A moving average control chart using a robust scale estimator for process dispersion

Statistical process control provides package of statistical tools applied for improving quality of manufacturing, production and services processes. Cumulative sum, exponentially weighted moving average (EWMA) and progressive mean charts belong to family of memory-type charts which effectively spot small and persistent shifts in the process parameter(s). EWMA chart requires normality and a proper choice of smoothing parameter to perform efficiently. Any deviation from these conditions affects its performance in terms of efficacy and robustness. For the said concerns, progressive exponentially weighted moving average (PEWMA) chart is developed to monitor the shifts in the process location. The performance of the proposed PEWMA chart is evaluated in terms of average run length and some other metrics of run length distribution. The assessment of the proposed chart has been made under standard normal, Student’s t, gamma, Laplace, logistic, exponential, contaminated normal and lognormal distributions. The performance of the proposed PEWMA chart is also compared with some existing competitors including the classical EWMA, classical CUSUM, HWMA, MEC, MCE and DEWMA charts. The analysis reveals that the proposal offers a design structure which has high sensitivity to small and persistent drifts in the process mean and has advantage of robustness under non-normal scenarios. An application from substrates manufacturing process (in which flow width of the resist is the key quality characteristic) is also provided for practical implementations.

PurposeThis work aims to focuse on improving the performance of the new exponentially weighted moving average (NEWMA) scheme for monitoring process dispersion. The authors use the generalized time-varying fast initial response (GFIR) to further enhance the detection ability of variability NEWMA control charts at the process startup. The performance of the proposed chart and other schemes discussed in this article are evaluated; and compared using the average run length (ARL) and standard deviation run length (SDRL) measures. It is observed that the ARL of the proposed scheme is quicker in detecting small and moderate shifts in the process dispersion than its counterparts. The real-life application of the proposed scheme is presented.Design/methodology/approachThe dynamic parameter of GFIR is used to enhance the detection ability of variability NEWMA control charts. The authors apply GFIR to the control limit of variability NEWMA scheme. This further narrows the control limit, hence enabling it to swiftly detect small and moderate changes in process dispersion.FindingsThe authors present the performance comparisons by examining the ARL properties of the proposed chart and its counterparts. The performance comparison shows that the proposed chart is highly sensitive in detecting small and intermediate process shifts. The real-life application presented also supports the study’s conclusion from the simulation studies. The performance comparison of the proposed chart and its counterparts shows that the proposed scheme is efficient in detecting process abnormalities, especially at the startup.Originality/valueIn terms of the control limits, the proposed chart is the generalized variability NEWMA control chart in which all the previously proposed NEWMA variant schemes can be obtained. Also, the newly proposed control scheme is more efficient in detecting small or moderate persistent shifts in the process dispersion.

Joint statistical design of double sampling [formula omitted] and s charts

ABSTRACTAn efficient alternative to the S control chart for detecting shifts of small magnitude in the process variability using a moving average based on the sample standard deviation s statistic is proposed. Control limit factors are derived for the chart for different values of sample size and span w. The performance of the moving average S chart is compared to the S chart in terms of average run length. The result shows that the performance of moving average S chart for varying values of w outweigh those of the S chart for small and moderate shifts in process variability.

ABSTRACTControl charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having non-normal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used in such circumstances. In this paper, we propose a new variance chart based on a simple statistic to monitor process variance shifts. We explore the sampling properties of the new monitoring statistic and calculate the average run lengths (ARLs) of the proposed variance chart. Furthermore, an arcsine transformed exponentially weighted moving average (EWMA) chart is proposed because the ARLs of this modified chart are more intuitive and reasonable than those of the variance chart. We compare the out-of-control variance detection performance of the proposed variance chart with that of the non-parametric Mood variance (NP-M) chart with runs rules, developed by Zombade and Ghute [Nonparametric control chart for variability using runs rules. Experiment. 2014;24(4):1683–1691], and the nonparametric likelihood ratio-based distribution-free exponential weighted moving average (NLE) chart and the combination of traditional exponential weighted moving average (EWMA) mean and EWMA variance (CEW) control chart proposed by Zou and Tsung [Likelihood ratio-based distribution-free EWMA control charts. J Qual Technol. 2010;42(2):174–196] by considering cases in which the critical quality characteristic has a normal, a double exponential or a uniform distribution. Comparison results showed that the proposed chart performs better than the NP-M with runs rules, and the NLE and CEW control charts. A numerical example of service times with a right-skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the application of the proposed variance chart and of the arcsine transformed EWMA chart and to compare them with three existing variance (or standard deviation) charts. The proposed charts show better detection performance than those three existing variance charts in monitoring and detecting shifts in the process variance.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

A new multivariate statistical process variability control scheme, the multivariate double sampling (MDS) |S| control chart scheme for controlling shifts in a variance–covariance matrix, is proposed. An MDS |S| chart is a double-stage extension of a single-stage control chart based on the sample generalized variance. The statistical efficiency in terms of average run length of the MDS |S| charts is compared with that of traditional and adaptive sample size control charts based on the sample generalized variance for a bivariate case. The results of the comparison show that the MDS |S| charts provide a significant improvement in efficiency for detecting shifts of any range over these schemes. The performance of the MDS |S| charts in terms of detecting power is also compared with that of the modified likelihood ratio test, the sum of standardized variances for principal components charts and a decomposition procedure. The results of the comparison show that for certain out-of-control situations, the performance of the MDS |S| chart is among those of the best schemes.

<h3>Background</h3> Traditional strategies for surveillance of surgical site infections (SSI) have multiple limitations, including delayed and incomplete outbreak detection. Statistical process control (SPC) methods address these deficiencies by combining longitudinal...

I analyze properties of misspecified discrete choice models and the efficacy of Huber-White (sometimes called ‘robust’) standard errors. The Huber-White correction provides asymptotically correct standard errors for a consistent estimator from a misspecified model. There is little justification for using Huber-White standard errors in discrete choice models since misspecification usually leads to inconsistent estimators. I derive necessary and sufficient conditions for consistency of the maximum likelihood estimator of any potentially misspecified random utility model (e.g. conditional logit). I also derive (easily satisfied) sufficient conditions for consistent estimation of the sign of the data generating parameter. It follows the researcher can consistently test the sign (or nullity) of the parameter from the data generating process using the (possibly) misspecified conditional logit. I investigate small sample properties of the Huber-White estimator via a simulation study and find the correction provides little to no improvement for inferences.

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.

Fog manufacturing is an advanced manufacturing system that integrates Fog computing with interconnected manufacturing processes. It can provide responsive and robust computation services compared with Cloud manufacturing. However, the performance of Fog manufacturing is still not satisfactory due to various anomalies such as inappropriate architecture designs, cyber-attacks, etc. These problems can lead to anomalies in Fog manufacturing and can impede the wide adoption of Fog manufacturing. To quickly detect the anomalies in Fog manufacturing during operations, a monitoring system is desirable. Therefore, in this paper, we proposed a monitoring system based on statistical process control (SPC) methods to comprehensively monitor different types of anomalies in Fog manufacturing. The exponentially weighted moving average (EWMA) and risk-adjusted (RA) charts are adopted to detect different anomalies based on corresponding monitoring statistics. A simulation study and a real case study based on a Fog manufacturing testbed are implemented to evaluate the performance of the proposed monitoring system. The result shows the proposed monitoring system can quickly and efficiently detect different types of anomalies in Fog manufacturing. This monitoring system can also potentially help to improve architecture designs and offloading strategies by further analyzing the root causes of a specific anomaly in future work.

Nonparametric estimation of averages and errors for small data-sets in isotope geoscience: a proposal

Principal component analysis-based control charts for multivariate nonnormal distributions

In this paper, a robust statistical method called projection statistics (PS) is developed into an TV-dimensional complex form required to detect strong nonhomogeneities, or TV-dimensional outlier vectors (i.e., outliers), in space-time adaptive processing (STAP) radar training data, where N is the number of degrees of freedom (DOF) associated with the STAP scenario. The PS technique does not require the estimation of a covariance matrix, as is the case with the generalized inner product (GIP) test. Rather, it uses robust estimators of location (the median) and scale (the median absolute deviation from the median (MAD)) to identify and then excise strong nonhomogeneities in STAP training data that are capable of rendering traditional nonhomogeneity detection (NHD) techniques, such as the GIP, ineffective. Shown in the results section of this paper is sample matrix inversion (SMI) STAP performance using three separate NHD techniques: 1) a power test for high power outlier snapshots, 2) a GIP test, and 3) a PS-based test. The performance when not using any form of NHD is shown for comparison. It is clear from the results that the PS NHD method provides an SMI-STAP processor the best training data selection in the multi channel airborne radar measurements (MCARM) [B.N.S Babu et al., 1996] based radar data scenario studied here, and does so across all range cells of the scenario.

In testing the equality of two independent groups, t-test plays a very important role for the purpose. This test is reliable when the data is normally distributed. Based on central limit theorem, the normality assumption is fulfilled with large data set, but getting large data set is not always feasible. Most of the time, the researchers have to make do with small sample sizes which are hardly normally distributed. There are many causes of non normality, and one of it is the presence of outliers. One way to handle outliers is by using robust estimator with trimming approach. In this study, robust estimators using different trimming approaches namely adaptive and automatic trimming were proposed as the center measures in Alexander-Govern (AG) test. The results of the Type I error rate was then compared with the original AG test and the classical t-test. The AG test with the adaptive and automatic trimming showed robustness across distributions. The two trimming approaches are comparable to each other in most conditions. As expected the original AG test and classical t-test cannot maintain their robustness especially under skewed distribution.