A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

New EWMA control charts for monitoring process dispersion using auxiliary information

The exponentially weighted moving average (EWMA) control chart is a well‐known statistical process monitoring tool because of its exceptional pace in catching infrequent variations in the process parameter(s). In this paper, we propose new EWMA charts using the auxiliary information for efficiently monitoring the process dispersion, named the auxiliary‐information–based (AIB) EWMA (AIB‐EWMA) charts. These AIB‐EWMA charts are based on the regression estimators that require information on the quality characteristic under study as well as on any related auxiliary characteristic. Extensive Monte Carlo simulation are used to compute and study the run length profiles of the AIB‐EWMA charts. The proposed charts are comprehensively compared with a recent powerful EWMA chart—which has been shown to be better than the existing EWMA charts—and an existing AIB‐Shewhart chart. It turns out that the proposed charts perform uniformly better than the existing charts. An illustrative example is also given to explain the implementation and working of the AIB‐EWMA charts.     

A new variable sampling control scheme at fixed times for monitoring the process dispersion

The variable sampling rate (VSR) schemes for detecting the shift in process mean have been extensively analyzed; however, adding the VSR feature to the control charts for monitoring process dispersion has not been thoroughly investigated. In this research, a novel VSR control scheme, sequential exponentially weighted moving average inverse normal transformation (EWMA INT) at fixed times chart (called (SEIFT) chart), which integrates the sequential EWMA scheme at fix times with the INT statistic, is proposed to detect both the increase and decrease in process dispersion. Moreover, the sample size at each sampling time is also allowed to vary. The Markov chain method is used to evaluate the performance of this new control chart. Numerical analysis reveals that this SEIFT chart gives significant improvement on detection ability than the fixed sampling rate schemes. Compared with other control schemes, the good properties of the INT statistic makes this SEIFT chart easy to design and convenient to implement. Copyright © 2009 John Wiley & Sons, Ltd.     

New GWMA‐CUSUM control chart for monitoring the process dispersion

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely accepted because of their fantastic speed in identifying small‐to‐moderate unusual variations in the process parameter(s). Recently, a new CUSUM chart has been proposed that uses the EWMA statistic, called the CS‐EWMA chart, for monitoring the process variability. On similar lines, in order to further improve the detection ability of the CS‐EWMA chart, we propose a CUSUM chart using the generally weighted moving average (GWMA) statistic, named the GWMA‐CUSUM chart, for monitoring the process dispersion. Monte Carlo simulations are used to compute the run length profiles of the GWMA‐CUSUM chart. On the basis of the run length comparisons, it turns out that the GWMA‐CUSUM chart outperforms the CUSUM and CS‐EWMA charts when identifying small variations in the process variability. A simulated dataset is also used to explain the working and implementation of the CS‐EWMA and GWMA‐CUSUM charts.     

Control charting and survey sampling techniques in process monitoring

Control charts are widely used for the detection of shifts in process parameters. In this study, we propose some enhanced Shewhart-type control charts using improved estimators based on auxiliary characteristics. A general control charting structure is developed that can be used with different location estimators. Performance of the proposed charts is compared using average run length (ARL), extra quadratic loss (EQL), and relative average run length (RARL) as performance measures. Comparisons are made among different proposals and the existing counterparts. It is observed that the proposed charts offer improved detection abilities depending upon the correlation structures among different variables under consideration. An illustrative example is also included to highlight the applications in practical situations.     

A fuzzy control charting method for individuals

Shewhart Statistical Quality Control (SQC) charts provide a graphical depiction and record of sample data points, to enable immediate recognition of special causes affecting the process output quality. These charts can detect changes in the mean level, and various other types of unnatural behaviour by the process. Control limits, together with heuristic run and zone rules, are used for the identification of these process behaviours, resulting in a complex situation in which charts must be examined for a number of features. This paper describes a simple method for identifying a criterion representing the state of control of manufacturing processes having a single critical variable characteristic. A fuzzy logic approach has been used to provide this single 'in-control' value. Two fuzzy sets are used, the Centred set and the Random set. The paper explains how the degree of membership of these sets is determined for each sample and how a single crisp in-control value is determined. The behaviour of the fuzzy control chart for three typical unnatural patterns (shift, trend and cyclical) is examined in detail. Some experimental results are provided, comparing the approach with the traditional methods used for control charting of individuals, and the potential of the approach is discussed.     

Multivariate control charts for process dispersion

The multivariate extension of control charts for process dispersion is not as straightforward as that for the process mean. A general model and techniques that would encompass a wide range of problems encountered in practice is not available. In most cases, particular problems need to be handled in a specific manner. In this paper we consider several special cases of a process displacement affecting the covariance matrix and we develop control charts (both Shewhart-type and CUSUM) to detect these process changes.     

Efficient bivariate EWMA charts for monitoring process dispersion

To ensure high quality standards of a process, the application of control charts to monitor process performance has become a regular routine. Multivariate charts are a preferred choice in the presence of more than one process variable. In this article, we proposed a set of bivariate exponentially weighted moving average (EWMA) charts for monitoring the process dispersion. These charts are formulated based on a variety of dispersion statistics considering normal and non-normal bivariate parent distributions. The performance of the different bivariate EWMA dispersion charts is evaluated and compared using the average run length and extra quadratic loss criteria. For the bivariate normal process, the comparisons revealed that the EWMA chart based on the maximum standard deviation (SMAX_E) was the most efficient chart when the shift occurred in one quality variable. It also performed well when the sample size is small and the shift occurred in both quality variables. The EWMA chart based on the maximum average absolute deviation from median (MDMAX_E) performed better than the other charts in most situations when the shift occurred in the covariance matrix for the bivariate non-normal processes. An illustrative example is also presented to show the working of the charts.     

A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance

This article compares the effectiveness and robustness of nine typical control charts for monitoring both process mean and variance, including the most effective optimal and adaptive sequential probability ratio test (SPRT) charts. The nine charts are categorized into three types (the type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and adaptive version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and adaptive charts are designed optimally in order to minimize an index average extra quadratic loss for the best overall performance. Moreover, the probability distributions of the mean shift δ_µ and standard deviation shift δ_σ are studied explicitly as the influential factors in a factorial experiment. The main findings obtained in this study include: (1) From an overall viewpoint, the SPRT‐type chart is more effective than the CUSUM‐type chart and type chart by 15 and 73%, respectively; (2) in general, the adaptive chart outperforms the optimal chart and basic chart by 16 and 97%, respectively; (3) the optimal CUSUM chart is the most effective fixed sample size and sampling interval chart and the optimal SPRT chart is the best choice among the adaptive charts; and (4) the optimal sample sizes of both the charts and the CUSUM charts are always equal to one. Furthermore, this article provides several design tables which contain the optimal parameter values and performance indices of 54 charts under different specifications. Copyright © 2011 John Wiley & Sons, Ltd.     

The SPRT control chart for process dispersion

This paper investigates the statistical performance of a sequential probability ratio test control chart for monitoring the dispersion of a normally distributed process. The expressions for statistical performance measures of the chart are derived using a Markov chain approach. It is shown through numerical comparisons that the overall statistical performance of this chart is superior to that of the existing competitor charts for dispersion. An example illustrating an application of the chart in practice is provided.     

Some effective control chart procedures for reliability monitoring

Control charts are widely used for process monitoring in the manufacturing industry. Little research is available on their use to monitor the failure process of components or systems, which is important for equipment performance monitoring. Some Shewhart control charts, especially those for the number of defects, can be used for monitoring the number of failures per fixed interval; however, they are not effective especially when the failure frequency becomes small. A recent control scheme based on the cumulative quantity between observations of defects has been proposed which can be easily adopted to monitor the failure process for exponentially distributed inter-failure time. An investigation of its use for reliability monitoring is presented in this paper and the scheme can be easily extended to monitor inter-failure times that follow other distributions such as the Weibull distribution. Furthermore, the scheme is extended to the monitoring of time required to observe a fixed number of failures. The advantages of this scheme include the fact that the scheme does not require any subjective sample size, can be used for both high and low reliability items and can detect process improvement even in a high-reliability environment.     

A GLR control chart for monitoring a multinomial process

The problem of detecting changes in the parameter p in a Bernoulli process with two possible categories for each observation has been extensively investigated in the SPC literature, but there is much less work on detecting changes in the vector parameter p in a multinomial process where there are more than two categories. A few papers have considered the case in which the direction of the change in p is known, but there is almost no work for the important case in which the direction of the change is unknown and individual observations are obtained. This paper proposes a multinomial generalized likelihood ratio (MGLR) control chart based on a likelihood ratio statistic for monitoring p when individual observations are obtained and the direction and size of the change in p are unknown. A set of 2‐sided Bernoulli cumulative sum (CUSUM) charts is proposed as a reasonable competitor of the MGLR chart. It is shown that the MGLR chart has better overall performance than the set of 2‐sided Bernoulli CUSUM charts over a wide range of unknown shifts. Equations are presented for obtaining the control limit of the MGLR chart when there are three or four components in p .     

A moving average S control chart for monitoring process variability

An 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.     

Performance comparison between on-line sensors and control charts in manufacturing process monitoring

The rapid evolution of sensor technology, using techniques such as lasers, machine vision and pattern recognition, provides the potential to greatly improve the Statistical Process Control (SPC) method for monitoring manufacturing processes. This paper studies the method of using on-line sensors to monitor manufacturing processes and compares that method with the control chart method, a widely used SPC tool. Two separate economic models are formulated for using either a sensor or a control chart to monitor a manufacturing process. Then, the two models are compared in a sensitivity analysis with lespect to several process parameters.     

A moving average control chart using a robust scale estimator for process dispersion

Control charts are one of the most powerful tools used to detect and control industrial process deviations in statistical process control. In this paper, a moving average control chart based on a robust scale estimator of standard deviation, namely, the sample median absolute deviation (MAD) statistic, for monitoring process dispersion, is proposed. A simulation study is conducted to evaluate the performance of the proposed moving average median absolute deviation (MA‐MAD) chart, in terms of average run length for various distributions. The results show that the moving average MAD chart performs well in detecting small and moderate shifts in process dispersion, especially when the normality assumption is violated. In addition, this chart is very efficient, especially when the quality characteristic follows a skewed distribution. Numerical and simulated examples are given at the end of the paper.     

A comparison study of control charts for statistical monitoring of functional data

The quality of products and processes is more and more often becoming related to functional data, which refer to information summarised in the form of profiles. The recent literature has pointed out that traditional control charting methods cannot be directly applied in these cases and new approaches for profile monitoring are required. While many different profile monitoring approaches have been proposed in the scientific literature, few comparison studies are available. This paper aims at filling this gap by comparing three representative profile monitoring approaches in different production scenarios. The performance comparison will allow us to select a specific approach in a given situation. The competitor approaches are chosen to represent different levels of complexity, as well as different types of modelling approaches. In particular, at a lower level of complexity, the ‘location control chart’ (where the upper and lower control limits are ±K standard deviations from the sample mean at each profile location) is considered to be representative of industrial practice. At a higher complexity level, approaches based on combining a parametric model of functional data with multivariate and univariate control charting are considered. Within this second class, we analyse two different approaches. The first is based on regression and the second focuses on using principal component analysis for modelling functional data. A manufacturing reference case study is used throughout the paper, namely profiles measured on machined items subject to geometrical specification (roundness).     

A control chart for monitoring process mean based on attribute inspection

This article proposes a new control chart, namely the MON chart, which employs attribute inspection (inspecting whether units are conforming or nonconforming) to monitor the mean value of a variable characteristic x. A unit is classified as nonconforming if the value of x falls beyond a fixed warning limit. A sample is regarded as suspect if more than m out of n units (referred to as MON) in the sample are nonconforming. A MON chart produces an out-of-control signal when the interval between two suspect samples is smaller than a control limit. The MON chart is distinctively advantageous owing to its simplicity in implementation. In particular, the MON chart uses attribute inspection and eliminates the need for any computation. In addition, the MON chart makes use of information not only about the magnitude of x, but also the interval between two suspect samples. Therefore, it always outperforms the X chart and often excels the CUSUM chart on the basis of same inspection cost. Furthermore, the MON chart performs more uniformly over a wide range of mean shift than other charts.     

A hybrid homogeneously weighted moving average control chart for process monitoring

Several modifications and enhancements to control charts in increasing the performance of small and moderate process shifts have been introduced in the quality control charting techniques. In this paper, a new hybrid control chart for monitoring process location is proposed by combining two homogeneously weighted moving average (HWMA) control charts. The hybrid homogeneously weighted moving average (HHWMA) statistic is derived using two smoothing constants λ₁ and λ₂ . The average run length (ARL) and the standard deviation of the run length (SDRL) values of the HHWMA control chart are obtained and compared with some existing control charts for monitoring small and moderate shifts in the process location. The results of study show that the HHWMA control chart outperforms the existing control charts in many situations. The application of the HHWMA chart is demonstrated using a simulated data.     

A nonparametric CUSUM chart for process dispersion

In the present article, we propose a nonparametric cumulative sum control chart for process dispersion based on the sign statistic using in‐control deciles. The chart can be viewed as modified control chart due to Amin et al, 6 which is based on in‐control quartiles. An average run length performance of the proposed chart is studied using Markov chain approach. An effect of non‐normality on cumulative sum S² chart is studied. The study reveals that the proposed cumulative sum control chart is a better alternative to parametric cumulative sum S² chart, when the process distribution is non‐normal. We provide an illustration of the proposed cumulative sum control chart.