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Multivariate Process Variability Monitoring Improvements

Ostad Sharif Memar, Ahmad | 2011

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 41651 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Akhavan Niaki, Taghi
  7. Abstract:
  8. We consider finding some efficient control schemes for multivariate variability monitoring with capability of working with individual observations. To do this, the existing efficient control charts for multivariate variability monitoring are studied first and it is determined that the and control statistics, defined by individual observations, estimate the covariance matrix quite well. However, the control method that is based on monitoring the trace of these matrices is not necessarily the best. Thus, by applying the first and the second norm on these two statistics, four new control schemes, namely MEWMSL1, MEWMVL1, MEWMVL1 and MEWMVL2are proposed. Performance comparison results show that all the four proposed charts outperform the existing ones. Moreover, the charts based on the statistics detect shifts much faster than the charts based on the statistiscs. Then, the statistic is generalized for the desired value of rational subgroup and its properties areinvestigated. The more important properties are the probability distribution of each of diagonal elements, sum of diagonal elements, and sum of all elements. Using these properties, MEWMSAS, MEWMSAT and MEWMSNL1 charts are developed. Performance comparison results indicate that when at least one of the variance components experiencesa shift, the MEWMSNL1 control scheme has the best performance in general. Furthermore, when the changes in a process only occur in the correlation coefficients, the MEWMSNL1 control chart has the best performance. However, if detecting the correlation coefficients shifts is desired, the MEWMSAS chart can be used along with the MEWMSNL1 chart. Finally, a single control chart for simultaneous monitoring of univariate mean and variance was proposed and its performance is compared with the ones corresponding to two other existing combination charts. The results of simulation studies show that the proposed chart works better than the other two charts in general. Moreover, best performance can be obtained using individual observations
  9. Keywords:
  10. Simultaneous Control of Mean & Variance ; Exponentially Weighted Moveing Average (EWMA) ; Variability Monitoring ; Multivariate Monitoring ; Individual Observations ; Squared Deviation From the Target ; Single Control Chart

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