Browsing by Author "Stoumbos, Zachary G."

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    Control charts applying a sequential test at fixed sampling intervals with optional sampling at fixed times
    Stoumbos, Zachary G. (Virginia Tech, 1993)
    In recent years, variable sampling interval (VSI) control charts have been intensively investigated. In contrast to traditional fixed sampling interval (FSI) control charts, VSI charts vary the sampling interval as a function of the data. VSI charts detect many process changes faster than their FSI counterparts. A disadvantage, however, of VSI charts as recently formulated is that the advance prediction of sampling times is impossible for more than the next sample. A control chart is proposed which applies a sequential probability ratio test (SPRT) at fixed sampling intervals, the SPRT chart, to monitor the mean of a process with a normal distribution. A natural modification of the SPRT chart, the SPRT chart with sampling at fired times (SFT), is also proposed in which samples are always taken at pre-specified, equally spaced fixed times, with additional samples taken between these times as indicated by the data. A third control chart is introduced as a generalization of the VSI cumulative sum (CUSUM) chart that uses two sampling intervals, called the universal CUSUM (UC) chart, in order to address the need for a general framework for the study of control charts that are equivalent to a sequence of SPRT’s. The UC chart can also be viewed as a generalization of the SPRT chart. The integral equation approach is adapted for the evaluation of properties of both the unmodified and modified with SFT versions of the SPRT chart, such as average time to signal (ATS), steady state ATS (SSATS), and average number of observations to signal (ANOS). After comparisons are performed within the general framework of the UC chart, the unmodified SPRT chart is found to be more efficient than both the FSI and VSI X charts and the FSI CUSUM chart, though very similar in efficiency to the VSI CUSUM chart. The modified SPRT chart with SFT is found to be more efficient than all five of the other control charts, including its unmodified version and the VSI CUSUM chart. General guidelines are provided for the design of both versions of the SPRT chart.
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    An Investigation of Combinations of Multivariate Shewhart and MEWMA Control Charts for Monitoring the Mean Vector and Covariance Matrix
    Reynolds, Marion R. Jr.; Stoumbos, Zachary G. (Virginia Tech, 2008-01-22)
    When monitoring a process which has multivariate normal variables, the Shewhart-type control chart (Hotelling (1947)) traditionally used for monitoring the process mean vector is effective for detecting large shifts, but for detecting small shifts it is more effective to use the multivariate exponentially weighted moving average (MEWMA) control chart proposed by Lowry et al. (1992). It has been proposed that better overall performance in detecting small and large shifts in the mean can be obtained by using the MEWMA chart in combination with the Shewhart chart. Here we investigate the performance of this combination in the context of the more general problem of detecting changes in the mean or increases in variability. Reynolds and Cho (2006) recently investigated combinations of the MEWMA chart for the mean and MEWMA-type charts based on squared deviations of the observations from the target, and found that these combinations have excellent performance in detecting sustained shifts in the mean or in variability. Here we consider both sustained and transient shifts, and show that a combination of two MEWMA charts has better overall performance than the combination of the MEWMA and Shewhart charts. We also consider a three-chart combination consisting of the MEWMA chart for the mean, an MEWMA-type chart of squared deviations from target, and the Shewhart chart. When the sample size is n = 1 this three-chart combination does not seem to have better overall performance than the combination of the two MEWMA charts. When n > 1 the three-chart combination has significantly better performance for some mean shifts, but somewhat worse performance for shifts in variability.