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This paper considers the problem of obtaining robust control charts for detecting changes in the mean µ and standard deviation σ of process observations that have a continuous distribution. The standard control charts for monitoring µ and σ are based on the assumption that the process distribution is normal. However, the process distribution may not be normal in many situations, and using these control charts can lead to very misleading conclusions. Although some control charts for µ can be tuned to be robust to non-normal distributions, the most critical problem with non-robustness is with the control chart for σ. This paper investigates the performance of two CUSUM chart combinations that can be made to be robust to non-normality. One combination consists of the standard CUSUM chart for µ and a CUSUM chart of absolute deviations from target for σ, where these CUSUM charts are tuned to detect relatively small parameter shifts. The other combination is based on using winsorized observations in the standard CUSUM chart for µ and a CUSUM chart of squared deviations from target for σ. Guidance is given for selecting the design parameters and control limits of these robust CUSUM chart combinations. When the observations are actually normal, using one of these robust CUSUM chart combination will result in some reduction in the ability to detect moderate and large changes in µ and σ, compared with using a CUSUM chart combination that is designed specifically for the normal distribution. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both small and large shifts in this mean. The performance of a generalized likelihood ratio (GLR) control chart is evaluated, where the likelihood ratio is based on a moving window of past observations, The performance of the GLR chart is compared with the performance of other options, such as combinations of Shewhart and cumulative sum (CUSUM) charts and an adaptive CUSUM chart, that have been proposed for detecting a wide range of shift sizes. Performance is evaluated for sustained shifts, transient shifts, and drifts in the mean. It is shown that the overall performance of the GLR chart is at least as good as these other options. These other options have multiple control-chart parameters that allow for the charts to be tuned to be more sensitive to certain shifts that may be of interest. However, the GLR chart does not require users to specify the values of any control-chart parameters other than the size of the window and the control limit. We recommend a specific window size and provide a table of control limits corresponding to specified values of the false-alarm rate, so it is very easy to design the GLR chart for use in applications. Simulating the performance of the GLR chart is time consuming, but approximating the GLR chart with a set of CUSUM charts provides a much faster way of evaluating the performance of the GLR chart for research purposes. [ABSTRACT FROM AUTHOR]

When traditional control charts are used to monitor a proportion p, it is assumed that the binary observations are independent. This paper investigates the problem of monitoring p when there is a continuous stream of autocorrelated binary observations that follow a two-state Markov chain model with first-order dependence. It is shown that both the Shewhart p-chart and the most efficient chart for independent observations, the Bernoulli CUSUM chart, are not robust to autocorrelation, and that adjusting the control limits of these traditional charts to account for the autocorrelation is not an efficient approach. Here we construct a Markov binary CUSUM (MBCUSUM) chart based on a log-likelihood-ratio statistic and show that this chart can be well approximated by using a Markov chain model, for which exact properties are calculable. Numerical results show that the MBCUSUM chart will detect most increases in p faster than competing charts. The effect of the size of the Phase I data set used in setting up the MBCUSUM chart is also investigated. [ABSTRACT FROM AUTHOR]

When control charts are used to monitor processes to detect special causes, it is usually assumed that a special cause will produce a sustained shift in a process parameter that lasts until the shift is detected and the cause is removed. However, some special causes may produce a transient shift in a process parameter that lasts only for a short period of time. Control charts are usually based on samples of n ≥ 1 observations using a sampling interval of fixed length, say d. When n > 1, the usual practice, based on the so-called rational subgroups concept, is to take a concentrated sample at one time point at the end of the sampling interval d, but another option is to disperse the sample over the interval d. In this paper, we investigate the question of whether it is better to use n = 1, or to use n ≥ 1 and either concentrated or dispersed samples. The objective of monitoring is assumed to be the detection of special causes that may produce either a sustained or transient shift in the process mean μ and/or process standard deviation σ. It is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so that the ratio n/d is fixed. The best sampling strategy depends on the type of control chart being used, so Shewhart and cumulative sum (CUSUM) charts are considered. For both types of control charts, a combination of two charts is investigated; one chart is designed to monitor μ, and the other is designed to monitor σ. The overall conclusion is that it is best to take samples of n = 1 and use a CUSUM chart combination. The Shewhart chart combination with the best overall performance is based on n > 1, but this combination has inferior statistical performance compared with the CUSUM chart combination. [ABSTRACT FROM AUTHOR]

Investigates Cumulative Sum (CUSUM) control charts based on residuals or on the original observation. AR(1) process with an additional random error; Comparison of CUSUM and Exponentially Weighted Moving Average (EWMA) charts; Issues in applying control charts in the presence of autocorrelation.

Considers CUSUM charts with the variable sample size (VSS) feature and with both the VSS and variable sampling interval features. Two ways of developing the control statistic of the charts; Guidelines for choosing the possible sample sizes and the possible sampling intervals for the charts; Methods for setting up the charts for practical applications; Conclusions.

This paper considers two Cumulative SUM (CUSUM) charts for monitoring a process when items from the process are inspected and classified into one of two categories, namely defective or non-defective. The purpose of this type of process monitoring is to detect changes in the proportion of items in the first category. The first CUSUM chart considered is based on the binomial variables resulting from counting the total number of defective items in samples of n items. A point is plotted on this binomial CUSUM chart after n items have been inspected. The second CUSUM chart considered is based on the Bernoulli observations corresponding to the inspection of the individual items in the samples. A point is plotted on this Bernoulli CUSUM chart after each individual inspection, without waiting until the end of a sample. The main objective of the paper is to evaluate the statistical properties of these two CUSUM charts under a general model for process sampling and for the occurrence of special causes that change the value of p. This model applies to situations in which there are inspection periods when n items are inspected and noninspection periods when no inspection is done. This model assumes that there is a positive time between individual inspection results, and that a change in p can occur anywhere within an inspection period or a non-inspection period. This includes the possibility that a shift can occur during the time that a sample of n items is being taken. This model is more general and often more realistic than the simpler model usually used to evaluate properties of control charts. Under our model, it is shown that there is little difference between the binomial CUSUM chart and the Bernoulli CUSUM chart, in terms of the expected time required to detect small and moderate shifts in p, but the Bernoulli CUSUM chart is better for detecting large shifts in p. It is shown that it is best to choose a relatively small sample size when applying the CUSUM charts. As expected, the CUSUM charts are substantially faster than the traditional Shewhart p-chart for detecting small shifts in p. But, surprisingly, the CUSUM charts are also better than the p-chart for detecting large shifts in p. [ABSTRACT FROM AUTHOR]

Studies the application of a cumulative sum chart (CUSUM) for monitoring a proportion when inspecting continuously. Discussion on the Bernoulli CUSUM chart; Properties of the chart; Method for designing the chart.

Proposes a modification of the standard cumulative sum (CUSUM) scheme that varies the time intervals between samples depending on the value of the CUSUM control statistic. Description of the variable sampling interval (VSI) CUSUM chart; Properties of VSI charts; Numerical evaluations of the average time to signal (ATS); Comparing fixed sampling interval and VSI charts; Guidelines for design of VSI CUSUM charts; Conclusions.

Presents the authors response on the comments of the discussants about the optimality, practicality design and model assumptions of the variable sampling interval cumulative sum (VSI CUSUM). Practicality of the VSI CUSUM; Optimality and design of the VSI CUSUM; Properties of the VSI CUSUM; Other technical issues regarding the VSI CUSUM chart.

A control chart based on applying a sequential probability ratio test (SPRT) at each sampling point is considered for the problem of monitoring a process proportion p. This SPRT chart can be applied in situations in which items are inspected one by one, and the results of each inspection can be conveniently recorded before the next item is inspected. Some corrected diffusion theory approximations are given for the statistical properties of the SPRT and the SPRT chart. These approximations are very accurate and provide a simple method for designing an SPRT chart for practical applications. The sample size for the SPRT chart at a particular sampling time depends on the observations at that time, but the chart can be designed to have a specified average sampling rate when the process is in control. When there is a small shift in p, the average sampling rate per unit time will increase, but for a large shift in p the average sampling rate will decrease. For a given in-control average sampling rate and a given false alarm rate, the SPRT chart will detect changes in p much faster than the standard p-chart, which has traditionally been used for monitoring p. The SPRT chart will also detect changes in p much faster than the CUSUM chart for p. Thus, the SPRT chart can be used in place of traditional control charts to provide faster detection of changes in p or to reduce the sampling effort required to provide a given detection capability. [ABSTRACT FROM AUTHOR]

An approximation to the average run length for cumulative sum control charts is derived using the analogy between this procedure and the sequential probability ratio test for normal observations. This approximation is also derived by using a Brownian motion approximation to the cumulative sum. The Brownian motion approximation dons not- require the normality assumption. The analytical expression for the average run length obtained from the approximation is then used to determine the optimal choice of parameters to minimize the average run length at a specified deviation from control, subject to a fixed average run length when in control. [ABSTRACT FROM AUTHOR]