Assignable Causes Of Variation Research Articles

Attribute statistical process control under nonconstant process deterioration

AbstractA statistical process control (SPC) model is introduced that incorporates sample data on the number of defectives and allows the probability that an assignable cause of variation in each time interval of a finite production process to be nonconstant. A Limited Memory Influence Diagram (LIMID) model is implemented to facilitate the decision in each time interval on whether or not to investigate the potential presence of the assignable cause of variation and restore the process to working condition. The method determines control limits that minimize the costs of inspection, repair, sampling, and operating under the assignable cause of variation. Sample size and sampling intervals can also be adjusted to further reduce the costs of maintaining quality control. This method expands on the capabilities of models that assume that the conditional probability of an assignable cause occurring remains constant throughout the production horizon.

Intermittent sampling for statistical process control with the number of defectives

An intermittent sampling model for statistical process control (SPC) is introduced to monitor the quality of output from a production process where the number of defective units in a sample is measured in selected time periods. A Limited Memory Influence Diagram (LIMID) model is implemented to determine the time periods in which to collect samples and the decision strategy to minimize total costs of quality control. In periods where samples are collected, the observed defectives determine whether the process is stopped to investigate and repair an assignable cause of variation. Based on sample results, the process can alternatively be allowed to run without interruption until the next predetermined sampling interval, or the results may suggest collecting a sample again in the next period. The model only requires the user to know the result of the current sample to make a decision, in contrast to Bayesian methods that require calculations based on all prior samples and a history of actions. Despite the limited and intermittent nature of the information, the model provides lower quality costs than existing methods for a wide range of production time horizons.

Application of Statistical Quality Control in Monitoring the Production, Packaging and Marketing Process of Sachet Water

Statistical process control is a technique employed to enhance the quality and productivity of processes and the distribution or marketing of its products. Sachet water is a product that has become popular and is being used as a replacement for lack of potable water. It is an alternative that is readily available, affordable but with questions about its purity, production and marketing processes. The objective of this study is to apply statistical control charts in monitoring the production, packaging and distribution or marketing processes of sachet water in Nigeria. This paper employed statistical quality control approach to monitor process stability in a Table Water manufacturing company. Quality control tools such as p-chart, u-chart, X-bar and R charts as well as process capability chart were use to observed field data obtained from the sachet water manufacturing company on important processes of sachet water production and marketing for 30 working days. This was done to check if the processes were in control or out of control and to verify the capability of the marketing process of the product meeting preset specifications. With this, the statistical control charts suitable for the processes were constructed using package “qcc” in R software version 3.6.1. The results from p-chart and u-chart showed that the production and packaging process of the product is not in control and hence the need for further investigations and corrective measures to prevent variability in the process and thus allowing improvement in the quality of the product. Also, the results from X-bar and R charts showed that the marking process was in statistical process control in respects of the product sales recorded by the four independent marketers, with no assignable cause of variation. It also revealed that, the product marketing process has low capability of successfully attending the preset specification limits in respect of the product sales and hence generating low profit for the company.

Generalized Regression Control Chart for Monitoring Crop Production

Recently, Nigeria focused on Agriculture as a way to diversify her economy. Crop production, which is a proxy to measure agricultural output is considered very important. So, controlling crop production (output) among states in Nigeria is very key. In this study, the generalized regression control chart was used rather than the conventional control chart. The conventional control chart does not put into consideration factor(s) that affect crop production. The generalized regression control chart considers the factor (independent variable) that affect crop production (dependent variable). The normal distribution is a special case of the generalized regression control chart. The possibility of using Weibull regression and other non-normal models were considered. In this research, Gaussian distribution was used as the underlying distribution because it fitted the crop production data. The cost of seed/seedling was selected from a set of independent variables, because it is most significant among other independent variables. The data were collected from secondary sources, precisely National Bureau of Statistics (NBS). All the 36 states in Nigeria, including the Federal Capital Territory (FCT) were involved in the study. The result of the generalized regression control chart showed that crop production is not in control in Nigeria, which was traced to assignable cause of variation in FCT, Abuja. This implied that FCT, Abuja produced below the lower control limit of crop production, despite the relative cost of seed/seedlings.

Economic statistical design of a multivariate control chart under a Burr XII shock model with multiple assignable causes

ABSTRACTControl charts show the distinction between the random and assignable causes of variation in a process. The real process may be affected by many characteristics and several assignable causes. Therefore, the economic statistical design of multiple control chart under Burr XII shock model with multiple assignable causes can be an appropriate candidate model. In this paper, we develop a cost model based on the optimization of the average cost per unit of time. Indeed, the cost model under the influence of a single match case assignable cause and multiple assignable causes under a same cost and time parameters were compared. Besides, a sensitivity analysis was also presented in which the changeability of loss-cost and design parameters were evaluated based on the changes in cost, time and Burr XII distribution parameters.

New Interquartile Range EWMA Control Charts with Applications in Continuous Stirred Tank Rector Process

Monitoring of process parameters via control charts is exceptionally common exercise in statistical process control (SPC). The exponentially weighted moving average (EWMA) control chart is one of an outstanding powerful tool of the SPC for monitoring of process parameters. The performance of any process can be improved by the careful monitoring and removing of assignable causes of variation. The existence of outliers may influence the performance of traditional charts in the monitoring of a process. This study is planned for the monitoring of dispersion parameter through the interquartile range (IQR). We proposed EWMA-type IQR charts based on auxiliary information for the efficient monitoring of process dispersion for the process following bivariate normal distribution. The comparison of these charts is made with usual IQR chart as well as traditional R and S charts. We evaluate the efficiency of charts by some commonly used run length measures. Both contaminated and uncontaminated processes are considered in this study to examine the robustness of charts. The results revealed that our proposed control charts exhibit superior performance in the presence of outliers. A real application of our study is also provided based on non-iso-thermal continuous stirred tank chemical reactor process.

APPLICATION OF STATISTICAL QUALITY CONTROL (SQC) IN THE CALIBRATION OF OIL STORAGE TANKS

Calibration of storage tanks is an exact means of determining the accurate capacity of storage tanks at a given incremental level. When calibrating a certain number of oil storage tanks having the same dimensions, it is assumed that if the specified tank dimensions are within the statistical control limits, a calibration chart generated for one tank can be used for the other tanks. This study used X-bar and R-control chart to investigate the stability of the tank calibration process for some fabricated oil storage tanks. The method of control chart was used to check if the process is under control or not. The variables of the calibration process are Circumference of each course shell, Height of each course shell and Elevations for the bottom profile. Results revealed that the calibration process was statistically stable and under control with no special or assignable cause of variation. Process capability conducted also showed that the calibrated tanks met the pre-set limits.

A Robust Dispersion Control Chart based on Modified Trimmed Standard Deviation

Control Chart is a widely used on-line process control techniques to control variability. This paper focuses on variability due to dispersion of a quality characteristic. Classical methods of estimating parameters of the distribu- tion of quality characteristic may be affected by the presence of outliers. In order to overcome such situation, robust estimators, which are less affected by the extreme values or small departures from the model assumptions, are introduced in industrial application. This article introduced a modification to trimmed standard deviation to increase its efficiency, and is used in con- trolling process dispersion. Authors constructed a phase-I control chart de- rived from standard deviation of trimmed mean, which is robust. Simulation study is conducted to assess its performance at phase-II. This robust control chart is compared with s -chart in terms of its efficiency to detect outliers or assignable causes of variation as well as its Average Run Length.

Using Bayesian models to assess the capability of a manufacturing process in the presence of unobserved assignable causes

The capability of a manufacturing process is a measure of how well the process is able to manufacture items within required engineering specifications. A process capability analysis is traditionally considered only after all assignable causes of variation have been removed. Under these conditions, a manufacturing process is considered to be in control. This is often an idealized situation since assignable causes such as tool wear, environmental conditions and batch variation in raw materials are inherent in many processes. In this article, the capability of a process is modelled in such a way that the process distribution is allowed to change between observed subgroups due to assignable causes. Standard and hierarchical Bayesian models are used. The Bayesian framework allows for prior information that is known about the manufacturing processes to be formally incorporated into the model. The hierarchical Bayesian framework is useful when the within group variation dominates the between group variation, and when an overall measure of process capability is desired for the entire process. The usefulness of the proposed methods is demonstrated through the application of several examples and issues such as practical implementation and computation are addressed.

Estimation of Change Point in Two-Stage Processes Subject to Step Change and Linear Trend

When a control chart signals, it shows the process parameters have changed due to assignable cause(s). However, control chart signal is not the real time of a change in the process. Knowing the real time of change would simplify the detection and elimination of the assignable causes of variation. In this paper, a two-stage process is considered when the mean values of quality characteristics are changed under step shift and linear drift. First, a control chart based on the discriminant analysis (DA) is utilized to monitor the process. Then, when the out-of-control signal is received, the maximum likelihood estimator (MLE) based on the DA statistics, and clustering approach based on Mahalanobis distance of residuals are developed to estimate the real time of the change. The performances of the proposed estimators under different shifts are evaluated through numerical examples and a real case. The results indicate the better performance of the clustering approach rather than the MLE in most cases under both step shift and drift.

Multivariate CUSUM control charts for monitoring the covariance matrix

Abstract This paper is a study on the multivariate CUSUM control charts using three di er-ent control statistics for monitoring covariance matrix. We get control limits and ARLsof the proposed multivariate CUSUM control charts using three di erent control statis-tics by using computer simulations. The performances of these proposed multivariateCUSUM control charts have been investigated by comparing ARLs. The purpose ofcontrol charts is to detect assignable causes of variation so that these causes can befound and eliminated from process, variability will be reduced and the process willbe improved. We show that the charts based on three di erent control statistics arevery e ective in detecting shifts, especially shifts in covariances when the variables arehighly correlated. When variables are highly correlated, our overall recommendationis to use the multivariate CUSUM control charts using trace for detecting changes incovariance matrix.Keywords: Average run length, covariance matrix, multivariate CUSUM control chart.

Development of fuzzy individual x and moving range control chart

Control charts are very effective tools which are used for detecting the assignable cause of variation. This paper investigated fuzzy individual x and moving range (IX-MR) control chart in the case of uncertainty for process parameters and data. In this paper, fuzzy mode method was employed to design fuzzy IX-MR control chart for triangular and trapezoidal fuzzy number fuzzy numbers coded by MATLAB software. Then unnatural patterns were studied in a fuzzy environment. To validate the model, an industrial example was utilised and then the results were verified. Results showed that the fuzzy one was more sensitive than the classic cases and more consistent with the actual situation. Also, fuzzy mode method was more sensitive for trapezoidal than triangular fuzzy numbers.

Experiential Learning in Metrology and Quality Engineering Course

Technical education programs have embraced experiential learning as a true learning methodology for students to obtain occupational skills valued by employers. Programs have integrated classroom instruction with laboratory experiences to provide students a significant opportunity to learn. A fundamental component in professional education is the link between theory and practice. However, many students in professional education programs experience a lack of coherence between theory and practice, which is often described as the theory practice gap. This work is apart of Bridging the Gap in metrology and quality engineering course, designed for the undergraduate students of VI Semester Industrial and Production Engineering of BVBCET, Hubli, an autonomous institute. Two problem statements were given to the students; one was on the process capability analysis of machines and another on the construction of control chart for variables, which they have to solve after conducting the experiments in machine shop in batches. The students had to chalk out the necessary information to conduct the experiment like profile, sample size, subgroup size and finally analyze the experimental data to decide whether machine is capable to meet the specifications of part and detect the presence of assignable or un assignable causes of variation using process capability analysis and control chart respectively. After the completion of this exercise, the students could realize the importance of process capability analysis and control charts in the manufacturing industries. This activity was step forward in bridging the gap between theory and lab through experiential learning. The performance indicators (PIs) of the ABET program outcome '3b' were underlying the motivators while designing the present experiential learning activity.

Implementation of Statistical Process Control for Proteomic Experiments Via LC MS/MS

Statistical process control (SPC) is a robust set of tools that aids in the visualization, detection, and identification of assignable causes of variation in any process that creates products, services, or information. A tool has been developed termed Statistical Process Control in Proteomics (SProCoP) which implements aspects of SPC (e.g., control charts and Pareto analysis) into the Skyline proteomics software. It monitors five quality control metrics in a shotgun or targeted proteomic workflow. None of these metrics require peptide identification. The source code, written in the R statistical language, runs directly from the Skyline interface, which supports the use of raw data files from several of the mass spectrometry vendors. It provides real time evaluation of the chromatographic performance (e.g., retention time reproducibility, peak asymmetry, and resolution), and mass spectrometric performance (targeted peptide ion intensity and mass measurement accuracy for high resolving power instruments) via control charts. Thresholds are experiment- and instrument-specific and are determined empirically from user-defined quality control standards that enable the separation of random noise and systematic error. Finally, Pareto analysis provides a summary of performance metrics and guides the user to metrics with high variance. The utility of these charts to evaluate proteomic experiments is illustrated in two case studies.

Application of clinical assay quality control (QC) to multivariate proteomics data: A workflow exemplified by 2-DE QC

Proteomics technologies can be effective for the discovery and assay of protein forms altered with disease. However, few examples of successful biomarker discovery yet exist. Critical to addressing this is the widespread implementation of appropriate QC (quality control) methodology. Such QC should combine the rigour of clinical laboratory assays with a suitable treatment of the complexity of the proteome by targeting separate assignable causes of variation. We demonstrate an approach, metric and example workflow for users to develop such targeted QC rules systematically and objectively, using a publicly available plasma DIGE data set. Hierarchical clustering analysis of standard channels is first used to discover correlated groups of features corresponding to specific assignable sources of technical variation. These effects are then quantified using a statistical distance metric, and followed on control charts. This allows measurement of process drift and the detection of runs that outlie for any given effect. A known technical issue on originally rejected gels was detected validating this approach, and relevant novel effects were also detected and classified effectively. Our approach was effective for 2-DE QC. Whilst we demonstrated this in a retrospective DIGE experiment, the principles would apply to ongoing QC and other proteomic technologies. This work asserts that properly carried out QC is essential to proteomics discovery experiments. Its significance is that it provides one possible novel framework for applying such methods, with a particular consideration of how to handle the complexity of the proteome. It not only focusses on 2DE-based methodology but also demonstrates general principles. A combination of results and discussion based upon a publicly available data set is used to illustrate the approach and allows a structured discussion of factors that experimenters may wish to bear in mind in other situations. The demonstration is on retrospective data only for reasons of scope, but the principles applied are also important for ongoing QC, and this work serves as a step towards a later demonstration of that application. This article is part of a Special Issue entitled: Standardization and Quality Control in Proteomics.

Robust control charts for controlling location parameter

Control charts are very effective tools used for detecting whether there is any assignable cause of variation. They are usually developed under the assumption of independent and normally distributed data, an assumption rarely true in practice, and implemented with estimated control limits. But in general, we essentially want to control the process mean value and the process standard deviation, independently of the data distribution. In order to monitor these parameters, it thus seems sensible to advance with control charts based on robust statistics, because these statistics are expected to be more resistant to moderate changes in the underlying process distribution. In this paper, we will propose some alternatives control charts for controlling location parameters based on some robust estimators. We will also show the performance of the proposed control charts and compare them with some existing robust control chart.

Switching properties of CUSUM charts for controlling mean vector

Abstract Some switching properties of multivariate control charts are investigated when theinterval between two consecutive sample selections is not xed but changes accordingto the result of the previous sample observation. Many articles showed that the perfor-mances of variable sampling interval control charts are more ecient than those of xedsampling interval control charts in terms of average run length (ARL) and average timeto signal (ATS). Unfortunately, the ARL and the ATS do not provide any informationon how frequent a switch is being made. We evaluate several switching properties oftwo sampling interval Shewhart and CUSUM procedures for controlling mean vectorof correlated quality variables.Keywords: Average number of switches to signal, average sampling interval, probabilityof switch. 1. Introduction The purpose of a control chart is to detect assignable causes of variation so that thesecauses can be found and eliminated. During the control process, one wishes to detect anydeparture from a satisfactory state as quickly as possible and identify which attributes areresponsible for the deviation. Thus, a good control chart detects shifts quickly in the processwhen the process is out-of-control state, and produces few false alarms when the process isin-control state.Many situations in industrial quality control involve a vector of measurements of twoor more related quality variables rather than a single quality variable. When the qualityvariables are correlated, one could obtain better sensitivity by using multivariate controlprocedures than separate control variables for each of the quality variables.Traditional sampling practice in using a control chart is to take samples from the processat xed sampling interval (FSI) and performances of control charts have been developedwhen the sampling interval between samples is xed. In recent years, application of variable

Assignable causes of variation and statistical models: another approach to an old topic

AbstractThis paper presents a fresh approach to the analysis of Shewhart control chart's performance. We consider two different types of assignable causes of variation. One—called type I—affects only the parameters of a model of the underlying distribution. The other—called type X—impacts the type of the original distribution. We analyze cases when the underlying normal distribution transforms into a uniform and log‐normal distribution after the intervention of an assignable cause of variation. It is shown that the Power Functions for control charts for individual measurements and control charts for means differ significantly from the well‐known traditional studies. We believe that this approach may open up new areas of research in the field of Statistical Process Control (SPC) and extend the spheres of SPC applications in practice. Copyright © 2011 John Wiley & Sons, Ltd.

Control Charts for Controlling Variability of Non-Normal Processes

Control charts represent a very effective tool used for reducing process variability by early detection of the occurrence of assignable causes of variation. -charts are applied to detect changes in process mean whereas S-charts are used to detect the same in process variability. Both charts are generally based on the normality assumption. The S-chart utilizes an unbiased estimator of the population standard deviation . However, it is highly affected by any violation of the normality assumption. In this paper, we propose some alternatives of S-charts based on some robust estimate of scale parameters. We will also illustrate the performance of the proposed control chart.

Six Sigma Based Exponentially Weighted Moving Average Control Chart

A control chart is a statistical device used for the study and control of repetitive process. Shewhart (1931) of bell telephone laboratories suggested control charts based on the 3 sigma limits. Now the companies started applying 6 sigma initiatives in their manufacturing process, which results in lesser number of defects, are focused in identifying the causes due to assignable causes of variation. The companies practicing 6 sigma initiatives is expected to produce 3.4 or less number of defects per million opportunities, a concept suggested by Motorola (1980). If the companies practicing 6 sigma initiatives use the control limits suggested by Shewhart, then no point fall outside the control limits because of reduced variation. In this paper an attempt is made to construct a 6 sigma based exponentially weighted moving average control chart specially designed for the companies adopting 6 sigma initiatives in their organization. Suitable table is also constructed and presented for the engineers to take quick decisions.