Shifts In Process Variability Research Articles

New Hybrid EWMA Charts for Efficient Process Dispersion Monitoring with Application in Automobile Industry

The EWMA charts are the well-known memory-type charts used for monitoring the small-to-intermediate shifts in the process parameters (location and/or dispersion). The hybrid EWMA (HEWMA) charts are enhanced version of the EWMA charts, which effectively monitor the process parameters. This paper aims to develop two new uppersided HEWMA charts for monitoring shifts in process variance, i.e., HEWMA1 and HEWMA2 charts. The design structures of the proposed HEWMA1 and HEWMA2 charts are based on the concept of integrating the features of two EWMA charts. The HEWMA1 and HEWMA2 charts plotting statistics are developed using one EWMA statistic as input for the other EWMA statistic. A Monte Carlo simulations method is used as a computational technique to determine the numerical results for the performance characteristics, such as average run length (ARL), median run length, and standard deviation run length (SDRL) for assessing the performance of the proposed HEWMA1 and HEWMA2 charts. In addition, to evaluate the overall performance of the proposed HEWMA1 and HEWMA2 charts, other numerical measures consisting of the extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) are also computed. The proposed HEWMA1 and HEWMA2 charts are compared to some existing charts, such as CH, CEWMA, HEWMA, AEWMA HHW1, HHW2, AIB-EWMA-I, and AIB-EWMA-II charts, on the basis aforementioned numerical measures. The comparison reveals that the proposed HEWMA1 and HEWMA2 charts achieve better detection ability against the existing charts. In the end, a real-life data application is also provided to enhance the implementation of the proposed HEWMA1 and HEWMA2 charts practically.

Reliability and sensitivity comparisons and average run lengths of CUSUM scale chart

ABSTRACTThe cumulative sum (CUSUM) control chart is considered one of the best methods used to detect process shifts. It has been observed that there are certain studies which focused on the analysis and description of the distribution of run-length of CUSUM charts under shifts in process variance. Keeping this in view, an efficient and accurate algorithm based on the distribution of run length of CUSUM chart for examining the variance changes of normal process is developed in this research. Since one of the measures for evaluating the performance of control chart is average run length (ARL), therefore it is considered for comparing the reliability and sensitivity of CUSUM scale chart. Simulation studies have been carried out to generate the data through which both in-control and out-of-control ARLs are calculated by varying sample size, decision limits and reference values. The efficiency of the proposed control chart is shown in terms of ARLs. A numerical example is given to illustrate the practical application of the proposed scheme.

COMPARING THE EFFECTS OF SKEWED DISTRIBUTIONS ON THE S-CHART AND -EWMA CHART BASED ON THE MEDIAN RUN LENGTH CRITERION

The S2-EWMA (called the S square exponentially weighted moving average) control chart is effective in detecting small and moderate process variance shifts. Previously, the chart was designed based on the assumption that the distribution of the quality characteristic is normally distributed. This study designs the S2-EWMA control chart for skewed distributions. The skewed distributions considered in this paper are the lognormal and gamma distributions. The performance of the S2-EWMA control chart is compared with that of the traditional Shewhart S-chart, in terms of median run length (MRL), based on simulation using the Statistical Analysis System (SAS). The results show that regardless of the type of skewed distributions, sample size and skewness level, , in most of the cases, the S2-EWMA chart outperforms the S-chart. Moreover, the findings reveal that the MRL performances of the S-chart and S2-EWMA chart are significantly influenced by skewed distributions.

A moving average S control chart for monitoring process variability

ABSTRACTAn efficient alternative to the S control chart for detecting shifts of small magnitude in the process variability using a moving average based on the sample standard deviation s statistic is proposed. Control limit factors are derived for the chart for different values of sample size and span w. The performance of the moving average S chart is compared to the S chart in terms of average run length. The result shows that the performance of moving average S chart for varying values of w outweigh those of the S chart for small and moderate shifts in process variability.

Run sum control charts for the monitoring of process variability

A two-sided run sum S control chart is proposed and its average run length performance is evaluated via a Markov chain technique. The performance of the chart is compared to several well-known control-charting procedures for the monitoring of process variability. One-sided counterparts of the proposed run sum charts are also discussed. The numerical results demonstrate an improved performance of the run sum S control charts as compared with control charts with runs rules, especially in the detection of increasing shifts in process variability. A practical guidance for the selection of the appropriate charting procedure is also given.

A new approach for monitoring process variance

ABSTRACTControl charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come 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 properly used in such circumstances. In this paper, we propose a new variance chart based on a simple statistic to monitor process variance shifts. We explore the sampling properties of the new monitoring statistic and calculate the average run lengths (ARLs) of the proposed variance chart. Furthermore, an arcsine transformed exponentially weighted moving average (EWMA) chart is proposed because the ARLs of this modified chart are more intuitive and reasonable than those of the variance chart. We compare the out-of-control variance detection performance of the proposed variance chart with that of the non-parametric Mood variance (NP-M) chart with runs rules, developed by Zombade and Ghute [Nonparametric control chart for variability using runs rules. Experiment. 2014;24(4):1683–1691], and the nonparametric likelihood ratio-based distribution-free exponential weighted moving average (NLE) chart and the combination of traditional exponential weighted moving average (EWMA) mean and EWMA variance (CEW) control chart proposed by Zou and Tsung [Likelihood ratio-based distribution-free EWMA control charts. J Qual Technol. 2010;42(2):174–196] by considering cases in which the critical quality characteristic has a normal, a double exponential or a uniform distribution. Comparison results showed that the proposed chart performs better than the NP-M with runs rules, and the NLE and CEW control charts. A numerical example of service times with a right-skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the application of the proposed variance chart and of the arcsine transformed EWMA chart and to compare them with three existing variance (or standard deviation) charts. The proposed charts show better detection performance than those three existing variance charts in monitoring and detecting shifts in the process variance.

Enhanced cumulative sum charts for monitoring process dispersion.

The cumulative sum (CUSUM) control chart is widely used in industry for the detection of small and moderate shifts in process location and dispersion. For efficient monitoring of process variability, we present several CUSUM control charts for monitoring changes in standard deviation of a normal process. The newly developed control charts based on well-structured sampling techniques - extreme ranked set sampling, extreme double ranked set sampling and double extreme ranked set sampling, have significantly enhanced CUSUM chart ability to detect a wide range of shifts in process variability. The relative performances of the proposed CUSUM scale charts are evaluated in terms of the average run length (ARL) and standard deviation of run length, for point shift in variability. Moreover, for overall performance, we implore the use of the average ratio ARL and average extra quadratic loss. A comparison of the proposed CUSUM control charts with the classical CUSUM R chart, the classical CUSUM S chart, the fast initial response (FIR) CUSUM R chart, the FIR CUSUM S chart, the ranked set sampling (RSS) based CUSUM R chart and the RSS based CUSUM S chart, among others, are presented. An illustrative example using real dataset is given to demonstrate the practicability of the application of the proposed schemes.

A Synthetic Control Chart for Monitoring Process Variability

The control chart based on Downton's estimator (D chart) has recently been introduced in the literature for monitoring the process variability. The D chart is found to be equally efficient to the S chart in terms of detecting shifts in process variability. In this paper, salient features of D chart and the conforming run length chart are combined to produce synthetic D chart. The average run length performance of the synthetic D chart is investigated using simulation study and is compared with the originally proposed D chart and some other procedures proposed in the literature. It is found that it has an improved performance in comparison with the traditional control charts for process variability. Copyright © 2013 John Wiley & Sons, Ltd.

Optimal Variable Sample Size and Sampling Interval MSE Chart Based on Improved Square Root Transformation

In the field of statistical process control (SPC), control charts for attributes are widely used to detect the out-of-control condition by checking the number of nondefective units or nondefective in a sample. In this article, we use the average time to signal (ATS) and the average number of observations to signal (ANOS) to evaluate the performance of the optimal variable sample size and sampling interval (VSSI) improved square root transformation (ISRT) mean square error (MSE) (VSSI_ ISRT_ MSE) control chart for attribute data. In addition, this control chart will be used to monitor: (1) the difference between the process mean and the target value, and (2) the process variance shifts. We found that the optimal VSSI_ ISRT_ MSE chart performs better than the specific VSSI, the optimal variable sampling interval (VSI), and the fixed parameters (FP) ISRT_MSE charts. An example is given to illustrate this new proposed approach.

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.

On the improvement of one-sided S control charts

The most common charting procedure used for monitoring the variance of the distribution of a quality characteristic is the S control chart. As a Shewhart-type control chart, it is relatively insensitive in the quick detection of small and moderate shifts in process variance. The performance of the S chart can be improved by supplementing it with runs rules or by varying the sample size and the sampling interval. In this work, we introduce and study one-sided adaptive S control charts, supplemented or not with one powerful runs rule, for detecting increases or decreases in process variation. The properties of the proposed control schemes are obtained by using a Markov chain approach. Furthermore, a practical guidance for the choice of the most suitable control scheme is also provided.

Using neural networks to detect the bivariate process variance shifts pattern

Most of the research in statistical process control has been focused on monitoring the process mean. Typically, it is also important to detect variance changes as well. This paper presents a neural network-based approach for detecting bivariate process variance shifts. Some important implementation issues of neural networks are investigated, including analysis window size, number of training examples, sample size, training algorithm, etc. The performance of the neural network, in terms of the ARL and run length distribution, is compared with that of traditional multivariate control charts. Through rigorous evaluation and comparison, our research results show that the proposed neural network performs substantially better than the traditional generalized variance chart and might perform better than the adaptive sizes control charts in the case that the out-of-control covariance matrix is not known in advance.

Runs rules schemes for monitoring process variability

To increase the sensitivity of Shewhart control charts in detecting small process shifts sensitizing rules based on runs and scans are often used in practice. Shewhart control charts supplemented with runs rules for detecting shifts in process variance have not received as much attention as their counterparts for detecting shifts in process mean. In this article, we examine the performance of simple runs rules schemes for monitoring increases and/or decreases in process variance based on the sample standard deviation. We introduce one-sided S charts that overcome the weakness of high false-alarm rates when runs rules are added to a Shewhart control chart. The average run length performance and design aspects of the charts are studied thoroughly. The performance of associated two-sided control schemes is investigated as well.

Monitoring Process Variability Using Gini’s Mean Difference

The study proposes a control chart namely G-Chart based on Gini’s mean difference for monitoring the changes in a process variability assuming normality of the quality characteristic to be monitored. The design structure of G-Chart is derived and its comparison is made with those of well-known R and S charts. It is observed G-Chart needs no coefficient as opposed to R and S charts which need d2 and c4 coefficients respectively to find an unbiased estimate of the process standard deviation σ. Using the power curves as a performance measure it is observed that G-Chart is more powerful than R-Chart and is very close competitor to the S-Chart in terms of discriminatory power for detecting shifts in process variability. The non-normality effect is also examined on the three charts and it is observed that G-Chart is least affected by the departure from normality.

Probability Weighted Moments Approach to Quality Control Charts

A new control chart namely Spw-Chart for monitoring the changes in the process variability is proposed and is based on Probability Weighted Moments (PWMs) and assuming that the quality characteristic follows a normal distribution. The coefficients r2 and r3 (similar as the d2 and d3 coefficients used for R-Charts) are derived for sample sizes n = 2, 3, . . . , 20, 25, 30, 35, 50, 100 by means of a simulation study. The quantiles of which are used for determining the values of the control limits and the power of the Spw-Chart to detect shifts in process variability, are also derived for n = 2, 3, . . . , 20, 25, 30, 35, 50, 100 by simulation. Each of the simulation studies is based on 10,000 random samples from the corresponding normal distribution. The performance of Spw-Chart is investigated by comparing its power curves with those of R and S Charts. It is observed that the power curves of the Spw-Chart are above those of the R-Chart, while slightly below those of the S-Chart in detecting shifts in the process variability. The effect of non-normality on the designs of S, R, and Spw Charts, is studied by simulating random samples from the exponential and the t distributions. The simulations reveal superiority of the Spw-Chart over both R and S Charts in the sense that the power curve of Spw-Chart is least affected by non-normality among all the three charts under study.

Inverse Gaussian Control Charts for Monitoring Process Variability

Control charts for detecting shifts in process variability are constructed under the assumption that the quality characteristic under study follows the inverse Gaussian IG(μ, λ) distribution with known parameter λ, and the location parameter μ is either known or unknown. The effects of the estimated probability limits on the performance of the proposed charts in detecting shifts in process variability are examined for the case when the parameter λ is unknown and must be estimated from preliminary subgroups taken from an in-control IG( μ, λ) process. The correction factors for evaluating the adjusted probability limits of the proposed charts that have a desired false alarm rate are given as well.

An ewma-cuscore quality control procedure for process variability

Combined Shewhart-cumulative score (cuscore) quality control schemes are available for controlling the mean of a continuous production process. In many industrial applications, it is important to control the process variability as well. The proposed exponentially weighted moving average combined Shewhart-cumulative score ewma-cuscore quality control procedure for detecting shifts in process variability uses the procedures developed by Ncube and Woodall [1] to monitor shifts in the process mean of continuous production processes. It is shown, in the one-sided case, by Average Run Length (ARL) comparisons, that the proposed scheme performs significantly and uniformly better than comparative standard cuscore procedures for shifts in the process standard deviation values considered.

Cumulative Score Quality Control Procedures for Process Variability

Combined Shewhart‐cumulative score (cuscore) quality control schemes are available for controlling the mean of a continuous production process. In many industrial applications, it is important to control the process variability as well. The proposed combined Shewhart‐cumulative‐score (cuscore) procedure for detecting shifts in process variability uses the procedures developed by Ncube and Woodall (1984) to monitor shifts in the process mean of continuous production processes. It is shown, in the one‐sided case, by average run length comparisons, that the proposed schemes perform significantly better than comparative Shewhart procedures and in some cases even better than cusum schemes when using some process variability quality characteristics.

Two parameter cuscore qualty control procedures

This paper is concerned with the problem of simultaneously monitoring the process mean and process variability of continuous production processes using combined Shewhart-cumulative score (cuscore) quality control procedures developed by Ncube and Woodall (1984). Two methods of approach are developed and their properties are investigated. One method uses two separate Shewhart-cuscore control charts, one for determining shifts in the process mean and the other for detecting shifts in process variability. The other method uses a single combined statistic which is sensitive to shifts in both the mean and the variance. Each procedure is compared to the corresponding Shewhart schemes. It will be shown by average run length calculations that the proposed Shewhart- cuscore schemes are considerably more efficient than the comparative Shewhart procedures for certain shifts in the process mean and process variability for the case when the underlying process control variable is assumed to be normally distributed.