1IE 361 Lab#3/ ANOVA-Based Gauge R&R Calculations _____________________ (Name) Attached to this lab is a JMP report for a Fit Model two-way ANOVA analysis of a standard "Gauge R&R" data set. (The data come from an IE 361 measurement study that was done using the same calipers and Styrofoam peanuts you used in Labs #1 and #2.) Use it and the Formula Sheet also provided to complete the calculations in this lab (covering the content of Module 6). After the in-class lab period, run JMP and get your own two-way ANOVA analysis and staple it to this lab before turning the lab in. How many peanuts were used in this study? I=____________ How many operators were involved in the study? J=____________ How many times did each operator measure each part? m=____________ The units of measurement were (as in Labs #1 and #2) inches. Be sure to attach units to answers that you give in this lab. Give a single-number estimate of the standard deviation that would be experienced by a single operator repeatedly remeasuring the same peanut. What degrees of freedom should be associated with the estimate above? Use the previous two answers and make 95% two-sided confidence limits for the standard deviation that would be experienced by a single operator repeatedly remeasuring the same peanut.2Give a single-number estimate of the standard deviation that would be experienced by many operators measuring the same peanut once each in the absence of repeatability variation. What approximate degrees of freedom should be associated with the estimate above? Use the previous two answers and make 95% two-sided confidence limits for the standard deviation that would be experienced by many operators measuring the same peanut once each in the absence of repeatability variation.3Give a single-number estimate of the standard deviation that would be experienced by many operators measuring the same peanut once each. What approximate degrees of freedom should be associated with the estimate above? Use the previous two answers and make 95% two-sided confidence limits for the standard deviation that would be experienced by many operators measuring the same peanut once each.4In light of the inferences on pages 1 through 3, how do the "repeatability" and "reproducibility" components of measurement variability seem to compare? If this were a real industrial situation and you were responsible for improving measurement consistency, what would you do first here? Suppose for sake of illustration that engineering specifications on the actual sizes of these peanuts are from .49 inch to .51 inch. Based on your first answer on page 3, what do you estimate to be the gauge capability ratio for calipers used in this study for purposes of checking conformance to these specifications. That is, estimate ()R&R6/GCR U Lσ=−. Use your last answer on page 3 and make approximate 95% confidence limits for the gauge capability ration (the "precision to tolerance" ratio). If this were a real industrial situation, would you consider the calipers adequate to check conformance of the peanuts to the engineering specifications? Explain.Form ulas for ANOVA-Based Gauge R &R Esti-mationWe consider a standard Gauge R&R data set consisting of m (repeat) mea-surements of I different parts by each of J operators. This sheet of formulassummarizes the computations dicsussed on the slides for IE 361 Module 6. Thet wo-way random effects model isyijk= μ + αi+ γj+ αγij+ ijkand the quantities of most obvious interest areσrepeatability= σσreproducibility=qσ2γ+ σ2αγandσR&R=qσ2re pr o d u cib il ity+ σ2=qσ2γ+ σ2αγ+ σ2Estimates of these are:ˆσrepeatability= bσ =√MSEˆσrep ro du cibility=smaxµ0,MSCmI+(I − 1)mIMSAC −1mMSE¶andˆσR&R=r1mIMSC +I − 1mIMSAC +m − 1mMSECorresponding (exact and approximate) degrees of freedom areνrepeatability= IJ (m − 1)ˆνre pr o d u cib il ity=ˆσ4re pr o d u cib il ity1m2µMSC2I2(J − 1)+(I − 1) MSAC2I2(J − 1)+MSE2IJ (m − 1)¶andˆνR&R=ˆσ4R&R1m2µMSC2I2(J − 1)+(I − 1) MSAC2I2(J − 1)+(m − 1) MSE2IJ¶to be used with the basic formulas for confidence limitsˆσrνχ2upperand ˆσrνχ2lowe
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