By Robert L. Mason, John C. Young
ISBN-10: 0898714966
ISBN-13: 9780898714968
This utilized, self-contained textual content offers unique insurance of the sensible facets of multivariate statistical approach regulate (MVSPC) in line with the applying of Hotelling's T2 statistic. MVSPC is the applying of multivariate statistical suggestions to enhance the standard and productiveness of an business procedure. The authors, major researchers during this quarter who've built significant software program for this sort of charting strategy, supply worthy perception into the T2 statistic. deliberately together with just a minimum volume of thought, they lead readers throughout the building and tracking stages of the T2 keep an eye on statistic utilizing quite a few business examples taken basically from the chemical and tool industries. those examples are utilized to the development of old information units to function some degree of reference for the keep watch over method and also are utilized to the tracking section, the place emphasis is put on sign place and interpretation when it comes to the method variables.
Specifically dedicated to the T2 method, Multivariate Statistical technique keep an eye on with business purposes is the one ebook to be had that concisely and carefully offers such themes as how you can build a historic information set; tips on how to money the mandatory assumptions used with this process; easy methods to chart the T2 statistic; tips on how to interpret its signs; easy methods to use the chart within the presence of autocorrelated facts; and the way to use the method to batch approaches. The publication comes with a CD-ROM containing a 90-day demonstration model of the QualStat™ multivariate SPC software program in particular designed for the appliance of T2 keep an eye on systems. The CD-ROM is suitable with home windows® ninety five, home windows® ninety eight, home windows® Me Millennium version, and home windows NT® working structures.
Audience Analysts trying to use Hotelling's T2 as a regulate statistic for a multivariate business procedure will locate this consolidated reference priceless. The ebook will express readers tips to determine and make the most of the multivariate keep watch over approach in response to Hotelling's T2 statistic and to use it to an commercial strategy. Readers can be conversant in univariate regulate chart development and tracking systems, yet needn't learn concerning the program of multivariate keep watch over systems in keeping with the T2 statistic.
Contents Preface; bankruptcy 1: advent to the T2 Statistic; bankruptcy 2: simple innovations concerning the T2 Statistic; bankruptcy three: Checking Assumptions for utilizing a T2 Statistic; bankruptcy four: building of old information Set; bankruptcy five: Charting the T2 Statistic in part I; bankruptcy 6: Charting the T2 Statistic in part II; bankruptcy 7: Interpretation of T2 indications for 2 Variables; bankruptcy eight: Interpretation of T2 signs for the overall Case; bankruptcy nine: bettering the Sensitivity of the T2 Statistic; bankruptcy 10: Autocorrelation in T2 regulate Charts; bankruptcy eleven The T2 Statistic and Batch techniques; Appendix: Distribution Tables; Bibliography; Index.
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Additional resources for Multivariate Statistical Process Control with Industrial Application
Example text
We now illustrate the appropriateness of the same chi-square distribution for the T2 statistic generated from the nonnormal distribution. Two hundred observations for five independent uniform variables and one independent exponential are generated. 01. 10. Our interest lies in the tail of the distribution. 81. 9 are near the UCL, the T2 chart indicates no signaling T2 values. 10. 5. 10: Q-Q plot based on simulated data from nonnormal distribution. 11: T2 chart based on simulated data from nonnormal distribution.
01. With this a, we would expect to observe two signals in the chart. However, there are five signaling T2 values, indicating the heavy tailed distribution expected by the high kurtosis value. 12. Note the severe deviation from the trend line in the upper tail of the plot of the T2 values. 44 Chapter 3. 12: Q-Q plot based on simulated data from nonnormal distribution. 13: Scatter plot of bivariate data. The conclusion is that a chi-square distribution does not provide a good fit to these data. To illustrate the appropriateness of the use of the beta distribution to describe the sampling distribution of the T2 statistic, we consider 104 bivariate observations taken from an actual industrial process.
If a distribution has a kurtosis value that exceeds 3, it is labeled "peaked" relative to the normal, and if its kurtosis value is less than 3, it is labeled "flat" relative to the normal. For example, the univariate exponential distribution has a kurtosis value of 9, whereas the univariate uniform and beta distributions have kurtosis values less than 3. " The gamma, lognormal, and weibull distributions have kurtosis values around 3 and thus are "peaked" similarly to the normal distribution. In a multivariate distribution, the kurtosis measure is closely related to the sampling distribution of the T2 statistic.