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Question 1 (. Gauge Repeatability and Reproducibility (GR&R) studies is a measure of the capability of a gauge or instrument to obtain the same measurement reading every time the measurement process is undertaken for the same characteristic or parameter. The following Table 1 shows the measurement result of part diameter (Tolerance = + 0.005mm – 0.004mm) by two appraisers (observers) through the use of an outside micrometer. Answer the following questions in order to perform a GR&R study. Refer Appendix 1 for major equations and constant factors.

Question 1 (. Gauge Repeatability and Reproducibility (GR&R) studies is a measure of the capability of a gauge or instrument to obtain the same measurement reading every time the measurement process is undertaken for the same characteristic or parameter. The following Table 1 shows the measurement result of part diameter (Tolerance = + 0.005mm – 0.004mm) by two appraisers (observers) through the use of an outside micrometer. Answer the following questions in order to perform a GR&R study. Refer Appendix 1 for major equations and constant factors.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 1 ( Gauge Repeatability and Reproducibility (GR&R) studies is a measure of the capability of a gauge or instrument to obtain the same measurement reading every time the measurement process is undertaken for the same characteristic or parameter. The following Table 1 shows the measurement result of part diameter (Tolerance = + 0.005mm – 0.004mm) by two appraisers (observers) through the use of an outside micrometer. Answer the following questions in order to perform a GR&R study. Refer Appendix 1 for major equations and constant factors. Table 1: GR&R Study Worksheet Appraiser: A B Sample (n) Trial 1 Trial 2 Mean Range (RA) Trial 1 Trial 2 Mean Range (RB) (r1) (r2) (Xbar.A) (r1) (r2) (Хьаг. в) 1 0.473 0.472 Xbar.n1A Rn1A 0.472 0.469 Xbar.n1B Rn1B 0.468 0.471 Xbar.n2A R12A 0.471 0.469 Xbar.n2B Rn2B 3 0.472 0.470 Xbar.n3A Rn3A 0.470 0.471 Xbar.n3B Rn3B 4 0.471 0.473 Xbar.n4A 0.470 0.471 Xbar.n4B RN4B 0.468 0.470 Xbar.n5A R15A 0.467 0.469 Xbar.n5B Rn5B Σ EXbar.A ΣRA EXbar.B ΣRB (a) Calculate: i. The mean (Xbar.n1A ~ Xbar.n5A ; Xbar.n1B - Xbar.n5B), range (RnA1 RnA5 ; Rn1B - Rn5B) and summation (EXbar.A ; EXbar.B ; ERA ; ERB) for each appraiser. ii. The mean of each appraiser's means (Xdoubleb: ar.A and Xdoublebar.B) iii. The different (Xdoublebar.diff.) between the maximum appraiser mean value and the minimum appraiser mean value. iv. The mean of range for each appraiser (Rpar.A and Rbar.B) and the grand range (Rbar). 2 V. The control limit (LCL and UCL) for R-chart. Give the comment on the R-chart. vi. The Equipment Variation (EV), Appraiser Variation (AV) and GR&R. vii. The Equipment Variation % (EV%), Appraiser Variation % (AV%) and GR&R%. (b) Briefly explain the conclusion on the Measurement System Analysis (MSA) based on the result you have calculated.
Transcribed Image Text:Question 1 ( Gauge Repeatability and Reproducibility (GR&R) studies is a measure of the capability of a gauge or instrument to obtain the same measurement reading every time the measurement process is undertaken for the same characteristic or parameter. The following Table 1 shows the measurement result of part diameter (Tolerance = + 0.005mm – 0.004mm) by two appraisers (observers) through the use of an outside micrometer. Answer the following questions in order to perform a GR&R study. Refer Appendix 1 for major equations and constant factors. Table 1: GR&R Study Worksheet Appraiser: A B Sample (n) Trial 1 Trial 2 Mean Range (RA) Trial 1 Trial 2 Mean Range (RB) (r1) (r2) (Xbar.A) (r1) (r2) (Хьаг. в) 1 0.473 0.472 Xbar.n1A Rn1A 0.472 0.469 Xbar.n1B Rn1B 0.468 0.471 Xbar.n2A R12A 0.471 0.469 Xbar.n2B Rn2B 3 0.472 0.470 Xbar.n3A Rn3A 0.470 0.471 Xbar.n3B Rn3B 4 0.471 0.473 Xbar.n4A 0.470 0.471 Xbar.n4B RN4B 0.468 0.470 Xbar.n5A R15A 0.467 0.469 Xbar.n5B Rn5B Σ EXbar.A ΣRA EXbar.B ΣRB (a) Calculate: i. The mean (Xbar.n1A ~ Xbar.n5A ; Xbar.n1B - Xbar.n5B), range (RnA1 RnA5 ; Rn1B - Rn5B) and summation (EXbar.A ; EXbar.B ; ERA ; ERB) for each appraiser. ii. The mean of each appraiser's means (Xdoubleb: ar.A and Xdoublebar.B) iii. The different (Xdoublebar.diff.) between the maximum appraiser mean value and the minimum appraiser mean value. iv. The mean of range for each appraiser (Rpar.A and Rbar.B) and the grand range (Rbar). 2 V. The control limit (LCL and UCL) for R-chart. Give the comment on the R-chart. vi. The Equipment Variation (EV), Appraiser Variation (AV) and GR&R. vii. The Equipment Variation % (EV%), Appraiser Variation % (AV%) and GR&R%. (b) Briefly explain the conclusion on the Measurement System Analysis (MSA) based on the result you have calculated.
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