWMA‐CUSUM charts in many cases under the normal distribution. The effect of the phase I sample size is also investigated on the phase II performance of the proposed charts. A numerical illustration is given to demonstrate the implementation and simplicity of the proposed charts.

Monitoring and control of beta-distributed multistage production processes

Multistage statistical process control (SPC) is an effective procedure for ensuring quality of products in multistage manufacturing processes. Effective SPC approaches for monitoring and controlling quality in multistage processes are limited. Beta distributed data explained by process input variables are generally prevalent in multistage process industries. In this paper, we propose a generalized linear model for beta-distributed data in multistage processes in order to estimate the distribution parameters and develop two approaches for process monitoring and control: they are model-based SPC charts and a beta regression model. The proposed control charts outperform the existing control charts in terms of the out-of-control average run length for the detection of process mean shifts.

Determination of the Resetting Time to the Process Mean Shift by the Loss Function

Determination of the Resetting Time to the Process Mean Shift by the Loss Function

The EWMA control chart based on robust scale estimators

The exponentially weighted moving average (EWMA) chart is very popular in statistical process control for detecting the small shifts in process mean and variance. This chart performs well under the assumption of normality but when data violate the assumption of normality, the robust approaches needed. We have developed the EWMA charts under different robust scale estimators available in literature and also compared the performance of these charts by calculating expected out-of-control points and expected widths under non-symmetric distributions (i.e. gamma and exponential). The simulation studies are being carried out for the purpose and results showed that amongst six robust estimators, the chart based on estimator Q_n relatively performed well for non-normal processes in terms of its shorter expected width and more number of expected out-of-control points which shows its sensitivity to detect the out of control signal.

Quality control in hard disc drive manufacturing using pattern recognition technique

Computerized monitoring-diagnosis is an efficient technique to identify the source of unnatural variation (UV) in manufacturing process. In this study, a pattern recognition scheme (PRS) for monitoring-diagnosis the UVs was developed based on control chart pattern recognition technique. This PRS integrates the multivariate exponentially weighted moving average (MEWMA) control chart and artificial neural network (ANN) recognizer to perform two-stage monitoring-diagnosis. The first stage monitoring was performed using the MEWMA statistics, whereas the second stage monitoring-diagnosis was performed using an ANN. The PRS was designed based on bivariate process mean shifts between 0.75σ and 3.00σ, with cross correlation between ρ=0.1 and 0.9. The performance of the proposed PRS has been validated in quality control of hard disk drive component manufacturing. The validation proved that it is efficient in rapidly detecting UV and accurately classify the source of UV patterns. In a nutshell, the PRS will aid in realizing automated decision making system in manufacturing industry.

Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts

ABSTRACTThe adaptive exponentially weighted moving average (AEWMA) control chart is a smooth combination of the Shewhart and exponentially weighted moving average (EWMA) control charts. This chart was proposed by Cappizzi and Masarotto (2003) to achieve a reasonable performance for both small and large shifts. Cappizzi and Masarotto (2003) used a pair of shifts in designing their control chart. In this study, however, the process mean shift is considered as a random variable with a certain probability distribution and the AEWMA control chart is optimized for a wide range of mean shifts according to that probability distribution and not just for a pair of shifts. Using the Markov chain technique, the results show that the new optimization design can improve the performance of the AEWMA control chart from an overall point of view relative to the various designs presented by Cappizzi and Masarotto (2003). Optimal design parameters that achieve the desired in-control average run length (ARL) are computed in several cases and formulas used to find approximately their values are given. Using these formulas, the practitioner can compute the optimal design parameters corresponding to any desired in-control ARL without the need to apply the optimization procedure. The results obtained by these formulas are very promising and would particularly facilitate the design of the AEWMA control chart for any in-control ARL value.

Bayesian Estimation of the Change Point Using CUSUM Control Chart

The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. The proposed approach combines the CUSUM control chart with the Bayesian estimation technique. We show that the control chart has some information about the change point and this information can be used to make an informative prior. Two Bayes estimators corresponding to the informative and a non informative prior along with MLE, frequentist approach, are considered. Their mean square error of estimators, are compared through a series of simulations. The results show that the Bayes estimator with the informative prior is more accurate and more precise for almost all values of the shift in the process mean compared to Bayes estimator with a non-informative prior and MLE.

A Robust Multivariate EWMA Control Chart for Detecting Sparse Mean Shifts

In multivariate statistical process control (MSPC) applications, process mean shifts sometimes occur in only a few components. To solve this MSPC problem, many control charts were proposed in the literature. Most of these charts assumed that the multivariate quality characteristics are normally distributed. Among them, the control chart proposed by Zou and Qiu (2009), incorporating the least absolute shrinkage and selection operator (LASSO) method into the EWMA scheme, has the best overall performance. In this paper, we extend the classical multivariate LASSO control chart to a robust version that has an affine-invariance property and is distribution free under the family of elliptical direction distributions, indicating that the in-control run-length distribution is the same for any continuous distribution in this family and the control limit can be acquired from the multivariate standard normal distribution. Our simulation results show that the proposed method is very efficient in detecting various sparse shifts under heavy-tailed and skewed multivariate distributions. In addition, it is easy to implement with an iterative algorithm and the least angle regression (LARS) algorithm. White-wine data illustrates that the proposed control chart performs quite well in applications.

Generalized smoothing parameters of a multivariate EWMA control chart

ABSTRACTThe Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is effective in detecting a small process mean shift. Its simplicity and generality stem from the assumption that the smoothing parameters of the variables are given constants and equally distributed on the diagonal of the smoothing matrix. Recently, the MEWMA model with the full non-diagonal smoothing matrix (FEWMA) is studied. The model, however, has limited use due to the assumption that the off-diagonal elements are the same; therefore, it would necessarily be sensitive to the correlation structure of observations. In this article, we propose a generalized model for the MEWMA, that uses appropriate non-diagonal elements in the smoothing matrix based on the correlation among variables. We also offer an interpretation of off-diagonal elements of the smoothing matrix and suggest an optimal design for a proposed MEWMA chart. A case study on the automatic monitoring of dimensions of bolts using an imaging processing system is presented to illustrate the proposed control chart. The proposed model is effective in detecting small mean shifts and shows improved performance when compared with MEWMA, FEWMA, and other recently improved control charts.

Applying fast initial response features on GWMA control charts for monitoring autocorrelation data

ABSTRACTA generally weighted moving average (GWMA) control chart with fast initial response (FIR) features is addressed to monitor an autoregressive process mean shift. Numerical simulations based on average run length (ARL) show that the GWMA control chart with additional FIR feature requires less time to detect small or moderate shifts than GWMA control chart at low level of autocorrelation; whereas these two control charts perform similarly at high level of autocorrelation. Regardless of any level of autocorrelation, GWMA control charts provided with additional FIR feature have a good performance in detecting large shifts during the initial stage.

Shewhart控制图与CUSUM控制图的比较研究

本文首先简单介绍了统计过程控制图的产生及其发展，分析了一般的Shewhart控制图和CUSUM控制图的优缺点，其次给出了Shewhart控制图的估计方法和CUSUM控制图的理论基础及其构造方法。最后，我们比较了在过程受控与失控两种情况下的一般的Shewhart控制图和CUSUM控制图的平均运行长度，得出了CUSUM控制图对监测过程均值小漂移比一般的Shewhart控制图更灵敏的结论。 This paper firstly presents a brief introduction to the emergence and development for the figure of statistical process control, and analyzes the advantages and disadvantages between Shewhart control chart and the CUSUM control chart, and then gives the Shewhart control chart estimation method and the theoretical basis and construction method for the CUSUM control chart. Finally, we compare the average run length in the process of controlled and uncontrolled under the two kinds of situations with Shewhart control chart and the CUSUM control chart. It is concluded that the CUSUM control chart for monitoring small process mean shifts is more sensitive than the Shewhart control chart.

와이블 고장모형 하에서의 이중샘플링 T<sup>2</sup> 관리도의 경제적-통계적 설계 (이중샘플링 T<sup>2</sup> 관리도의 경제적-통계적 설계)

Purpose: Double sampling   chart is a useful tool for detecting a relatively small shift in process mean when the process is controlled by multiple variables. This paper finds the optimal design of the double sampling   chart in both economical and statistical sense under Weibull failure model. Methods: The expected cost function is mathematically derived using recursive equation approach. The optimal designs are found using a genetic algorithm for numerical examples and compared to those of single sampling   chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the single sampling   chart in terms of the expected cost per unit time and Type-I error rate for all the numerical examples considered. Conclusion: Double sampling   chart can be designed to satisfy both economic and statistical requirements under Weibull failure model and the resulting design is better than the single sampling counterpart.

Change-point detection for shifts in control charts using fuzzy shift change-point algorithms

Knowing the real time of changes, called change-point, in a process is essential for quickly identifying and removing special causes. Many change-point methods in statistical process control assume the distribution and the in-control parameters of the process known, however, they are rarely known accurately. Small errors accompanied with estimated parameters may lead to unfavorable change-point estimates. In this paper, a new method, called fuzzy shift change-point algorithm, which does not require the knowledge of the distribution nor the parameter of the process, is proposed to detect change-points for shifts in process mean. The fuzzy c-partition concept is embedded into change-point formulation in which any possible collection of change-points is considered as a partitioning of data with a fuzzy membership. These memberships are then transferred into the pseudo memberships of observations belonging to each individual cluster, so the fuzzy c-means clustering can be used to obtain the estimates for shifts. Subsequently, the fuzzy c-means algorithm is used again to obtain new iterates of change-point collection memberships by minimizing an objective function concerning the deviations between observations and the corresponding cluster means. The proposed algorithm is nonparametric and applicable to normal and non-normal processes in both phase I and II. The performance of the proposed fuzzy shift change-point algorithm is discussed in comparison with powerful statistical methods through extensive simulation studies. The results demonstrate the superiority and usefulness of our proposed method.

A Bayesian variable selection method for joint diagnosis of manufacturing process and sensor faults

ABSTRACTThis article presents a Bayesian variable selection–based diagnosis approach to simultaneously identify both process mean shift faults and sensor mean shift faults in manufacturing processes. The proposed method directly models the probability of fault occurrence and can easily incorporate prior knowledge on the probability of a fault occurrence. Important concepts are introduced to understand the diagnosability of the proposed method. A guideline on how to select the values of hyper-parameters is given. A conditional maximum likelihood method is proposed as an alternative method to provide robustness to the selection of some key model parameters. Systematic simulation studies are used to provide insights on the relationship between the success of the diagnosis method and related system structure characteristics. A real assembly example is used to demonstrate the effectiveness of the proposed diagnosis method.

Standard Deviation of the Run Length (SDRL) and Average Run Length (ARL) Performances of EWMA and Synthetic Charts

Statistical process control (SPC) techniques are applied to monitor a process. The control chart is a valuable tool in SPC. the shewhart control chart was the first chart proposed in the literature of SPC and it is still used in process monitoring in today's manufacturing and service industries. both the exponentially weighted moving average (EWMA) and synthetic charts outperform the shewhart control chart for detecting shifts in the process mean. Since both the EWMA and synthetic charts provide better process mean shifts detection performance, a study on which chart to use in process monitoring under different situations is the aim of this work. this paper compares the average run length (ARL) and standard deviation of the run length (SDRL) profiles of the EWMA and synthetic charts. comparisons are made based on the normality assumption. The mathematica programs are used to compute the ARLs and SDRLs of the EWMA and synthetic charts. the ARL results indicate that the EWMA chart is superior to the synthetic chart for detecting small mean shifts, but the latter prevails for detecting moderate and large shifts. however, in terms of the SDRL, the EWMA chart surpasses the synthetic chart for small and moderate shifts. Index Terms—Average run length (ARL), exponentially weighted moving average (EWMA) chart, synthetic chart, standard deviation of the run length (SDRL).

Control Chart Limits for Monitoring Process Mean Based on Downton's Estimator

Control charts are important tools in statistical process control used to monitor shift in process mean and variance. This paper proposes a control chart for monitoring the process mean using the Downton estimator and provides table of constant factors for computing the control limits for sample size (n ≤ 10). The derived control limits for process mean were compared with control limits based on range statistic. The performance of the proposed control charts was evaluated using the average run length for normal and non-normal process situations. The obtained results showed that the control chart, using the Downton statistic, performed better than Shewhart chart using range statistic for detection of small shift in the process mean when the process is non-normal and compares favourably well with Shewhart chart that is normally distributed. Copyright © 2015 John Wiley & Sons, Ltd.

An Efficient Shewhart-Type Control Chart to Monitor Moderate Size Shifts in the Process Mean in Phase II

According to Shewhart, control charts are not very sensitive to small and moderate size process shifts that is why those are less likely to be effective in Phase II. So to monitor small or moderate size process shifts in Phase II, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are considered as alternate of Shewhart control charts. In this paper, a Shewhart-type control chart is proposed by using difference-in-difference estimator in order to detect moderate size shifts in process mean in Phase II. The performance of the proposed control chart is studied for known and unknown cases separately through a detailed simulation study. For the unknown case, instead of using reference samples of small sizes, large size reference sample(s) is used as we can see in some of nonparametric control chart articles. In an illustrative example, the proposed control charts are constructed for both known and unknown cases along with Shewhart -chart, classical EWMA, and CUSUM control charts. In this application, the proposed chart is found comprehensively better than not only Shewhart -chart but also EWMA and CUSUM control charts. By comparing average run length, the proposed control chart is found always better than Shewhart -chart and in general better than classical EWMA and CUSUM control charts when we have relatively higher values of correlation coefficients and detection of the moderate shifts in the process mean is concerned. Copyright © 2015 John Wiley & Sons, Ltd.