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Unformatted text preview: IE 361 Module 6 Gauge R&R Studies Part 2: TwoWay ANOVA and Corresponding Estimates for R&R Studies Reading: Section 2.2 Statistical Quality Assurance for Engineers (Section 2.4 of Revised SQAME ) Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 6 1 / 21 ANOVA and R&R Analysis The rangebased Gauge R&R estimates of SQAME are fairly simple and serve the purpose of helping make the analysis goals easy to understand. But we have no good handle on how reliable these estimates are. In order to 1) produce Gauge R&R estimates that are typically better than rangebased ones, and 2) produce con¡dence limits, we must instead use "ANOVAbased" estimates. A careful treatment of ANOVA would require its own course. We¢ ll simply make use of its main "output" and direct the interested student to books on engineering statistics (like Vardeman¢s Statistics for Engineering Problem Solving ) for more details. The fact is that an I & J & m data set of y ijk ¢s like that produced in a typical Gauge R&R study is often summarized in a socalled ANOVA table. A generic version of such a table is Vardeman and Morris (Iowa State University) IE 361 Module 6 2 / 21 ANOVA and R&R Analysis Source SS df MS Part SSA I & 1 MSA = SSA / ( I & 1 ) Operator SSB J & 1 MSB = SSB / ( J & 1 ) Part ¡ Operator SSAB ( I & 1 ) ( J & 1 ) MSAB = SSAB / ( I & 1 ) ( J & 1 ) Error SSE IJ ( m & 1 ) MSE = SSE / IJ ( m & 1 ) Total SSTot IJm & 1 Any decent statistical package (and even EXCEL) will process a Gauge R&R data set and produce such a summary table. In this table the "mean squares" are essentially sample variances (squares of sample standard deviations). ( MSA is essentially a sample variance of part averages, MSB is essentially a sample variance of operator averages, MSE is an average of within cellsample variances, " MSTot " isn¡t typically calculated, but is a grand sample variance of all observations, ...) The mean squares indicate how much of the overall variability is accounted for by the various sources. Vardeman and Morris (Iowa State University) IE 361 Module 6 3 / 21 ANOVA and R&R Analysis Example 61 We¡ ll use the data set with I = 4 , J = 3 , m = 2 from the inclass R&R study (used as a numerical example in Module 5) to illustrate. The JMP data table and some screen shots for using the program to get the sums of squares follow....
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 Fall '09
 Variance, Prof. Steve Vardeman

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