I need help with part b please. Problem 8-3 TABLE BE.9 Measurement Data for Exer

Question

I need help with part b please.

Problem 8-3 TABLE BE.9 Measurement Data for Exercise 831 Ten parts are measured three times by the same operator in a gauge capability study. The data are shown in table 8E.9 Part 00 10 00 95 93 97 0 103 00 96 95 97 a) b) Estimate total variability and product c) What percentage of total variability is due to d) If specifications on the part are at 100+/-15 Describe the measurement error that results from the use of this gauge. variability the gauge? Find the P/T ratio for this gauge. Comment on 96 9998 9 5 97 98 100 99 98 00100 9 10098” 10 the adequacy of the gauge.

Explanation / Answer

(b)

So, from the above calculations, note:

R_bar = 2.3
S = sample std. deviation = 2.17
d2 (from table for n=3) = 1.693

gauge = R_bar / d2 = 2.3 / 1.693 = 1.359
or. 2gauge = Gauge variability = 1.359^2 = 1.85

2total = Total variability = S2 = 2.17^2 = 7.29
2product = Product Variability = 2total - 2gauge = 7.29 - 1.85 = 5.44

Part No. Measurements Mean Range Sum of squares 1 2 3 x_bar R = max.(xi) - min.(xi) i (xi - x_double bar)^2 1 100 101 100 100.33 1 14.32 2 95 93 97 95.00 4 38.72 3 101 103 100 101.33 3 34.12 4 96 95 97 96.00 2 16.52 5 98 98 96 97.33 2 4.92 6 99 98 98 98.33 1 0.72 7 95 97 98 96.67 3 11.72 8 100 99 98 99.00 2 3.92 9 100 100 97 99.00 3 7.92 10 100 98 99 99.00 2 3.92 Averages = 98.20 2.30 Total = 136.80 x_double bar R_bar S = = sqrt(136.80/29) = 2.17

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