Different Types Of Control Charts Research Articles

Adjustment of Measurement Error Effects on Dispersion Control Chart with Distribution-Free Quality Variable

In industrial processes, control charts are useful tools to monitor the quality of products and detect possibly out-of-control processes. While many types of control charts have been available for data analysts, they were developed by assuming that the variables are precisely measured. In applications, however, measurement error is ubiquitous when data are falsely recorded by investigators or imprecisely collected by unadjusted machines. Even though the impacts of measurement error for different types of control charts have been explored, error-corrected control charts are still unavailable. In this study, we propose a new dispersion control chart with error correction to fill out this research gap. Our key idea is to convert the observed distribution-free process variables into a flexible sign statistic, and then adopt a function to adjust the measurement error effects on the sign statistic. Finally, we develop an exponentially weight-moving average dispersion control chart with measurement error correction based on the corrected sign statistic. The proposed error-corrected dispersion control chart not only eliminates measurement error effects, but also provides more reliable control limits for monitoring process dispersion. Throughout the numerical examination, we find that the proposed error-corrected dispersion control chart is effective in handling moderate and large levels of measurement error and shows good out-of-control detection performance. Finally, the proposed error-corrected dispersion control chart is implemented in the semiconductor data.

Time and magnitude monitoring using Weibull based Max-EWMA chart

To monitor time and magnitude, different types of control charts have been proposed in the literature. This article proposes a new maximum exponentially weighted moving average (Max-EWMA) control chart by assuming Weibull distribution. The test-statistic of the Max-EWMA chart consists of two EWMA statistics, where one statistic is used for monitoring magnitude while the other to monitor time interval between events. The performances of the proposed chart is assessed on the basis of run length characteristics like, average run length (ARL), standard deviation of the run length (SDRL), and quantiles of the run length distribution. Besides extensive simulation studies, real data sets are also considered to show the applications of the proposed chart. The results show that the proposed chart is efficient in detecting different size of small shifts.

Comparing the performance of Kernel PCA Mix Chart with PCA Mix Chart for monitoring mixed quality characteristics

Along with the development of information and technology, the quality characteristics of a product cannot be monitored separately in the different types of control charts. In the past, conventional control charts were developed to monitor only one type of quality characteristic. The variable control charts are used to observe the variable or metric quality characteristics. Meanwhile, in monitoring non-metric characteristics or categorical data, attribute control charts are employed. To accommodate these two types of data, the PCA Mix control chart is suggested to simultaneously monitor these two types of data in one chart. However, some drawbacks occur when this chart is applied to monitor non-metric data which has an imbalanced proportion. Therefore, the Kernel PCA Mix control chart is created to overcome the gaps that occurred in the PCA Mix chart. Similar to the previous chart, this chart is also constructed using Hotelling’s T2 statistics with Kernel Density Estimation control limit. Several simulations are used to evaluate the performance of the proposed control charts. The simulation results show that the proposed chart has a better result than the previous control chart, especially for a small mean shift with an imbalanced proportion of non-metric data. However, the PCA Mix chart has a similar performance to the proposed chart when it is applied to monitor the balanced proportion of categorical data with a large mean shift. The application with simulated data with various scenarios and the real-world case also shows that the Kernel PCA Mix chart performs better compared to the performance of the PCA Mix chart.

On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion.

Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research works have been conducted on the conditional ARL performance of different types of control charts. In this paper, by simulating the empirical distribution of the conditional ARL and especially using the exceedance probability criterion (EPC), we study the conditional ARL performance of the synthetic chart. Our results show that a large amount of Phase I samples is needed to obtain a specified EPC of the synthetic chart. For the available number of Phase I samples, the control limits of the synthetic chart are adjusted using the EPC method to improve its conditional in-control performance. It is shown that, for small mean shift sizes, a tradeoff should be made between the conditional in-control and out-of-control performances. For moderate to large shifts, the conditional performance of the synthetic chart using the adjusted control limits is generally satisfied. By comparing the results with the ones using the bootstrap approach, it can also be concluded that the conditional performances of both approaches are comparable. While the method proposed in this paper requires much less computation work than the bootstrap approach.

Process control in electron beam sterilization of medical devices and a pathway to parametric release

This paper presents a review of process control methods in electron beam sterilization of medical devices. Starting from normative requirements, the proper use of different types of control charts to demonstrate that the process is in statistical control, is discussed in depth. Special emphasis is laid on the establishment of control limits. Their performance is analyzed using data from an actual electron beam process. In addition to SPC charts for monitoring doses, the concept of a performance index based on processing parameters is proposed and its implementation in control charts is discussed. It is shown that these charts allow an extraordinary tight control of the sterilization process which is superior to standard monitoring dosimetry. Especially time-weighted control (CUSUM) charts are identified as means to control a process effectively.Subsequently, the process parameter analysis approach is extended towards assessment and decision whether product specifications have been met and a potential pathway to parametric release from electron beam sterilization is outlined. A process definition method which addresses minimum and maximum dose specifications directly and does not rely on monitoring doses is presented in an example using actual data. Terminology and the treatment of uncertainties follow closely the ISO 11137 family of standards.A discussion of potential advantages of parametric release and a roadmap and requirements for this paradigm shift in electron beam sterilization of medical devices complement the paper.

On process monitoring using location control charts under different loss functions

Process monitoring is essential and plays a vital role in enhancing the quality of the output. For this purpose, many statistical tools are used in practice and the control chart is one of the most popular choices. Bayesian and classical set-ups are two major and popular categories for defining the design structures of different types of control charts. This study planned to investigate the Bayesian control charts under different loss functions to ensure an efficient monitoring of process parameters for quality control. The performance measures used in this study are average run length (ARL), relative ARL (RARL), extra quadratic loss (EQL) and performance comparison index (PCI). It has been observed that the application of Bayesian structure of process monitoring needs careful consideration in terms of prior distribution, sampling and posterior (predictive) distributions, and the choice of loss functions, in order to obtain reliable outcomes.

On the Efficiency of Runs Rules Schemes for Process Monitoring

There are two main types of variations, namely, common and special causes leading to in-control and out-of-control states, respectively. Control charts are popular tools used to differentiate between these two states of a process. Implementation of runs rules schemes with control charts is an attractive approach for process monitoring. This study is designed to describe the methodology of runs rules schemes and discuss their implementation for different types of control charts. We have considered memory-less charts, namely, , S, and R charts for our study purposes. It is examined that the efficiency gain depends on the number of decision points utilized to implement a given rule. Moreover, superiority of runs rules schemes may vary for different types of location and dispersion charts. An application example using a dataset is also included in the study for practical considerations. Copyright © 2015 John Wiley & Sons, Ltd.

A Comparison of Normal Approximation Rules for Attribute Control Charts

Control charts, known for more than 80 years, have been important tools for business and industrial manufactures. Among many different types of control charts, the attribute control chart (np-chart or p-chart) is one of the most popular methods to monitor the number of observed defects in products, such as semiconductor chips, automobile engines, and loan applications. The attribute control chart requires that the sample size n is sufficiently large and the defect rate p is not too small so that the normal approximation to the binomial works well. Some rules for the required values for n and p are available in the textbooks of quality control and mathematical statistics. However, these rules are considerably different and hence it is less clear which rule is most appropriate in practical applications. In this paper, we perform a comparison of five frequently used rules for n and p required for the normal approximation to the binomial. Based on this result, we also refine the existing rules to develop a new rule that has a reliable performance. Datasets are analyzed for illustration.

Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

AbstractTo use control charts in practice, the in‐control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured by the false alarm probability or the average run length. We suggest an adjustment of the monitoring schemes to overcome these problems. It guarantees, with a certain probability, a conditional performance given the estimated in‐control state. The suggested method is based on bootstrapping the data used to estimate the in‐control state. The method applies to different types of control charts, and also works with charts based on regression models. If a non‐parametric bootstrap is used, the method is robust to model errors. We show large sample properties of the adjustment. The usefulness of our approach is demonstrated through simulation studies.

The Ex-Vivo Expansion of Cytokine Induced Killer (CIK) Cells Can Be Optimized Predicting Cell Expansion Dynamics by Means of Multivariate Statistical Data Analysis

AbstractAbstract 4125 Introduction and Aims.CIK cells are CD3+/CD56+ T lymphocytes known for their antitumour effect against several haematological malignancies and solid tumours. CIK cells are obtained ex-vivo by stimulating peripheral blood mononucleated cells (MNC) with IFN-gamma (day 0), IL-2, anti-CD3 monoclonal-antibody (day 1) and IL2 every 3 days from day 1 to the 21st when maximum expansion of CD3+/CD56+ is expected as firstly described by Negrin. The percentage of CIK cells at the end of expansion represents a criteria for batch release: if CIK cells are less than 40% of the bulk population at the end of the culture, the batch should be considered suboptimal for transplantation. We have analyzed cell expansion dynamics of 30 samples evaluating the composition of cells constituting the bulk. In 11 samples (37%) CIK percentage reached plateau on day 17 instead of day 21, and then started to decrease rapidly. We believe that it is fundamental for the operator to predict in advance the harvest day in which CIK cells reach the maximal concentration in the bulk. Thus, the aim of this study was to introduce a new approach to control and optimize the expansion process based on multivariate statistical data analysis in order to improve its quality. Methods.Multivariate Batch Statistical Process Control (BSPC) and regression models based on Bidirectional-Orthogonal Projections to Latent Structures (O2PLS) were applied for monitoring the expansion process. Phenotypical analysis of cell populations was performed by flow cytometry by measuring the following different cellular subsets (11 variables): total T lymphocytes (CD3+), T-Helper lymphocytes (CD3+4+), T-cytotoxic lymphocytes (CD3+8+), CIK cells (CD3+56+), NK cells (CD3–56+), T lymphocytes (CD3+56-), monocytes (CD14+), B lymphocytes (CD19+), granulocytes (CD33+) and the undifferentiated subset CD3–56-. BSPC allowed us to produce suitable control charts while to estimate the level of CIK cells on days 17 and 21 we built different O2PLS regression models using as predictors the descriptions of the cellular population of the previous days. The chained use of the obtained regression models enabled us to predict in advance unsatisfactory expansions. Results.The expansions having a percentage of CIK cells ≥40% were used to build different types of control charts. In particular, the charts based on DModX and on T2 resulted predictive in the detection of unsatisfactory expansions. Indeed the expansions having CIK <40% on day 17 or on day 21 showed at least one time point out of the control limits for the two charts (Figure 1). Three O2PLS regression models were calculated. By considering the first three time points of expansion (day 0, day 4 and day 7), we obtained a regression model to estimate the CIK percentage on day 21 highly predictive (in Figure 2 we report the behavior of the model during cross validation). The interpretation of the model in terms of single measured variable pointed out that to estimate CIK percentage on day 21, only four out of eleven variables could be considered significant markers able to predict growth kinetic of CIK population during expansion. These variables are: the % of CIK cells on day 7, % of cytotoxic T lymphocytes on day 4 and % of NK at the beginning of the culture.Other two independent regression models were built to estimate CIK percentage on day 17 and on day 21 respectively These models used data collected until day 14 and resulted more accurate than the screening model.To validate the procedure based on the chained use of these three regression models, we tested it on three new batches. All new batches were correctly estimated as optimal or suboptimal at the end of the culture. Discussion.Multivariate statistical data analysis has been shown to be useful in generating suitable control charts and predictive models for biological experiments usually full of variables. In our study we showed that it is possible to predict the composition of the harvested population by considering the description of the cellular bulk population at the very early stages of the expansion realizing in advance if a batch will achieve acceptance criteria for release or not. The proposed approach is promising both for improving the quality of the process and for saving time and resources. Furthermore, the developed models are dynamics since they can be constantly refined by adding new data. [Display omitted] [Display omitted] Disclosures:No relevant conflicts of interest to declare.

Quality Initiatives: Statistical Control Charts: Simplifying the Analysis of Data for Quality Improvement

Quality improvement (QI) projects are an integral part of today's radiology practice, helping identify opportunities for improving outcomes by refining work processes. QI projects are typically driven by outcome measures, but the data can be difficult to interpret: The numbers tend to fluctuate even before a process is altered, and after a QI intervention takes place, it may be even more difficult to determine the cause of such vacillations. Control chart analysis helps the QI project team identify variations that should be targeted for intervention and avoid tampering in processes in which variation is random or harmless. Statistical control charts make it possible to distinguish among random variation or noise in the data, outlying tendencies that should be targeted for future intervention, and changes that signify the success of previous intervention. The data on control charts are plotted over time and integrated with various graphic devices that represent statistical reasoning (eg, control limits) to allow visualization of the intensity and overall effect-negative or positive-of variability. Even when variability has no substantial negative effect, appropriate intervention based on the results of control chart analysis can help increase the efficiency of a process by optimizing the central tendency of the outcome measure. Different types of control charts may be used to analyze the same outcome dataset: For example, paired charts of individual values (x) and the moving range (mR) allow robust and reliable analyses of most types of data from radiology QI projects. Many spreadsheet programs and templates are available for use in creating x-mR charts and other types of control charts.

The Performance of the Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters

The adaptive exponentially weighted moving average (AEWMA) control chart has the advantage of detecting balance mixed range of mean shifts. Its performance has been studied under the assumption that the process parameters are known. Under this assumption, previous studies have shown AEWMA to provide superior statistical performance when compared with other different types of control charts. In practice, however, the process parameters are usually unknown and are required to be estimated. Using a Markov Chain approach, we show that the performance of the AEWMA control chart is affected when parameters are estimated compared with the known‐parameter case. In addition, we show the effect of different standard deviation estimators on the chart performance. Finally, a performance comparison is conducted between the exponentially weighted moving average (EWMA) chart and the AEWMA chart when the process parameters are unknown. We recommend the use of the AEWMA chart over the ordinary EWMA chart especially when a small number of Phase I samples is available to estimate the unknown parameters. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Continuously Monitoring Categorical Processes

Practitioners from diverse fields are concerned with the continuous monitoring of categorical quality characteristics. For this purpose, we propose different types of control charts to detect both violations of the in-control marginal distribution and of the serial dependence structure. We discuss approaches for designing and evaluating these charts, and we investigate their out-of-control performance. Brief summaries about basic concepts and models from categorical time series analysis complete the article.

A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts

Despite their capability in monitoring the variability of the processes, control charts are not effective tools for identifying the real time of such changes. Identifying the real time of the change in a process is recognized as change-point estimation problem. Most of the change-point models in the literature are limited to fixed sampling control charts which are only a special case of more effective charts known as variable sampling charts. In this paper, we develop a general fuzzy-statistical clustering approach for estimating change-points in different types of control charts with either fixed or variable sampling strategy. For this purpose, we devise and evaluate a new similarity measure based on the definition of operation characteristics and power functions. We also develop and examine a new objective function and discuss its relation with maximum-likelihood estimator. Finally, we conduct extensive simulation studies to evaluate the performance of the proposed approach for different types of control charts with different sampling strategies.

Surveillance of the covariance matrix of multivariate nonlinear time series

In this paper, sequential procedures for the surveillance of the covariance matrices of multivariate nonlinear time series are introduced. Two different types of control charts are proposed. The first type is based on the exponential smoothing of each component of a local measure for the covariances. The control statistic is equal to the Mahalanobis distance of this quantity with its in-control mean. In our second approach, the Mahalanobis distance is first determined and after that it is exponentially smoothed. We discuss three examples of local measures. Several properties of the proposed schemes are discussed assuming the target process to be generated by a multivariate GARCH(1, 1) model. The generalization to the family of spherical distributions allows the modelling of frequently observed fat tails in financial data. Some results of an extensive Monte Carlo simulation study are provided in order to judge the performance of the presented control schemes. As a performance measure we use the average run length. An empirical example illustrates the importance of the fast detection of the changes in the covariance structure of the returns of financial assets.

Health care organization improvement reports using control charts for key quality characteristics: ORYX measures as examples.

Some medical centers have developed quarterly quality performance reports consisting of key quality characteristics reported in the form of annotated control charts. The content of these reports needs to be linked with the mission, vision, values, and the structure of the organization. A partial example using one hospital's Joint Commission on Accreditation of Healthcare Organizations' ORYX measures is presented along with comments. The examples have been chosen to show the use of different types of control charts (XmR, P, and rare events) and different clinical conditions (congestive heart failure, low birth weight, and chronic obstructive pulmonary disease).

The Statistical Design of Quality Control Charts

A method is presented for designing quality control charts on the basis of their statistical performance over specified in-control and out-of-control regions of parameter values. This approach provides a rationale for choosing between different types of control charts. It is shown that a reference value larger than the value recommended by Ewan & Kemp (1960) is appropriate for the two-sided CUSUM quality control procedure when the in-control region consists of an interval of parameter values.