Model-Based and Model-Free Control of Autocorrelated Processes

Runger, George C.; Willemain, Thomas R.

doi:10.1080/00224065.1995.11979608

Cited by 99 publications

(48 citation statements)

References 20 publications

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“…We compare the distribution-free Tabular CUSUM with distribution-free SPC procedures due to Johnson and Bagshaw (1974), , and Runger and Willemain (1995). Then give an out-of-control signal if |UBM i | ≥ z ON · σ UBM , where UBM i is the ith uncorrelated batch mean (UBM) and σ 2 UBM is the marginal variance of the UBMs (which is assumed to be known).…”

Section: Methodsmentioning

confidence: 99%

A distribution-free tabular CUSUM chart for autocorrelated data

et al. 2007

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A distribution-free tabular CUSUM chart is designed to detect shifts in the mean of an autocorrelated process. The chart's average run length (ARL) is approximated by generalizing Siegmund's ARL approximation for the conventional tabular CUSUM chart based on independent and identically distributed normal observations. Control limits for the new chart are computed from the generalized ARL approximation. Also discussed are the choice of reference value and the use of batch means to handle highly correlated processes. The new chart is compared with other distribution-free procedures using stationary test processes with both normal and nonnormal marginals. IntroductionGiven a stochastic process to be monitored, a statistical process control (SPC) chart is used to detect any practically significant shift from the in-control status for that process, where the in-control status is defined as maintaining a specified target value for a given parameter of the monitored process-for example, the mean, the variance, or a quantile of the marginal distribution of the process. An SPC chart is designed to yield a specified value ARL 0 for the in-control average run length (ARL) of the chart-that is, the expected number of observations sampled from the in-control process before an out-of-control alarm is (incorrectly) raised. Given several alternative SPC charts whose control limits are determined in this way, one would prefer the chart with the smallest out-of-control average run length ARL 1 , a performance measure analogous to ARL 0 for the situation in which the monitored process is in a specific out-of-control condition. If the monitored process consists of independent and identically distributed (i.i.d.) normal random variables, then control limits can be determined analytically for some charts such as the Shewhart and tabular CUSUM charts as detailed in Montgomery (2001).It is more difficult to determine control limits for an SPC chart that is applied to an autocorrelated process; and much of the recent work on this problem has been focused on developing distribution-based (or model-based) SPC charts, which require one of the 2 following:1. The in-control and out-of-control versions of the monitored process must follow specific probability distributions.2. Certain characteristics of the monitored process-such as such as the first-and secondorder moments, including the entire autocovariance function-must be known.Moreover, the control limits for many distribution-based charts can only be determined by trial-and-error experimentation. Of course, if the underlying assumptions about the probability distributions describing the target process are violated, then these charts will not perform as advertised. Another limitation is that determining the control limits by trialand-error experimentation can be very inconvenient in practical applications-especially in circumstances that require rapid calibration of the chart and do not allow extensive preliminary experimentation on training data sets to estimate ARL 0 for various trial...

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Section: Methodsmentioning

confidence: 99%

A distribution-free tabular CUSUM chart for autocorrelated data

et al. 2007

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“…normal as the batch size increases. For brevity, the chart of Runger and Willemain (1995) is called R&W in the rest of this paper. Johnson and Bagshaw (1974) and Kim et al (2007) develop CUSUM charts that use individual (raw, unbatched) observations as the basic data items; and in the rest of this article, these charts are called J&B and DFTC, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Maragah and Woodall (1992) show that retrospective Shewhart charts generate an increased number of false alarms when they are applied to processes with positive lag-one autocorrelation. For correlated data, Runger and Willemain (1995) use nonoverlapping batch means as their basic data items and apply classical Shewhart charts designed for i.i.d. normal data, exploiting the well-known property that under broadly applicable conditions, the batch means are asymptotically i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Monitoring autocorrelated processes using a distribution-free tabular CUSUM chart with automated variance estimation

et al. 2009

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We formulate and evaluate distribution-free statistical process control (SPC) charts for monitoring shifts in the mean of an autocorrelated process when a training data set is used to estimate the marginal variance of the process and the variance parameter (i.e., the sum of covariances at all lags). We adapt two alternative variance estimators for automated use in DFTC-VE, a distribution-free tabular CUSUM chart, based on the simulation-analysis methods of standardized time series and a simplified combination of autoregressive representation and nonoverlapping batch means. Extensive experimentation revealed that these variance estimators did not seriously degrade DFTC-VE's performance compared with its performance using the exact values of the marginal variance and the variance parameter. Moreover, DFTC-VE's performance compared favorably with that of other competing distribution-free SPC charts.

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“…The first method is based on an effort to modify control limits of the traditional control charts by taking the effect of autocorrelation into account (e.g. see Vasilopoulos and Stamboulis [3], Runger [4], Kramer and Schmid [5], Zhang [6], Jiang, Tsui, and Woodall [7], Atienza, Tang and Ang [8] and references there in). The other attempts to transform the original data to uncorrelated data by fitting time series models and then monitoring a process through one-step ahead forecast errors (residuals) (e.g.…”

Section: Introductionmentioning

confidence: 99%