mont4e_sm_ch16_sec07 - I-MR Chart of SIZE U C L=127.08...

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Section 16-7 16-18. a) The natural tolerance limits are 100 18 ± . 40 1.1111 63 6 USL LSL PCR σ == = Since the mean of the process is centered at the nominal dimension, 1.1111 k PCR PCR Since the process natural tolerance limits lie inside the specifications, very few defective units will be produced. The fraction defective is 2 ( 20/ 6) 0.0858% Φ− = b) The natural tolerance limits are 106 18 ± . 40 1.1111 6 USL LSL PCR = Since the mean of the process is not centered at the nominal dimension, 14 26 min , 0.7778 18 18 k PCR ⎡⎤ ⎢⎥ ⎣⎦ The small PCRK indicates that the process is likely to produce units outside the specification limits. The fraction defective is ( ) ( ) ( ) ( ) 14/ 6 26/ 6 0.0098+0=0.0098 PX L SL PX U SL PZ PZ <+>=< +> = 16-19 a) 12 1.5 66 USL LSL PCR σσ = so 1.3333 = b) (20+32)/2=26 When the process is centered at the nominal dimension, the fraction defective is minimized for any . 16-16
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16-20 a) The natural tolerance limits are 20 6 ± . 20 1.6667 61 2 USL LSL PCR σ == = Since the mean of the process is centered at the nominal dimension, 1.6667 k PCR PCR Since the process natural tolerance limits lie inside the specifications, very few defective units will be produced. The fraction defective is 2(1 0 / 2 ) 0 Φ− = b) The natural tolerance limits is 23 6 ± . 20 1.6667 2 USL LSL PCR = Since the mean of the process is not centered at the nominal dimension, 13 7 min , 1.1667 66 k PCR ⎡⎤ ⎢⎥ ⎣⎦ The fraction defective is 00023 . 0 00023 . 0 0 ) 2 / 7 ( ) 2 / 13 ( ) ( ) ( = + = > + < = > + < Z P Z P USL X P LSL X P c) The measure of actual capability decreases and the fraction defective increases when the process mean is shifted from the center of the specification limits. 16-21 a) If the process uses 66.7% of the specification band, then 6 σ = 0.667(USL-LSL). Because the process is centered LSU USL USL LSL USL = = = = = μμ μ 5 . 4 ) ( 667 . 0 ) ( 677 . 0 ) ( 667 . 0 3 5 . 1 3 5 . 4 , 3 5 . 4 min = = = K PCR PC
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This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.

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mont4e_sm_ch16_sec07 - I-MR Chart of SIZE U C L=127.08...

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