Construction Of Control Charts Research Articles

Flexible Control Limits for Interval-Valued Data Using Mixture Probability Distributions

Availability of data in different forms is a boon or bane as it may require different approaches to deal with. In fact, while the construction of control charts is straightforward if the data are real-valued, in many practical situations data are essentially interval-valued with observations often represented by minimum and maximum values. While there are only fewer attempts to develop control charts for interval-valued data, no simple-to-use approaches have been proposed to deal with such type of data. In this paper, considering the idea of the development of control limits for multi-stream processes, we propose to make use of the mixture probability distributions approach to determine control limits for the interval-valued data. The resulting control limits are flexible in nature as they are linked to the control limits of the overall distribution that is based on the average of the means of two upper and lower populations along with their respective standard deviations. We have studied and numerically evaluated the average run length (ARL) properties of the proposed control chart to demonstrate the ways of determining the control chart coefficients. The proposed control chart is then illustrated using a dataset and conclusions are drawn based on the results.

INDIVIDUAL CONTROL CHARTS FOR NON-NORMAL DATA

Individual control charts are a suitable option to consider when the processes being studied change slowly. If obtaining standard samples for Shewhart control charts is expensive or in the case of studying statistical characteristics of the technological process, they are used. Control charts are used to control technological processes in the case of a normal distribution of the possible values of the controlled parameter. Sometimes a quasi-normal distribution of the studied parameter is allowed. In practice, it is often necessary to deal with technological processes in which samples are not distributed according to a normal distribution. In such cases, using individual control charts can lead to type I and II errors. This is because the control limits of the charts are calculated for the mean and standard deviation of the normal distribution. Control charts of individual values are most sensitive to the deviation of the distribution from the normal one since individual values are used to construct the limits, to which the central limit theorem does not apply, as in the case of control charts of mean values. Therefore, it is extremely important to develop methods of applying the individual control charts for random samples, the general population of which is not normally distributed. The study examines the application of individual control charts for a random process that is non-normally distributed. This is achieved by using the normalization method to transform samples of the studied parameter into samples that are distributed normally or quasi-normally. The normalization is performed using the Box-Cox method with further construction of control charts based on the transformed samples. The mathematical apparatus of the individual control chart application for samples with non-normal distribution is described. Numerical modeling of the application of individual control charts for the chi-square distributed samples, which have a significant distribution asymmetry for small values of the shape factor, and for the samples obtained by normalizing the chi-square one, was performed. According to the research findings, the utilization of individual control charts for samples exhibiting a significantly asymmetric distribution results in a higher likelihood of type I errors being detected. However, when the method of sample normalization is employed, this issue is almost entirely eliminated. Modeling process disruption, by changing a certain individual value, also demonstrated the emergence of false signals of process disruption.

Construction of Six Sigma-based control chart for interval-valued data

Construction of control charts is straightforward if the data are real-valued. However, there are situations where data are essentially interval-valued in which each observation is represented by minimum and maximum values. While there are only few attempts to develop control charts for interval-valued data, there have been no simple-to-use approaches developed to deal with such type of data. In this article, we propose to make use of the popular Taguchi orthogonal array experiment to first redefine the data for experimental setup and then use Six Sigma control limits to determine overall control limits for interval-valued data. The resulting multiple control limits have inner and outer control limits for simultaneously monitoring minimum and maximum values of the averages of interval-valued data. The proposed control chart is then illustrated using a data set, and conclusions are drawn based on the results. It is observed that the proposed Six Sigma-based control chart for interval-valued data is, in fact, easy-to-use, and it performs better in detecting the out-of-control situations. We have established this using average run length comparisons as well with the traditional charts.

Construction of Control Charts to Help in the Stability and Reliability of Results in an Accredited Water Quality Control Laboratory

Overall, laboratory water quality analysis must have stability in their results, especially in laboratories accredited by ISO 17025. Accredited parameters should be strictly reliable. Using control charts to ascertain divergences between results is thus very useful. The present work applied a methodology of analysis of results through control charts to accurately monitor the results for a wastewater treatment plant. The parameters analyzed were pH, BOD5, COD, total suspended solids, and total phosphorus. The stability of the results was analyzed from the control charts and 30 analyses performed in the last 12 months. From the results, it was possible to observe whether the results are stable, according to the rehabilitation factor that cannot exceed WN = 1.00 and the efficiency of removal of pollutants that remained above 70% for all parameters. The method of determining the technological reliability and stability of the treatment station using control charts is an efficient tool for detecting any instability in the results. These results help to monitor the results of the analyses more clearly and thus enable a rapid response to possible disturbances and maintain the quality of the analysis control, as well as determining the accreditation entities.

Construction of Control Charts for Monitoring Various Parameters Related to the Management of the COVID-19 Pandemic

To monitor the quality characteristics of a process, appropriate graphical and statistical tools must be used. These tools are capable of showing the evolution over time of the behavior of the quality characteristics (measurable or countable) and detecting situations that seem to present certain anomalies. The control chart is one of these tools widely used in quality management. In the process of managing the COVID-19 pandemic, this tool will make it possible to know at all times whether the parameters monitored such as the positivity rate, the recovery rate, and the mortality rate, are under control and to act accordingly. Monitoring cure and mortality rates will also show us the effectiveness of the treatments used.

An alternative expression for the constant c4[n] with desirable properties

The constant c4[n] is commonly used in the construction of control charts and the estimation of process capability indices, where n denotes the sample size. Assuming the Normal distribution the unbiased estimator of the population standard deviation is obtained by dividing the sample standard deviation by the constant c4[n]. An alternative expression for c4[n] is proposed, and the mathematical induction technique is used to prove its validity. Some desirable properties are described. First, the suggested expression provides the exact value of c4[n]. Second, it is not a recursive formula in the sense it does not depend on the previous sample size. Finally, the value of c4[n] can be directly computed for large sample sizes. Such properties suggest that the proposed expression may be a convenient solution in computer programming, and it has direct applications in statistical quality control.

The role of automation in improving the quality of enterprise business processes

The enterprise has to determine and manage numerous and interrelated activities for successful work and to maximize profits. According to the international standard ISO 9001-2011, the activity using resources and managed in order to transform inputs to outputs can be considered as a business process. Using a process system in an organization along with their identification and interaction, as well as process management aimed at obtaining the desired result, can be defined as a “process approach”. The object of this study is a business process that is one of the key concepts of the international standard ISO 9001-2011. This standard establishes the requirements for quality management systems and describes the principles of applying the process approach, the essence of which is continuous process management. The article deals with the individual business processes in the enterprise and their subsequent task automation with using information technology. An automated application was proposed within the study that provides automatic search for part sizes that do not correspond to the tolerance field, automatic construction of control charts of average values and ranges, as well as calculation of process reproducibility indices.

Multivariate cumulative sum control chart and measure of process capability based on bivariate ranked set schemes

In this article we have proposed multivariate cumulative sum control chart based on bivariate ranked set schemes for quick identification of small variation in the process mean vector. Also, we have offered multivariate measure of process capability based on bivariate ranked set schemes for testing the customer requirements. In the construction of control chart, we have designed plotting statistic, and derived control limit. Regarding the multivariate measure of process capability, we have defined an estimator and then computed the critical values for inference purposes. In order to compare the performance of existing and proposed control charts, we have obtained various performance measures. Results reveal that performance of proposed control chart based on bivariate ranked set schemes depends on the choice of the factors such as sampling scheme, sample size, magnitude of association between concomitant variable and study variables, and size of the shift. Furthermore, comparative analysis shows that the performance of the proposed control chart based on bivariate ranked set schemes outperforms the existing methods. Finally, real life example is included in which we have applied proposed and existing control charts for monitoring calcium–magnesium and residual sodium contents in irrigation water. In addition, the implementation of the proposed multivariate measure of process capability ensures the level of calcium–magnesium and residual sodium contents in irrigation water to satisfy the requirements of customers or engineering tolerance.

Long-Term Quantitative Assessment of Women Survivability from Cancer: A Unique Descriptive Analysis

Statistical Process Control (SPC) methodologies are a set of statistical methods and techniques that were initially designed for industrial processes but could be adopted for non-industrial applications. The current prospective study aimed to provide a unique quantitative investigation of an epidemiological disease using the SPC program platform. The selected case herein was a long-term monitoring record of the yearly cancer mortality rates in women worldwide. Multidimensional segregation of the dataset into subgroups was conducted to visualize the clustering pattern based on nations (42 countries as boxplot), time and the Gaussian Mixture Model (two-interfering bell-shaped distributions approach). The trend of death rates versus the elapsed years would demonstrate a moderately negative correlation with the time following the theory of splines. Construction of control chart based on the fitted Weibull distribution showed a gradual steady improvement in survivability rates from malignancy. The greatest variations in the mortality ratios existed within the European countries.

Control charts based on quantiles: New approaches

Contemporary development of Statistical quality control includes researches on different control charts, which could be easily implemented in production processes due to facilities offered by computers. New control charts give more information about production processes than the conventional ones, that's why there is a lot of investigation in this area of applied statistics. In this paper, we shall explain some new ideas concerning the construction of control charts based on quantiles, empirical distribution function and p-value.

Minimization of energy demand in slaughterhouses: Estimated production of biogas generated from the effluent

Many studies have evaluated agroindustrial effluent treatment systems. However, the use of quality control tools in this area is still not widespread, while reports of the use of such tools to monitor slaughterhouse waste treatment systems are practically non-existent. Investigation of exploitation of the energy potential of waste produced within these industries is a strategically important issue, considering the current drive to minimize environmental impacts and to generate power from renewable sources. Therefore, the purpose of this study was to monitor the biological treatment of effluents, using control charts, as well as to estimate the potential production of methane and biogas in a slaughterhouse in southern Brazil. Wastewater samples were collected weekly and measurements were made of ambient and liquid temperatures, pH, solids (total and volatile), chemical oxygen demand (COD), oils and greases (OG), nitrogen, and phosphorus. The potential for methane and biogas production was estimated using the average daily effluent flow rate and the average organic load removal in the anaerobic pond. The effluent treatment system was evaluated by means of the construction of control charts, using the measured variables. This enabled the identification of factors that influenced the effluent treatment process, such as changes in the affluent load, environmental conditions, waste characteristics, and mechanical and human parameters. In terms of energy potential, the use of a covered pond (biodigester) would partially meet the energy demand of the industry, which consumed approximately 66 m3 of firewood per month, hence requiring 42969 m3 of biogas per month to supply all its needs. According to theoretical data, the waste could generate around 6790 m3 of biogas, which would supply 16% of the energy demand, besides providing environmental advantages such as improved efficiency of the treatment system and reduced emissions of greenhouse gases.

A regression spline control chart for monitoring characteristics exhibiting nonlinear profile over time

Purpose The purpose of this paper is to demonstrate the application of the control chart procedure to monitor the characteristics whose profile over time resembles a set of connected line segments. Design/methodology/approach Fit a regression spline model by taking the subgroup average of the characteristic as response variable and time as the explanatory variable. Then monitor the response variable using the regression spline control chart with the fitted model as center line and upper and lower control limits at three standard deviation units of the response variable above and below the center line. Findings The proposed chart is successfully deployed to monitor the daily response time profile of a client server of an application support process. The chart ensured the stability of the process as well as detected the assignable cause leading to the slowing down of the server performance. Practical implications The methodology can be used to monitor any characteristics whose performance profile over time resembles a set of connected line segments. Some of the examples are the consumption profile of utility providers like power distribution companies, usage profiles of telecom networks, loading profile of airline check-in process, e-commerce websites, etc. Originality/value To the best of the author’s knowledge, construction of control charts using regression spline is new. The usage of the control chart to monitor the performance characteristics which exhibits a nonlinear profile over time is also rare.

Monitoring the process location by using new ranked set sampling-based memory control charts

ABSTRACTThe process monitoring and construction of control charts involves the measurement of the quality characteristic under certain time and cost constraints. Ranked set sampling (RSS) is a very useful and inexpensive method of obtaining a more representative sample when the actual quantification of sampling units is expensive or destructive, while the ranking of the observations is easier. In this paper, RSS and its variation, extreme RSS, median RSS and neoteric RSS are employed to construct new memory type homogeneously weighted moving average (HWMA) control charts to monitor the process location. The HWMA chart assigns a particular weight to the most recent sample, while all the previous samples are assigned an equal proportion of the remaining weight. The run length properties of the proposed control charts are studied by using extensive Monte Carlo simulations. The performance of the proposed charts is compared with the simple random sampling-based exponentially weighted moving average (EWMA) and HWMA besides RSS-based EWMA counterparts. The comprehensive comparisons established the better shift detection ability of the proposed control charts. To demonstrate the practical implementation of the proposed charts, a real industrial dataset is used which also confirms the better mean shift detection ability of the proposed charts.

Robust control charts for percentiles based on location‐scale family of distributions

AbstractIn this paper, robust control charts for percentiles based on location‐scale family of distributions are proposed. In the construction of control charts for percentiles, when the underlying distribution of the quality measurement is unknown, we study the problem of discriminating different possible candidate distributions in the location‐scale family of distributions and obtain control charts for percentiles which are insensitive to model mis‐specification. Two approaches, namely, the random data‐driven model selection approach and weighted modeling approach, are used to construct the robust control charts for percentiles in order to effectively monitor the manufacturing process. Monte Carlo simulation studies are conducted to evaluate the performance of the proposed robust control charts for various settings with different percentiles, false‐alarm rates, and sample sizes. These proposed procedures are compared in terms of the average run length. The proposed robust control charts are applied to real data sets for the illustration of robustness and usefulness.

Construction of Control Chart Based on Six Sigma Initiatives for Regression

Construction of Control Chart Based on Six Sigma Initiatives for Regression

Simulação de Monte Carlo para construção de gráficos de controle no processo de carregamento de etanol no setor sucroalcooleiro

O objetivo deste trabalho foi aplicar a simulação de Monte Carlo para construção de gráficos de controle no processo de carregamento de etanol de uma empresa do setor sucroalcooleiro. O estudo foi desenvolvido utilizando simulação de Monte Carlo atrelada à distribuição triangular, e o resultado usado na definição dos limites superiores e inferiores dos gráficos de controle construídos de modo a identificar falhas no processo de carregamento de etanol. O experimento foi conduzido com informações de uma empresa de etanol situada no noroeste paulista, que forneceu parte de sua base de dados com os tempos de espera dos caminhões em cada etapa do processo de carregamento com destino às distribuidoras localizadas em cidades distintas. Concluiu-se que a metodologia aplicada foi satisfatória na análise das cidades atípicas, permitindo visualização prática e precisa para identificar falhas ou atrasos no processo e, consequentemente, reduzir a dispersão do tempo de carregamento de etanol entre as distribuidoras.

Order statistics in control charts construction

Order statistics are applied in construction of control charts that are used in statistical process control. Control charts monitor the average process level, volatility or extreme values: maximum and minimum. In the paper selected control charts are presented. They were used to analyze the quality of component of a home appliance which are produced by a home appliance manufacturer.

Attribute Control Chart Construction Based on Fuzzy Score Number

There is much uncertainty and fuzziness in product quality attributes or quality parameters of a manufacturing process, so the traditional quality control chart can be difficult to apply. This paper proposes a fuzzy control chart. The plotted data was obtained by transforming expert scores into fuzzy numbers. Two types of nonconformity judgment rules—necessity and possibility measurement rules—are proposed. Through graphical analysis, the nonconformity judging method (i.e., assessing directly based on the shape feature of a fuzzy control chart) is proposed. For four different widely used membership functions, control levels were analyzed and compared by observing gaps between the upper and lower control limits. The result of the case study validates the feasibility and reliability of the proposed approach.

Control charts for monitoring accumulating adverse event count frequencies from single and multiple blinded trials.

Conventional practice monitors accumulating information about drug safety in terms of the numbers of adverse events reported from trials in a drug development program. Estimates of between-treatment adverse event risk differences can be obtained readily from unblinded trials with adjustment for differences among trials using conventional statistical methods. Recent regulatory guidelines require monitoring the cumulative frequency of adverse event reports to identify possible between-treatment adverse event risk differences without unblinding ongoing trials. Conventional statistical methods for assessing between-treatment adverse event risks cannot be applied when the trials are blinded. However, CUSUM charts can be used to monitor the accumulation of adverse event occurrences. CUSUM charts for monitoring adverse event occurrence in a Bayesian paradigm are based on assumptions about the process generating the adverse event counts in a trial as expressed by informative prior distributions. This article describes the construction of control charts for monitoring adverse event occurrence based on statistical models for the processes, characterizes their statistical properties, and describes how to construct useful prior distributions. Application of the approach to two adverse events of interest in a real trial gave nearly identical results for binomial and Poisson observed event count likelihoods. Copyright © 2016 John Wiley & Sons, Ltd.

Robustness of retrospective weighted control charts

This study considers the construction of control charts when outliers could occur in the data. Simply increasing the width of control limits will make it more difficult to detect an out-of-control signal. This study aims to determine weights for each observation by measuring their respective distances to the average. The study proposes a retrospective weighted average and weighted inter-quartile range (WIQR) control chart based on the normal distribution that accounts for the false alarm rate, special causes, outliers, and a combination of special causes and outliers that might exist within the process. In addition to validating the detection effectiveness of the proposed control charts, this study also compares various average-type and range-type control charts for detecting the outliers and special causes. The proposed control charts show superior detection effectiveness in four tested scenarios compared to other types of control charts. Finally, the study also illustrates the practical application of the control charts for measuring the tensile strength of a deformed bar in coil. [Received 10 February 2014; Revised 21 August 2015; Revised 3 November 2015; Accepted 14 December 2015]