Variable Control Charts Research Articles

A Hybrid Learning-Based Model for Simultaneous Monitoring of Process Mean and Variance

Unnatural patterns exhibited on process mean and variance control charts can be associated separately with different assignable causes. Quick and accurate knowledge of the type of control chart patterns (CCPs), either because of process mean or variance, can greatly facilitate identification of assignable causes. Over the past few decades, however, process mean and variance CCPs are seldom studied simultaneously in the statistical process control literature. This study proposes a hybrid learning-based model for simultaneous monitoring of process mean and variance CCPs. In this model, a self-organization map neural network-based quantization error control chart is responsible for detecting the out-of-control signals, a discrete particle swarm optimization-based selective ensemble of back-propagation networks is responsible for classifying the detected out-of-control signals into categories of mean and/or variance abnormality, and two discrete particle swarm optimization-based selective ensembles of learning vector quantization networks are responsible for further identifying the detected mean and variance out-of-control signals as one of the specific CCP types, respectively. Extensive simulations indicate that the proposed hybrid learning-based model outperforms other existing approaches in detecting mean and variance changes, while also capable of CCP recognition. In addition, a case study is conducted to demonstrate how the proposed hybrid learning-based model can function as an effective tool for monitoring mean and variance simultaneously. Copyright © 2013 John Wiley & Sons, Ltd.

An Improved Distribution-free EWMA Mean Chart

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used here. In this article, we propose an improved asymmetric EWMA mean chart based on a simple statistic to monitor process mean shift. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed asymmetric EWMA mean chart. We recommend the proposed improved asymmetric EWMA mean chart because the average run lengths of the modified charts are more accurate and reasonable than those of the five existed mean charts. A numerical example of service times with a right skewed distribution from a service system of a bank branch is used to illustrate the application of the improved asymmetric EWMA mean chart and to compare it with the five existing mean charts. The proposed chart showed better detection performance than those of the five existing mean charts in monitoring and detecting shifts in the process mean.

Economic Design of Variable Sampling Interval X-Bar Control Charts for Monitoring Correlated Non Normal Samples

Recent studies have shown the X-bar control chart with variable sampling interval detects shifts in the process mean faster than the traditional X-bar chart. These studies are usually based on the assumption that the process data are independently and normally distributed. However, many situations in practice violate these assumptions. In this study, a methodology is developed to economically design a variable sampling interval X-bar control chart that takes into consideration correlated non normal sample data. An example is provided to illustrate the solution procedure. A sensitivity analysis on the input parameters (i.e., the cost and the process parameters) is performed taking into account the non normality and the correlation on the optimal design of the chart.

The variable sample size variable dimension T2 control chart

In this paper, we describe the development of the variable dimension and variable sample size T2 control chart (VSSVDT2), which is an enhancement of the variable dimension T2 chart (VDT2). In the VDT2 control chart, the number of variables that are measured to compute the T2 statistic is made variable. Some of the variables are easy or inexpensive to measure and are always monitored. The variables that are more difficult or expensive to measure are measured only when the T2 value from the previous sample exceeds a specified threshold. The VDT2 control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart’s performance in detecting such shifts, we propose the application of the variable sample size technique to the VDT2 control chart, resulting in the VSSVDT2 control chart. To promote the use of the VSSVDT2 chart, a user-friendly software has been developed, which the final user can use to find the best parameters of the VSSVDT2 chart for a particular process.

A Multivariate Change Point Detection Procedure for Monitoring Mean and Covariance Simultaneously

The signal issued by a control chart triggers the process professionals to investigate the special cause. Change point methods simplify the efforts to search for and identify the special cause. In this study, using maximum likelihood estimation, a multivariate joint change point estimation procedure for monitoring both location and dispersion simultaneously is proposed. After a signal is generated by the simultaneously used Hotelling's T 2 and/or generalized variance control charts, the procedure starts detecting the time of the change. The performance of the proposed method for several structural changes for the mean vector and covariance matrix is discussed.

Optimizing tablets’ quality with multiple responses using fuzzy goal programming

Process analytical technology is considered to be a system for designing, analyzing, and controlling pharmaceutical manufacturing to ensure final product quality. This research, therefore, utilized the process analytical technology framework to improve the performance of tableting process. Two main responses are of main interest including hardness and weight. At initial factor levels, the [Formula: see text] charts are established and found in control for both responses. However, the process capability index, [Formula: see text], values are calculated to be 0.42 and 0.51 for hardness and weight, respectively. Moreover, the multiple process capability index, MCpm, is 0.46. These values indicate that the tableting process is incapable of producing quality tablets. The L27 is used for conducting designed experiments. The weighted additive model in fuzzy goal programming is then used to determine optimal factor settings. Confirmation experiments are then conducted at optimal factor settings. It is found that the [Formula: see text] values are calculated to be 2.13 and 1.85 for hardness and weight, respectively. The MCpm value significantly improved to 1.99, which means that the process is highly capable. Consequently, the T2 and the sample generalized variance control charts are established and further used for monitoring future production. In conclusion, the tools used in the process analytical technology framework are found effective for improving the performance of tableting process.

Using Golden Ratio Search to Improve Paired Construction of Quality Control Charts

Our purpose is to indicate a new method for determining the control limits of univariate control charts to show the effectiveness of golden ratios search. We examine a solution to a problem when signals from mean and variance charts differ. Lack of concordance in the signals from mean and variance (or standard deviation) control charts bring confusion to Quality Control managers which in turn may lead to sub optimal management quality practices. To achieve better quality management practice, we provide a solution to the problem of finding different decision signals for in-control processes for quality control charts for mean and variability. We construct the control charts in experimental conditions for in-control average run length using the methods of simulation. Finally, we employ the golden ratio search method to identify the control limit parameters which differ from standard methods for constructing quality control charts. Last, we minimize the length of time in computation in the construction of these new quality control charts.

The economic design of multivariate binomial EWMA VSSI control charts

Since multi-attribute control charts have received little attention compared with multivariate variable control charts, this research is concerned with developing a new methodology to employ the multivariate exponentially weighted moving average (MEWMA) charts for m-attribute binomial processes; the attributes being the number of nonconforming items. Moreover, since the variable sample size and sampling interval (VSSI) MEWMA charts detect small process mean shifts faster than the traditional MEWMA, an economic design of the VSSI MEWMA chart is proposed to obtain the optimum design parameters of the chart. The sample size, the sampling interval, and the warning/action limit coefficients are obtained using a genetic algorithm such that the expected total cost per hour is minimized. At the end, a sensitivity analysis has been carried out to investigate the effects of the cost and the model parameters on the solution of the economic design of the VSSI MEWMA chart.

Economic Design of the Variable Parameters Control Chart with a Corrected A&L Switching Rule

The variable parameters (VP) control chart is more efficient than the fixed parameters control chart. However, an obvious shortcoming of the VP control chart is its excessive number of switches among different design parameters, which significantly increases the complexity of operations for administer and the costs of maintaining the control chart. Amin and Letsinger (1991) proposed a switching rule, denoted by A&L switching rule, to reduce the number of switches. In this paper, we investigated the economic design of the VP control chart by using the corrected A&L switching rule scheme, which makes some corrections to the existing study of the A&L switching rule scheme. A three‐state Markov model is proposed to derive the performance measures of the suggested control chart. An expected cost model for the process is established with the cost function derived. The genetic algorithm is then employed to search for the solution for the economic design of the proposed control chart. The results obtained show that the developed model can significantly reduce the average number of the parameter's switches and save the expected cost in comparison with the conventional VP control scheme in detecting small and moderate mean shifts. A sensitivity analysis is also carried out to examine the effects of cost and model parameters on the solution of the economic design for the proposed control chart. The analysis demonstrates the expected cost per time unit is positively affected by the cost associated with a false signal, the average cost of repairs when a true signal is identified, the sampling cost and the cost associated with a switch, and is negatively affected by the cost associated with running the process in‐control per hour. Copyright © 2013 John Wiley & Sons, Ltd.

Six Sigma Implementation to reduce rejection rate of Pump Casings at local Manufacturing Company

Six Sigma is being Implemented all over the World as a successful Quality Improvement Methodology. This article provides a description of Six Sigma Project implemented at Local manufacturing Company. The Company Manufactures Pump Casings where it was receiving high nonconformance rate that resulted in to Rejection of Product. This study deals with Six Sigma DMAIC methodology implementation and gives a frame work of how the non-conformance rate was first monitored and then brought in to acceptance limits. A complete Coverage of the statistical analysis performed during the study is given and results are shown to describe that how Six Sigma helped the Project members to Improve Quality of Pump casings at manufacturing facility. Keywords: Statistical Process Control (SQC), Process Capability Indices, Six Sigma, Variable control chart, Pareto charts, Standard deviation, Critical to Quality (CTQ), Analysis of Variance (ANOVA), DMAIC, Total quality Management (TQM)

Exponentially weighted moving average control charts for monitoring customer service quality comments

This paper examines the use of variable control charts with data that originates in text form and uses factors extracted from the text by latent semantic analysis. We demonstrate how text data from customer comments is analysed as well as the steps necessary to visualise the extracted factors on an Exponentially Weighted Moving Average (EWMA) chart. We also show how the factors correspond to latent service related issues and how using the EWMA chart to monitor those factors allows for addressing and improving service quality issues. We also review issues in text mining and suggest areas for future research.

Effects of Measurement Error on Process Signal Detection

Many data comes from a process with variables having non-normal distributions. The commonly used Shewhart variable control charts which depend heavily on the normality assumption should not be applied here. Further, measurement error of an instrument or gauge is an important factor in industry that influences the outcome of a process. Incapability of the instrument or gauge would cause the observation measure deviates from the true value and consequently lead to a false discrimination between good and bad service quality and manufacturing parts. In this study, we propose a new EWMA control chart to monitor the exponentially distributed service time between consecutive events with the measurement error instead of monitoring the number of events in a given time interval. We showed that, in the case of the measurement error following a normal distribution, the performance of the EWMA-M chart is significantly affected. We suggest letting for keeping the chart with the same detection ability; otherwise, the chart’s detection ability would be much poor than the charts with no measurement errors

Extreme Value Charts & ANOM based on IRD

A measurable quality characteristic is assumed to follow Inverse Rayleigh Distribution. Variable control charts based on extreme values of each subgroup are constructed. The technique of analysis of means (ANOM) is adopted to workout the decision lines of Inverse Rayleigh Distribution(IRD). The preferability of the proposed ANOM decision lines over that of Ott(1967) is illustrated by some examples.

Extreme Value Charts and Analysis of Means (ANOM) Based on the Log Logistic Distribution

A probability model of a quality characteristic is assumed to follow a log logistic distribution. This article proposes variable control charts, termed extreme value charts, based on the extreme values of each subgroup. The control chart constants depend on the probability model of the extreme order statistics and the size of each subgroup. The analysis of means (ANOM) technique for a skewed population is applied with respect to log logistic distribution. Results are illustrated using examples based on real data.

Phase II Monitoring of Nonlinear Profile Variance Using Wavelet

In some statistical process control applications, the quality of a process or a product can be characterized by a nonlinear relationship between a response variable and one or more explanatory variables. Monitoring nonlinear profiles using nonlinear regression has been proposed by several researchers as a potential area for research. To avoid disadvantages of parameter estimation in nonlinear regression, we used nonparametric regression with wavelets for monitoring nonlinear profiles. In nonparametric regression framework, traditional variance estimator is not proper; other estimators should be used instead. Parametric or nonparametric control charts in phase II are proposed to monitor error term variance when nonparametric regression with wavelet is used. Multivariate control chart based on regression coefficients (approximate wavelet coefficients) is added to variance control chart to check stability in the process mean. It is well known that the performance of control schemes in detecting shifts in multivariate control charts deteriorates as the dimension of regression coefficient increases. To improve the performance of control schemes, we considered decomposition level as a smoothing parameter, which determines the form of regression function (size of approximate wavelet coefficients vector) in nonparametric regression with wavelet. A method based on an analysis of variance is proposed to determine the optimal decomposition level. The statistical performances of the proposed methods are evaluated using average run length criterion using vertical density profile data. Numerical results indicate that the proposed methods perform satisfactorily. Copyright © 2012 John Wiley & Sons, Ltd.

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

Evaluation of exponentially weighted moving variance control chart subject to linear drifts

The exponentially weighted moving average chart of the squared deviation (EWMAS) is often applied for monitoring changes such as step shifts and linear drifts in process variation when no subgrouping is available. This paper analyzes the performance of the EWMAS chart under drifts in process variation. A fast and accurate algorithm based on the piecewise collocation method is presented for computing both the zero-state and steady-state average run lengths of the EWMAS chart. It is shown that the proposed method can provide accurate approximation results in both zero-state and steady-state cases. Some optimal design tables are also provided to facilitate the design of EWMAS charts in practice.

Signal Detection for Process with Unknown Distribution

Control charts are effective tools for monitoring both manufacturing processes and service processes. Much service data comes from a process with variables having non-normal or unknown distributions. The commonly used Shewhart variable control charts which depend heavily on the normality assumption should not be applied here. Hence, an alternative is desired to handle these types of process data. In this paper, we propose a new Variance Chart based on a simple statistic to monitor process variance shifts. The sampling properties of the new monitoring statistic are explored. A numerical example of service times from a bank service system with a right skewed distribution is used to illustrate the proposed Variance Chart. A comparison with two existing charts is also performed. The Variance Chart showed better ability than those two charts in detecting shifts in the process variance.

An economic design of combined double sampling and variable sampling interval control chart

A combination of double sampling X¯ chart and variable sampling intervals X¯ chart (DSVSI) can successfully reduce the detection time of small mean shift. Before a DSVSI X¯ chart is used, its design parameters should be determined. This study constructs an economic design model of DSVSI X¯ chart for the determination of the design parameters. Then, the Genetic Algorithms (GA) are used to solve the optimal designs of DSVSI X¯ chart. Finally, a numerical example is provided to illustrate the use of this model. A sensitivity analysis of the effects of model parameters on the optimal design of DSVSI X¯ chart is also performed.

Integrated SPC-based scheme utilising variable control charts and C<SUB align="right">pm ratio to improve manufacturing quality of empty hard gelatin capsules

Quality control and improvement at the process level is a vital activity for the achievement of quality in products and services. This paper presents a three-phase scheme based on statistical process control methodology that employs variable control charts and process capability indices for quality improvement. The control charts employed are , s and the exponentially weighted moving average. The centred process capability ratio (Cpm) is employed for process capability assessment. The scheme accounts for both short-term and long-term changes in process performance and it is designed for a structured and less-complex implementation of control charts and process capability assessment. The proposed scheme has been implemented to the manufacturing process of empty hard gelatin capsules as a case study. This implementation has led to an expected reduction in the number of defective capsules by 29% relative to the stage before implementation.