Control Chart For Individual Observations Research Articles

Bivariate robust control charts for individual observations

This article introduces a novel robust Shewhart-type control chart designed for monitoring the location of a bivariate process using the Comedian and Sn Covariance estimators. The process of setting control limits for the proposed control charts is demonstrated. To evaluate the performance of the newly proposed control charts, simulations are conducted and compared against existing methods found in the current literature. Furthermore, the article discusses the application of the proposed method using real-life data.

Fuzzy control charts for individual observations to analyze variability in health monitoring processes

In healthcare monitoring, the quality of medical services and patient outcomes are significantly influenced by the unnatural variations emphasizing the importance of effective control and monitoring strategies. In such scenarios the quality is compromised when a shift in the medical process is not detected timely. In this study, we commenced a comprehensive analysis of the variability present in the patient's hematocrit levels. We introduced a novel approach using fuzzy control charts for individual measurements to detect shift within hematocrit levels effectively. For the initial forecasting of hematocrit level variability, we employed the exponential smoothing method by using R software. Following this, we proposed a set of fuzzy control charts intended for individual measurements, including the fuzzy moving average control chart, fuzzy weighted moving control chart, and fuzzy moving range control chart. These control charts are defined with fuzzy control rules, allowing them to analyze and interpret the small shifts in the process precisely. Also, to measure the process's capability for providing a deeper understanding of the processes, fuzzy process capability indices are introduced. A Monte Carlo simulation approach is employed to obtain the performance metrics. Finally, a case study sourced from Kaggle was conducted to evaluate the performance of the proposed fuzzy control charts for assessing hematocrit levels.

Enhancing Multivariate Control Charts for Individual Observations Using ROC Estimates

Abstract Classical Hotelling’s T 2 T^{2} control chart is frequently used for monitoring a multivariate process. The existence of outlying observations in the Phase I data used to determine the control limit can have a significant impact on the accuracy of such control charts, as is well known. Based on the robust reweighted orthogonalized comedian estimates, a robust multivariate quality control chart for individual observations is proposed in this study. Control limit of the proposed robust control chart is estimated by modelling the simulated quantiles for any sample size. A Simulation study has been conducted to examine the performance of the proposed method and compare it with the performances of the classical Hotelling T 2 T^{2} control chart, a robust control chart based on shrinkage reweighted estimator and two robust control charts based on the reweighted minimum covariance determinant estimator. The results demonstrate the effectiveness of the proposed method, even under high-dimensional settings or when the contamination in the Phase I data is high, with both independent and correlated variables. Performance of the proposed method is also illustrated by implementing in a real-world example

Probability‐type, Shewhart‐type and EWMA control charts for individual observations from the two‐parameter Lindley distribution

AbstractLindley distribution is a continuous distribution with various applications some of which are in medicine, genetics, epidemiology, biology, finance and actuarial sciences, ecology, meteorology, sociology, demography, agriculture, hydrology, geosciences, reliability and engineering, life testing and survival analysis, airborne systems and communications, environmental studies and modeling and describing of human mistakes, strikes, accidents, behavioural and emotional or IQ test scores and waiting times of customers in queues until service, etc. Due to its variety of applications, it appears to be important that control charts for detected shifts in a process should be constructed under the assumption that the quality characteristic of interest follows a Lindley‐related distribution. Here, we construct probability‐type, Shewhart‐type and EWMA control charts (and deal with the optimal choice of its parameters) for individual observations from the two‐parameter Lindley distribution, investigate and compare their performance and illustrate them using examples with both simulated and real data. The whole analysis reveals the superiority of using skewness correction for the construction of the control charts against not using it.

Modified hotelling’s T2 control charts using modified mahalanobis distance

This paper proposed new adjusted Hotelling’s T^2 control chart for individual observations. For this objective, bootstrap method for producing the individual observations were employed. To do so, both arithmetic mean vector and the covariance matrix in the traditional Hotelling’s T^2 chart were substituted by the trimmed mean vector and the covariance matrix of the robust scale estimators〖 Q〗_n, respectively which, in turn, its performance is carried out by simulated. In fact, the calculation of false alarms and the probability of detection outlier is used for determining the validity of this modified chart. The findings revealed a considerable significance in its performance.

Statistical Quality and Process Control in Biopharmaceutical Manufacturing-Practical Issues and Remedies.

Statistical quality and process controls (SQC and SPC) are used for monitoring, trending, and ultimately improving biopharmaceutical manufacturing processes and operations. The purpose of this paper is to highlight characteristic features of bioprocess data and their impact on typical SQC and SPC applications, specifically control charts for individual observations (I-chart) and estimation of process performance index (Ppk). Simulated data were used in an attempt to mimic bioprocess data by inducing inhomogeneity, nonstationarity, autocorrelation, and outliers. The first specific part highlights the roles of within and overall standard deviation (SD) estimates for 3σ limits and their impacts on frequently applied sensitizing rules for control charts, i.e. Nelson's rules 1-4. The second part deals with the often-asked question of how many observations are required for estimation of robust 3σ limits. In the third part, five popular approaches for treating censored data (results below or equal to limit of quantification, ≤LOQ) were compared and their impact on 3σ limits and Ppk estimates were assessed. The final section summarizes the typical issues faced by the practitioner in the application of SQC and SPC and provides remedies for setting up robust and efficient control charts for biopharmaceutical process monitoring. Overall, this study shows that process monitoring and subsequent assessment without taking into consideration this atypical nature of biopharmaceutical process can lead to increased false alarm rates, thus impacting the batch release or even possibility of rejecting good batches.

Control chart based on residues: Is a good methodology to detect outliers?

The purpose of this article is to evaluate the application of forecasting models along with the use of residual control charts to assess production processes whose samples have autocorrelation characteristics. The main objective is to determine the efficiency of control charts for individual observations (CCIO) and exponentially weighted moving average (EWMA) charts when they are applied to residuals of models of AR(1) or MA(1) to detect outlier in autocorrelated processes. Considering autocorrelation strength and sign in the data series and the outlier range, the series were simulated accomplishing 640,000 sets. The series were contaminated by anomalous observations at 100th position, an AR(1) or MA(1) model were fitted, and the residuals were evaluated by CCIO and EWMA control charts; the points correctly detected as an autocorrelation were recorded. For the parameters investigated (autocorrelation and outlier range), a detection rate was generated in each chart, and nonparametric comparison tests were applied. The result of the tests showed the superiority (p < 0.05) of the CCIO chart for both models. The study of the influence of the sign and magnitude of the autocorrelation parameter showed no significant (p > 0.05) for either AR(1) or MA(1) charts and models. In this context, control charts for individual observations (CCIO) were confirmed to effectively detect outliers through residuals in industrial autocorrelated processes originated in first-order AR and MA models.

The performance of control charts for large non‐normally distributed datasets

AbstractBecause of digitalization, many organizations possess large datasets. Furthermore, measurement data are often not normally distributed. However, when samples are sufficiently large, the central limit theorem may be used for the sample means. In this article, we evaluate the use of the central limit theorem for various distributions and sample sizes, as well as its effects on the performance of a Shewhart control chart for these large non‐normally distributed datasets. To this end, we use the sample means as individual observations and a Shewhart control chart for individual observations to monitor processes. We study the unconditional performance, expressed as the expectation of the in‐control average run length (ARL), as well as the conditional performance, expressed as the probability that the control chart based on estimated parameters will have a lower in‐control ARL than a specified desired in‐control ARL. We use recently developed factors to correct the control limits to obtain a specified conditional or unconditional in‐control performance. The results in this paper indicate that the control chart should be applied with caution, even with large sample sizes.

A Nonparametric Phase I Control Chart for Individual Observations Based on Empirical Likelihood Ratio

One common challenge in nonmanufacturing control chart applications is that many of the nonmanufacturing quality characteristics are not normally distributed. In these applications, normal transformation of the observations is certainly feasible; however, it will be done at the expense of the interpretability of the analysis that is particularly important to control chart users in nonmanufacturing industries.Most of the existing nonparametric control charts are designed for Phase II monitoring. Little has been done in developing nonparametric Phase I control charts especially for individual observations that are prevalent in nonmanufacturing applications. In this work, we propose a new nonparametric Phase I control chart for monitoring the location parameter whose construction is essentially based on the empirical likelihood ratio test. The performance of the proposed chart, in terms of the signal probability, compares favorably with the recently developed charts for individual observations. A nonmanufacturing example is included in which the proposed chart and the other competing charts are applied and compared. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables

Statistical Process Control monitoring of the ratio Z of two normal variables X and Y has received too little attention in quality control literature. Several applications dealing with monitoring the ratio Z can be found in the industrial sector, when quality control of products consisting of several raw materials calls for monitoring their proportions (ratios) within a product. Tables about the statistical performance of these charts are still not available. This paper investigates the statistical performance of a Phase II Shewhart control chart monitoring the ratio of two normal variables in the case of individual observations. The obtained results show that the performance of the proposed chart is a function of the distribution parameters of the two normal variables. In particular, the Shewhart chart monitoring the ratio Z outperforms the (p = 2) multivariate T2 control chart when a process shift affects the in‐control mean of X or, alternatively, of Y and the correlation among X and Y is high and when the in‐control means of X and Y shift contemporarily to opposite directions. The sensitivity of the proposed chart to a shift of the in‐control dispersion has been investigated, too. We also show that the standardization of the two variables before computing their ratio is not a good practice due to a significant loss in the chart's statistical performance. An illustrative example from the food industry details the implementation of the ratio control chart. Copyright © 2013 John Wiley &amp; Sons, Ltd.

A Short Biogram of Ryszard Zieliński

Ryszard Zielinski Normal 0 21 false false false EN-AU ZH-CN X-NONE (1 July1932 - 30 April 2012) Ryszard Zielinski was born on 1 July 1932 in Warsaw, where he lived till the fall of the Warsaw Uprising in October 1944. After the Uprising the whole family was relocated from Warsaw to the German transit camp in Prushkov, near Warsaw. After his mother passed away he moved to the nearby city of Piastow. In 1950 he enrolled in the Main School of Planning and Statistics (SGPIS, currently The Warsaw School of Economics), and in 1953 he obtained his bachelor’s degree in Statistical Quality Control. In 1955 he was awarded a Master’s degree for a thesis “Power of control chart for individual observations” prepared under the supervision of Prof. Wieslaw Sadowski. Normal 0 21 false false false EN-AU ZH-CN X-NONE Immediately after graduation he was ordered to work in POLAM (Rosa Luxemburg Lamp Manufacturing Facility) in Warsaw. He was appointed as an engineer in the department of Quality Control and later as a specialist in Quality Control. Ryszard continued to develop his research interests towards his PhD degree that was awarded by SGPiS in 1961. His PhD project on the “Operation of a railway interchange: economical and organisational problems” was developed under the supervision of Prof. Wieslaw Sadowski. During his PhD project, he also enrolled in a second degree at the Department Mathematics and Physics at the Warsaw University and completed his Master degree with the thesis “Applications of mathematical statistics to estimate carbon content in steel”, again under the supervision of Prof. Wieslaw Sadowski. On 30 June 1959 he resigned from his position at POLAM. On his departure Ryszard received an opinion of “an accurate, conscientious and disciplined employee, extremely creative and with administrative talents”. On 1 July 1959 he joined the Facility for Experimental Production of Computers where he stayed until 30 October 1963. “He was a leader of the team working on applications of Mathematics to solving problems in Engineering and Economics including the development of numerical algorithms implemented on the computer ZAM-2. Wide knowledge of methods of Applied Mathematics and a thorough understanding of diverse physical situations was required in order to build mathematical models for a large variety of problems. “ (a quotation from a written assessment Ryszard received on 2 September 1963 from Krzysztof Moszynski, Head of the Office of Programming and Applications of Computers, now Professor of Mathematics. From 2 November 1963 until 30 September 1965 Ryszard was employed at the Air Force Technical Institute, where he initiated and convened a seminar “Monte-Carlo methods and mathematical modelling”. While working at the Facility for Experimental Production of Computers and at the Air Force Technical Institute, Richard maintained a part time appointment at IMPAN, the Institute of Mathematics of the Polish Academy of Sciences (since 1 March 1960). It was to be his life-long association with IMPAN. On 1 October 1965 his appointment was converted to full time. In 1976 Richard was awarded the highest academic degree (equivalent to a D.Sc.) at IMPAN on the basis of a dissertation “ Global stochastic approximation”. Twelve years later, in 1988 he was promoted to a Professor of Mathematical Science and finally, in 1997 he was offered a post of a Professorial Chair at IMPAN. Normal 0 21 false false false EN-AU ZH-CN X-NONE

Some Notes on Multivariate Statistical Process Control

Received: 29 October 2012 Abstract Accepted: 23 November 2012 In the article some features of multivariate statistical process control were introduced. Advantages and disadvantages of multivariate control charts (Hotelling charts) – counterpart of traditional Shewhart control charts in multivariate space – were also shown. The author pointed out the advantage of Hotelling charts over traditional ones in some situations. The main part of the paper is a multivariate surveillance procedure based on the division on two stages: Phase I (phase of stabilization) and Phase II (phase of monitoring). After describing some elements of multivariate statistical process control implementation (considered from the methodological point of view) author introduced two most popular control charts used in industrial practice: control charts for individual observations and for means. The article is summarized by some author’s conclusions concerning popularity of multivariate surveillance and future directions of his work.

An Adaptive Multivariate Control Chart for Individual Observations with Adaptive EWMS Star Glyphs for Diagnosis

A time-weighted multivariate control chart for individual observations is introduced to monitor process variability changes in multiple quality characteristics in phase II applications. Because of adaptive adjustments, the proposed control chart is sensitive to total variation increase in a multivariate manufacturing process. A new visualization tool, named adaptive EWMS star glyphs, is proposed for process diagnosis once an out-of-control signal is found. An example is presented to illustrate the application of the proposed charting procedure.

Robustness of the EWMA control chart for individual observations

The traditional exponentially weighted moving average (EWMA) chart is one of the most popular control charts used in practice today. The in-control robustness is the key to the proper design and implementation of any control chart, lack of which can render its out-of-control shift detection capability almost meaningless. To this end, Borror et al. [5] studied the performance of the traditional EWMA chart for the mean for i.i.d. data. We use a more extensive simulation study to further investigate the in-control robustness (to non-normality) of the three different EWMA designs studied by Borror et al. [5]. Our study includes a much wider collection of non-normal distributions including light- and heavy-tailed and symmetric and asymmetric bi-modal as well as the contaminated normal, which is particularly useful to study the effects of outliers. Also, we consider two separate cases: (i) when the process mean and standard deviation are both known and (ii) when they are both unknown and estimated from an in-control Phase I sample. In addition, unlike in the study done by Borror et al. [5], the average run-length (ARL) is not used as the sole performance measure in our study, we consider the standard deviation of the run-length (SDRL), the median run-length (MDRL), and the first and the third quartiles as well as the first and the 99th percentiles of the in-control run-length distribution for a better overall assessment of the traditional EWMA chart's in-control performance. Our findings sound a cautionary note to the (over) use of the EWMA chart in practice, at least with some types of non-normal data. A summary and recommendations are provided.

An Alternative Hotelling T^2 Control Chart Based on Minimum Vector Variance (MVV)

The performance of traditional Hotelling T 2 control chart using classical estimators in Phase I suffers from masking and swamping effect. To alleviate the problem, robust location and scale estimators are recommended. This paper proposed a robust Hotelling T 2 control chart for individual observations based on minimum vector variance (MVV) estimators as an alternative to the traditional multivariate T 2 control chart for Phase II data. MVV is a new robust estimator which possesses the good properties as in minimum covariance determinant (MCD) with better computational efficiency. Through simulation study, we evaluate the performance of the proposed chart in terms of probability of detection and false alarm rates and compared with the performance of the traditional charts and the chart issued from MCD estimators. The results showed that MVV control chart has competitive performance relative to MCD and traditional control charts even under certain location parameter shifts in Phase I data.

A comparative study of phase II robust multivariate control charts for individual observations

Use of Hotelling's T2 charts with high breakdown robust estimates to monitor multivariate individual observations are the recent trend in the control chart methodology. Vargas (J. Qual. Tech. 2003; 35: 367-376) introduced Hotelling's T2 charts based on the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD) estimates to identify outliers in Phase I data. Studies carried out by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615-629) indicated that the performance of these charts heavily depends on the sample size, amount of outliers and the dimensionality of the Phase I data. Chenouri et al. (J. Qual. Tech. 2009; 41: 259-271) recently proposed robust Hotelling's T2 control charts for monitoring Phase II data based on the reweighted MCD (RMCD) estimates of the mean vector and covariance matrix from Phase I. They showed that Phase II RMCD charts have better performance compared with Phase II standard Hotelling's T2 charts based on outlier free Phase I data, where the outlier free Phase I data were obtained by applying MCD and MVE T2 charts to historical data. Reweighted MVE (RMVE) and S-estimators are two competitors of the RMCD estimators and it is a natural question whether the performance of Phase II Hotelling's T2 charts with RMCD and RMVE estimates exhibits similar pattern observed by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615-629) in the case of MCD and MVE-based Phase I Hotelling's T2 charts. In this paper, we conduct a comparative study to assess the performance of Hotelling's T2 charts with RMCD, RMVE and S-estimators using large number of Monte Carlo simulations by considering different data scenarios. Our results are generally in favor of the RMCD-based charts irrespective of sample size, outliers and dimensionality of Phase I data. Copyright © 2010 John Wiley & Sons, Ltd.

A Multivariate Robust Control Chart for Individual Observations

To monitor a multivariate process, a classical Hotelling's T2 control chart is often used. However, it is well known that such control charts are very sensitive to the presence of outlying observations in the historical Phase I data used to set the control limit. In this paper, we propose a robust Hotelling's T2-type control chart for individual observations based on highly robust and efficient estimators of the mean vector and covariance matrix known as reweighted minimum covariance determinant (RMCD) estimators. We illustrate how to set the control limit for the proposed control chart, study its performance using simulations, and illustrate implementation in a real-world example.

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts (one for each quality characteristic). A numerical example illustrates the proposed control charts.

On the Superiority of a Variable Sampling Interval Control Chart

The paper establishes the analytical grounds of the uniform superiority of a variable sampling interval (VSI) Shewhart control chart over the conventional fixed sampling interval (FSI) control chart, with respect to the zero-time performance, for a wide class of process distributions. We provide a sufficient condition on the distribution of a control chart statistic, and propose a criterion to determine the control limits and the regions in the in-control area of the VSI chart, corresponding to the different sampling intervals used by it. The condition and the criterion together ensure the uniform zero-time superiority of the VSI chart over the matched FSI chart, in detecting a process shift of any magnitude. It is shown that normal, Student's t and Laplace distributions satisfy the sufficient condition. In addition, chi-square, F and beta distributions satisfy it, provided that these are not extremely skewed. Further, it is illustrated that the superiority of the VSI feature is not trivial and cannot be assured if the sufficient condition is not satisfied or the control limits and the regions are not determined according to the proposed criterion. An application of the result to confirm the superiority of the VSI feature is demonstrated for the control chart for individual observations used to monitor a milk-pouch filling process.

A Comparison of Shewhart Individuals Control Charts Based on Normal, Non‐parametric, and Extreme‐value Theory

AbstractSeveral control charts for individual observations are compared. Traditional ones are the well‐known Shewhart individuals control charts based on moving ranges. Alternative ones are non‐parametric control charts based on empirical quantiles, on kernel estimators, and on extreme‐value theory. Their in‐control and out‐of‐control performance are studied by simulation combined with computation. It turns out that the alternative control charts are not only quite robust against deviations from normality but also perform reasonably well under normality of the observations. The performance of the Empirical Quantile control chart is excellent for all distributions considered, if the Phase I sample is sufficiently large. Copyright © 2003 John Wiley &amp; Sons, Ltd.