Control Chart Schemes Research Articles

Economic designs of constrained EWMA and combined EWMA-X¯ control schemes

This research presents a comparison between the cost performance of the Exponentially Weighted Moving Average EWMA) and the combined EWMA-X¯ control chart schemes. In particular, we explore the impact of constraining the in-control average run length on the optimal cost performance of both schemes. Methodologically, we incorporate traditional expected cost models and study the robustness of the two approaches. In general, there appears to be minimal motivation to combine the use of both charts within the same application. The cost model for the combined chart is not a well-behaved function, and yields varying optimal parameters when the in-control average run length is constrained.

Economic designs of constrained EWMA and combined EWMA-X¯ control schemes

Abstract This research presents a comparison between the cost performance of the Exponentially Weighted Moving Average EWMA) and the combined EWMA-X¯ control chart schemes. In particular, we explore the impact of constraining the in-control average run length on the optimal cost performance of both schemes. Methodologically, we incorporate traditional expected cost models and study the robustness of the two approaches. In general, there appears to be minimal motivation to combine the use of both charts within the same application. The cost model for the combined chart is not a well-behaved function, and yields varying optimal parameters when the in-control average run length is constrained.

Statistically constrained economic design of the multivariate exponentially weighted moving average control chart

AbstractThis paper shows that economic statistical design can provide for better statistical properties without significantly increasing optimal total costs. Cost comparisons between optimal economic statistical designs and optimal economic designs show no significant cost increases. The average run length (ARL) constraints added by economic statistical design significantly improve the statistical properties of the control chart scheme. False alarm frequency is limited while keeping good shift detection characteristics. In addition, the Multivariate Exponentially Weighted Moving Average (MEWMA) control schemes performed better from the cost standpoint than the benchmark pure statistical design—the Hotelling T2 control chart. This improvement held for unconstrained and constrained designs. Finally, cost comparisons at small values of n showed significant advantage for the MEWMA schemes. Copyright © 2001 John Wiley & Sons, Ltd.

Two Alternatives to the Shewhart X̄ Control Chart

Average run length (ARL) values are calculated for two X̄ control chart schemes and compared with those of a standard Shewhart chart. Both control charts are based on runs rules and are easily implemented. An out-of-control condition for one of the charts is a run of two of two successive points beyond a special control limit. The other chart uses a run of two of three successive points beyond a different control limit. Both schemes are shown to have better, that is, lower, ARL values than the standard Shewhart chart for process average shifts as large as 2.6 standard deviations from the mean.

Guidelines for the application of adaptive control charting schemes

A comprehensive performance study and comparison of several adaptive statistical process control procedures is presented. These adaptive control chart procedures are modifications to standard Shewhart control charts that include changing the sampling interval, the sample size or both according to rules based on the value of the sample statistic. Adaptive control techniques are known to improve the performance of the standard Shewhart control charts. In this paper we develop a four-state adaptive sample size control chart and several variations of a three-state combined adaptive sample size and sampling interval control chart. We then compare these new schemes with the previously developed schemes, the two-state adaptive sampling interval, the two-state adaptive sample size and two-state combined adaptive sample size and sampling interval control chart, three-state adaptive sample size control chart and non-adaptive Shewhart control charts. These results show that the addition of the third and fourth states on the adaptive control chart schemes improve the control chart performance; however, the improvement is relatively modest.

Efficient Design and Sensitivity Analysis of Control Charts Using Monte Carlo Simulation

The design of control charts in statistical quality control addresses the optimal selection of the design parameters (such as the sampling frequency and the control limits) and includes sensitivity analysis with respect to system parameters (such as the various process parameters and the economic costs of sampling). The advent of more complicated control chart schemes has necessitated the use of Monte Carlo simulation in the design process, especially in the evaluation of performance measures such as average run length. In this paper, we apply two gradient estimation procedures—perturbation analysis and the likelihood ratio/score function method—to derive estimators that can be used in gradient-based optimization algorithms and in sensitivity analysis when Monte Carlo simulation is employed. We illustrate the techniques on a general control chart that includes the Shewhart chart and the exponentially-weighted moving average chart as special cases. Simulation examples comparing the estimators with each other and with “brute force” finite differences demonstrate the possibility of significant variance reduction in settings of practical interest.

Evaluation of a three-state adaptive sample size X control chart

A three-state adaptive sample size control chart is developed and its performance is compared with the standard Shewhart control chart and a two-state adaptive sample size control chart. In general, significant improvements in shift detection capability results from using an adaptive sample size control chart, and the threestate adaptive control chart is superior to the two-state adaptive control for small shifts in the process mean. The improvements found in the two-state and threestate adaptive control chart schemes are gained without increasing the average incontrol sample size over the standard non-adaptive Shewhart control chart. The three-state procedure is only slightly better than the two-state scheme, and so the two-state scheme is likely adequate in most applications. The three process monitoring techniques are compared using both steady-state and start-up cases.

Inverse Gaussian cumulative sum control charts for location and shape

Cumulative sum (CUSUM) control charts are very effective at detecting persisting special causes. The most common CUSUM chart assumes that the process measurement being monitored follows the normal distribution. Many industrial problems yield measures with skewed, positive distributions—examples are component reliabilit ies, times to completion of tasks and insurance claims. Non-normal meas ures such as these should not be monitored using procedures based on the normal distribution. The inverse Gaussian distribution provides a flexible distribution that can be used to model positive skew quantities, and therefore provides an effective framework for statistical process control on processes producing such measu res. This paper defines the optimal CUSUM control chart schemes for location and shape of the inverse Gaussian distribution and evaluates its perfor mance in detecting step changes in each of these parameters. The inverse Gaussian distribution has been shown to be a good fit to a long record of task completion times on a General Motors assembly line. We extend this application, showing how our CUSUMS may be used to detect changes in the distribution of these task completion times

DETECTING EFFECTIVENESS MEASURED BY AURL

This communication addresses the problem of comparing the effectiveness of different control-charting schemes. The measure of average unit run length (AURL) is used to compare the effectiveness of the x-bar charts and the R charts with different sampling frequencies and different sample sizes. Since the trade-off between the frequency of false alarm and the detecting effectiveness is the most critical issue in the design of the control charts, we adjust the control limits of the charts in order to conduct the fair comparisons based on equal frequency of false alarm. © 1997 by John Wiley & Sons, Ltd.

Joint Monitoring of Process Mean and Variance Using Exponentially Weighted Moving Average Control Charts

The performances of control-charting schemes for thejoint monitoring of a process mean and a variance are evaluated and compared. Certain schemes are shown to be inadequate for this purpose, and the potential risk of using these schemes alone is discussed. A combined scheme consisting of a two-sided exponentially weighted moving average (EWMA) mean chart and a two-sided EWMA variance chart is found to perform well under several types of out-of-control situations. A simple method is provided for approximating the average run length and the percentage points of a run-length distribution of a combined EWMA scheme. A simple procedure is also proposed for the design of a combined EWMA scheme.

Laboratory Control of Analytical Method Inaccuracy with Respect to a Given Inaccuracy Standard

A typical laboratory control chart provides a means for detecting any intolerable change in the precision or bias of an analytical method away from its historical performance level. But in many laboratories, it would be more desirable to control accuracy, rather than either precision or bias. Thus, a procedure is given here for preparing an accuracy (or more correctly, inaccuracy) control chart for an analytical method. The procedure assumes that the user knows the minimum accuracy that the method is required to exhibit. In this case, knowledge of the prior performance characteristics of the analytical method is not required for establishing the control Limits, as is commonly true for other control-charting schemes. This control-charting procedure involves the daily analysis of spiked control samples. The estimation of total method inaccuracy from the control sample data, the computation of control limits, and the plotting of the control parameter (i.e., inaccuracy) on the control chart. Although the cont...

On Some Non-Manufacturing Applications of Counted Data Cumulative Sum (CUSUM) Control Chart Schemes

A cumulative sum control chart scheme is designed for the detection of the outbreak of an epidemic to demonstrate the use of CUSUM chart in the non-manufacturing sector. The designed schemes are then applied on data on diabetic disease to illustrate the detection of outbreak of epidemic and also a retrospective analysis is carried out and the local means are computed

Accounting for Managerial Control: An Application of Chance-Constrained Programming

An important function of managerial accounting is the provision of information for controlling activities. In this regard, the data generated by the accounting process should facilitate: (1) evaluations of the degree of conformance between actual states of affairs and goals, (2) the selection of managerial actions that will contribute to the conformance of actualities and goals, and (3) evaluations of the need for exploratory efforts directed towards developing additional alternative actions, modifying managerial goals, or both. Several proposals have appeared which are designed to enhance the degree to which the accounting process facilitates managerial control. Most of these proposals focus upon two actions that may be initiated in order to a particular process, i.e., investigate or do not investigate. Also, most of these proposals only consider a probability distribution defined on the current state of the system (and, usually, conditional upon a set of observations or experimental outcomes).' Optimal action is defined by some of the proposed approaches by comparing a measurable characteristic of the process to be controlled with a stipulated managerial goal or a stipulated standard. Simple control chart schemes and schemes that embrace the use of information-theory measures are examples of such ap-

A Survey of Sampling Procedures for Continuous Production

SUMMARY This survey reviews the main papers written on sampling procedures for attribute and continuous variable inspection of continuous production. Dodge-type continuous sampling plans and multi-level plans are described for rectifying inspection of attributes as are the criteria for choosing such plans. A number of models for process control schemes for attributes are given. Then follows an account of the various control chart schemes, e.g. the Shewhart chart and the Cumulative Sum chart, used when continuous variables are observed. The Average Run Length (A.R.L.), the V-mask and decision interval schemes and models for process control are discussed. Finally, there is a criticism of present procedures and a guide to the methods of choosing these various sampling procedures. THis paper sets out to review the papers written in the field of continuous production inspection. These procedures (or plans) are used when it is undesirable to consider inspection in terms of lot-by-lot acceptance plans and the process must be treated continuously in time. All cases considered here assume that sample items are produced at unit time intervals. When inspection takes place it is assumed that either: (a) the items can be correctly classified as defective or non-defective, or (b) a random variable xt is observed which is conditional on the true value mt of the process. The paper will be divided into two main sections which deal with the above two cases.

A modified control chart with warning lines

A recently published comparison between process inspection schemes based on control charts with both Warning and Action Lines and schemes based on runs seemed to suggest that the latter had advantages in detecting the change in the mean of a normal population. This comparison is reconsidered and the adoption of Warning and Action Line schemes designed for noticing a change in mean only and not to give some protection against other types of process change is shown to be generally better than run rules. Tables of the control chart schemes are provided.