Standard Control Charts Research Articles

On median control charting under double sampling scheme

Standard Shewhart control charts are often based on the assumption that the observations follow a specific parametric distribution, such as the normal, and outlier-free samples are initially selected to construct control limits for future monitoring of process parameters, e.g., location, dispersion, etc. The median is a popular measure of location which is more robust than mean for heavily skewed distributions. In ideal circumstances (where all the underlying assumptions such as normality and independence are met), the median chart is shown to be less efficient that the mean chart. To overcome the efficiency loss of the median chart, this study presents a set of auxiliary information-based median type Shewhart charts based on parent normal, t and gamma distributed process environments under double sampling scheme. The performance of these charts is evaluated in terms of run length (RL) characteristics such as: average run length (ARL), median run length (MDRL), standard deviation of the run length distribution (SDRL), extra quadratic loss (EQL) and relative ARL (RARL). Moreover, the effects of Step 1 sample size and contaminated environments are examined on the ARL performance of different median-based charting structures, under double sampling scheme. Illustrative examples are also provided to explain the working of the said charts.

Quality Quandaries: How to Set Up a Robust Shewhart Control Chart for Dispersion?

In this article, the authors have outlined procedures to construct Phase I and Phase II standard deviation control charts.

Robust Surveillance of Covariance Matrices Using a Single Observation

In this paper a new technique for monitoring shifts in covariance matrices of Gaussian processes is developed. The processes we monitor are obtained from the covariance matrices estimated using a single observation. These processes follow independent Gaussian distribution in the in-control state, thus allowing for application of standard control charts. Furthermore, in contrary to the existing literature, the suggested procedure is asymptotically robust to the shifts in the mean. The explicit out-of-control distribution for an arbitrary moment of the shift is derived. The performance of numerous multivariate control charts is evaluated in an extensive simulation study and applied to monitoring volatilities on financial markets.

The Synthetic Mean Square Error Control Chart

A synthetic mean square error (MSE) control chart is presented in this study for monitoring the changes in the mean and standard deviation of a normally distributed process. The synthetic MSE control chart is a combination of the standard MSE control chart and the conforming run length (CRL) control chart. From the numerical comparisons, the synthetic MSE control chart is always more efficient than the standard MSE control chart in detecting shifts in the process mean and standard deviation. The synthetic MSE chart also performs better than the exponentially weighted moving average-semicircle (EWMA-SC) chart, except for some cases where the process mean shifts are small.

Process Visualization in Medical Device Manufacture: an Adaptation of Short Run SPC Techniques

ABSTRACT Visualizing and understanding the underlying processes in short production run environments is not possible with standard Shewhart control charts. Administration of multiple charts, frequent setups and changeovers, and the truncated nature of data collection limit the effectiveness of standard statistical process control (SPC) approaches. This article introduces a process visualization approach by adapting short-run SPC and recommends new rules for interpretation.

Design of cumulative sum control schemes for truncated Poisson distribution

The cumulative sum (CUSUM) control chart procedures have proven to be more effective than the standard Shewhart control charts at detecting small shifts in mean under statistical control of any production processes. When one specific size of the mean shift is assumed, the CUSUM chart can be optimally designed in terms of average run length. In this paper, design and implementation procedures of CUSUM control schemes based on zero truncated Poisson distribution are given since zero truncated Poisson distribution has wide applications in industries. These truncated Poisson CUSUMs are easy to design and implement. The proposed design procedure can be used to detect both increasing and decreasing rate cases. The feature of fast initial response (FIR) of the truncated Poisson CUSUM is also discussed. Examples are also illustrated.

Data mining model adjustment control charts for cascade processes

Control charts have been widely recognised as important tools in system monitoring of abnormal behaviour and quality improvement. Traditional control charts have a major assumption that successive observations are uncorrelated and normally distributed. When this assumption is violated, the traditional control charts do not perform well, but instead show increased false alarm rates. In this study, we propose a data mining model adjustment control chart to address autocorrelation problems for cascade processes. The basic idea of the proposed control chart is to monitor the residuals obtained by data mining models. The data mining models used in this study include support vector regression and artificial neural networks. A simulation study was conducted to evaluate the performance of the proposed control chart and compare it with the standard regression adjustment control chart and the observations-based control chart in terms of average run length performance. The results showed that the proposed data mining model adjustment control charts yielded better performance than the two other methods considered in this study.

Probabilidade do erro do tipo I nas cartas X e S de Shewhart sob não normalidade

O objetivo deste artigo é verificar o comportamento das cartas de média e desvio padrão de Shewhart em relação à probabilidade do erro do tipo I quando da violação da suposição de normalidade. Foi realizada a simulação de uma série de 500.000 amostras (subgrupos) de tamanho n = 3, 5, 7, 10, 15, 20 e 25. As amostras foram simuladas a partir das distribuições normal, t de Student, exponencial, qui-quadrado, gamma e Weibull. Verificou-se em dados não normais o aumento na probabilidade de erro do tipo I na carta de médias em todas as distribuições simuladas. O mínimo tamanho da amostra necessário está relacionado ao grau de assimetria da distribuição dos dados, sendo que, em alguns casos, nem mesmo n = 25 apresentou resultados satisfatórios. No gráfico S, o aumento da probabilidade de erro do tipo I é significativamente superior em quase todas as distribuições simuladas e seu comportamento é influenciado não só pelo tipo de distribuição, mas também pelo tamanho da amostra.

Estimating the change point of the cumulative count of a conforming control chart under a drift

In a high quality process, the fraction of nonconforming is very low. In this area, standard Shewhart control charts are no longer useful. The Cumulative Count of Conforming (CCC) control charts, which enumerates the number of conforming items between the occurrences of two nonconforming ones, have been shown to be effective in the monitoring of high quality processes. When the CCC control chart signals an out-of-control condition, the process engineers should search for the source of the assignable causes. Knowing the exact time of the process change would help them to reduce the time for identification of the assignable causes. This paper provides a maximum likelihood estimator for the change point of the nonconforming level of the high quality process with a linear trend. Then, a Monte Carlo simulation is applied to evaluate the performance of the proposed estimator. In addition, the proposed estimator is compared with the MLE of the process fraction nonconforming, derived under a single step change. The results show that the proposed estimator outperforms the MLE designed for step change, when a linear trend disturbance is present in the process.

A Robust Standard Deviation Control Chart

This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse disturbances, that is, outliers spread over the subgroups, or localized disturbances, which affect an entire subgroup. In this article, we compare various robust standard deviation estimators and propose an algorithm that is robust against both types of disturbances. The algorithm is intuitive and is the best estimator in terms of overall performance. We also study the effect of using robust estimators from Phase I on Phase II control chart performance. Additional results for this article are available online as Supplementary Material.

Design and Analysis of Control Charts for Standard Deviation with Estimated Parameters

This paper concerns the design and analysis of the standard deviation control chart with estimated limits. We consider an extensive range of statistics to estimate the in-control standard deviation (Phase I) and design the control chart for real-time process monitoring (Phase II) by determining the factors for the control limits. The Phase II performance of the design schemes is assessed when the Phase I data are uncontaminated and normally distributed as well as when the Phase I data are contaminated. We propose a robust estimation method based on the mean absolute deviation from the median supplemented with a simple screening method. It turns out that this approach is efficient under normality and performs substantially better than the traditional estimators and several robust proposals when contaminations are present.

A Review and perspective on surveillance of Bernoulli processes

Bernoulli processes have been monitored using a wide variety of techniques in statistical process control. The data consist of information on successive items classified as conforming (nondefective) or nonconforming (defective). In some cases, the probability of obtaining a nonconforming item is very small; this is known as a high quality process. This area of statistical process control is also applied to health‐related monitoring, where the incidence rate of a medical problem such as a congenital malformation is of interest. In these applications, standard Shewhart control charts based on the binomial distribution are no longer useful. In our expository paper, we review the methods implemented for these scenarios and present ideas for future work in this area. We offer advice to practitioners and present a comprehensive literature review for researchers. Copyright © 2011 John Wiley & Sons, Ltd.

A robust fault detection and diagnosis strategy for pressure-independent VAV terminals of real office buildings

A robust fault detection and diagnosis (FDD) strategy using a hybrid approach is presented for pressure-independent variable air volume (VAV) terminals in this paper. The residual-based cumulative sum (CUSUM) control charts are utilized to detect faults in VAV terminals. The residuals between the temperature error and its predication are generated using autoregressive time-series models. The standard CUSUM control charts are used to monitor the residuals which are statistically independent. If the CUSUM value exceeds the chart limits, it means the occurrence of fault or abnormity in the corresponding VAV terminal. The residual-based CUSUM control chart can improve the accuracy of fault detection through eliminating the effects of serial correlation on the performance of control charts. Also, the residual-based CUSUM control chart can enhance the robustness and reliability of fault detection through reducing the impacts of normal transient changes. A rule-based fault classifier consisting of expert rules and fault isolation algorithms is developed to isolate 15 fault sources. The FDD strategy was online tested and validated using in real time data collected from real VAV air-conditioning systems.

Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix with Variable Sampling Intervals

Traditional control charts for process monitoring are fixed sampling rate (FSR) control charts based on taking samples of fixed size with a fixed sampling interval between samples. Variable sampling rate (VSR) control charts vary the sampling rate as a function of the data from the process, and can detect most process changes significantly faster than traditional FSR control charts. The main focus of this article is on a type of VSR control chart called a variable sampling interval (VSI) control chart, but another type of VSR control chart based on sequential sampling is also considered. We consider the problem of detecting sustained or transient shifts in the mean or variability of a process. We investigate Shewhart control charts and multivariate exponentially weighted moving average (MEWMA) control charts based on sample means and on the sum of the squared deviations from target. We show that the combination of the standard MEWMA chart and an MEWMA-type chart based on squared deviations from target gives excellent overall performance. When the VSI feature is used with this combination, the performance is dramatically better than the performance of the standard FSR multivariate control charts that have traditionally been used.

Statistical Control and Investigation of Capability of Process and Machine in Wire Cut Edm Process of Gas Turbine Blade Airfoil Tip

Statistical process control (spc), as one of the quality devices, can be help manufacturers improve the quality of their products in today’s competitive world. This research examines the statistical method of wire-cut electric discharge machining (WEDM) process of the turbine blade airfoil tip for control and consistency of the process. For this purpose, the standard deviation control chart, S, and the average data, , which are applied for identifying the acquired factors, have been used. Next, regarding the plan features, the manufacturing process is assessed to determine whether the products meet quality and the customer requirements or not. Therefore, the coefficients Cpk is applied which indicate the capability of the manufacturing process. Then, in order to produce high quality blades within the tolerance range, the capability of WEDM machine is examined, using coefficients CM. Finally, it is shown that in order to produce the desired product, the process can be controlled and fixed by using the statistical process control devices and inspecting the standard deviation of data and investigation of capability of process and machine.

Multivariate EWMA Control Chart with Adaptive Sample Sizes

Standard multivariate control charts usually employ fixed sample sizes at equal sampling intervals to monitor a process. In this study, a multivariate exponential weighted moving average (MEWMA) chart with adaptive sample sizes is investigated. Performance measure of the adaptive-sample-size MEWMA chart is obtained through a Markov chain approach. The performance of the adaptive-sample-size MEWMA chart is compared with the fixed-sample-size control chart in terms of steady-state average run length for different magnitude of shifts in the process mean. It is shown that the adaptive-sample-size chart is more efficient than the fixed-sample-size MEWMA control chart in detecting shifts in the process mean.

Use of quality control charts for detection of outliers and temporal trends in cumulative meta-analysis.

Cumulative meta-analysis (CMA) aims to aggregate accumulating evidence. Essentially a visual tool, CMA should be supplemented by formal statistical methods for assessment of the significance of the accumulating evidence, and for detection of temporal trends in effect sizes. These methods should also take into account multiple testing inherent in CMA. We review the existing methods for detection of temporal trends in effect sizes and suggest a new approach, namely the use of standard quality control (QC) charts, in particular X charts and CUSUM charts, to detect possible outliers and trends over time. We discuss the application of the QC charts to four popular measures of effect size: the odds ratios, the relative risks, the correlation coefficients and the standardized mean differences. Applications of QC charts are illustrated by three meta-analysis examples from medicine, ecology and evolutionary biology. Copyright © 2011 John Wiley & Sons, Ltd.

Robust CUSUM charts for monitoring the process mean and variance

AbstractThis paper considers the problem of obtaining robust control charts for detecting changes in the mean µ and standard deviation σ of process observations that have a continuous distribution. The standard control charts for monitoring µ and σ are based on the assumption that the process distribution is normal. However, the process distribution may not be normal in many situations, and using these control charts can lead to very misleading conclusions. Although some control charts for µ can be tuned to be robust to non‐normal distributions, the most critical problem with non‐robustness is with the control chart for σ. This paper investigates the performance of two CUSUM chart combinations that can be made to be robust to non‐normality. One combination consists of the standard CUSUM chart for µ and a CUSUM chart of absolute deviations from target for σ, where these CUSUM charts are tuned to detect relatively small parameter shifts. The other combination is based on using winsorized observations in the standard CUSUM chart for µ and a CUSUM chart of squared deviations from target for σ. Guidance is given for selecting the design parameters and control limits of these robust CUSUM chart combinations. When the observations are actually normal, using one of these robust CUSUM chart combination will result in some reduction in the ability to detect moderate and large changes in µ and σ, compared with using a CUSUM chart combination that is designed specifically for the normal distribution. Copyright © 2009 John Wiley & Sons, Ltd.

A Two Control Limits Double Sampling Control Chart by Optimizing Producer and Customer Risks

Standard Shewhart process control chart has been widely used, but it is not sensitive in detecting small shift. A number of alternatives have been proposed to improve the capability of control chart. The double sampling (DS) control chart is aimed at improving the capability to detect any small shift out-of control condition by observing the second sample without interruption. The capabilities of DS control chart were measured as the expected sample size (as a measure of inspection cost) or the control chart power (as a measure for customer risk). Optimization of these criteria is used to determine the control limits. In this paper, we optimize both producer and customer risks under a certain expected number of sample sizes as the constraint. Comparing the result to the previous procedure that only optimize customer risk, the proposed optimization procedure gives the same first control limit but smaller second control limits with higher value of control chart power.

A Multivariate Synthetic Control Chart for Monitoring the Process Mean Vector of Skewed Populations Using Weighted Standard Deviations

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method. The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart. The standard multivariate synthetic chart consists of the Hotelling's T 2 chart and the conforming run length chart. The weighted standard deviation method adjusts the variance–covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric. In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T 2 chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses.