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Stat Proc Cntrl & Metrology

by: Arlene Runolfsdottir III

Stat Proc Cntrl & Metrology MEGR 3282

Arlene Runolfsdottir III
GPA 3.98

Edward Morse

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Edward Morse
Class Notes
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This 7 page Class Notes was uploaded by Arlene Runolfsdottir III on Sunday October 25, 2015. The Class Notes belongs to MEGR 3282 at University of North Carolina - Charlotte taught by Edward Morse in Fall. Since its upload, it has received 116 views. For similar materials see /class/228990/megr-3282-university-of-north-carolina-charlotte in Mechanical Engineering at University of North Carolina - Charlotte.


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Date Created: 10/25/15
Equation Sheet for MEGR 3282 SPC amp Metrology Distributions Name pdf mean variance 71D D N n Hypergeometric px x 01 2 minnD 71 N 1 n n Binomial px p 1 pH x 01 2n VIP npl p x 71 a Poisson e A x 01 A j x Normal fxe jz oolt xlt 00 u 02 042 Exponential e jx x Z 0 i i l 12 Lastmodified II Febmary 2003 Page 1 of 7 Equation Sheet for MEGR 3282 SPC amp Metrology Twosided confidence intervals statistic Interval m e an variance known m e an variance unknown v arianc e difference between means variance known difference between means variance unknown Slz quot2 1S22 n1 H2 2 where S p 2 2 S2 Ratio of variances 1 F lt 1 lt 1 F for normal distributions 2 lidZvnrlvnrl 2 2 allmrlmrl S 2 039 2 S 2 Lastmodi ed II Febmary 2003 Page 2 Of 7 Equation Sheet for MEGR 3282 SPC amp Metrology Hypothesis tests Test on means with known variance Hypothesis Criteria for Rejection Test Statistic H IZogtZaz H1 o H Tc y 0 0 ZOlt Z1 Zo H11lt0 0 H H 0 ZOgtZa H1gto H i l 2 ZOgtZa le lwz H0lu1lu2 Z ltZ ZO 2 2 H11 1ltI 2 0 a 1 2 n1 quot2 H i l 2 ZOgtZa H11gt2 Lastmodified II Febmary 2003 Page 3 of 7 Equation Sheet for MEGR 3282 SPC amp Metrology Hypothesis tests continued Test on means of normal distributions with unknown variance Hypothesis Criteria for Rejection Test Statistic H0Iulu0 Ital gt tam H1 o H 9 C 0 I 0 t0lttanrl to 0 H1lto 39 SN H 0 I 0 IOgtIIIYH H1gto H01Myz III ifaf if afiai 0 a2v HlMHLZ x C l 1 Z 0 2 2 S HoIuizluz tltt 12 H1 lul ltqu 0 div to x1 x2 n1 quot2 S 2 p n n H LL1u 1 2 2 0 2 t0gttm V nln2 2 Szn 2 Sin 2 HIMgtz n11 n21 Lastmodified II Febmary 2003 Page 4 of 7 Equation Sheet for MEGR 3282 SPC amp Metrology Hypothesis tests continued Tests on variances of normal distributions Hypothesis Criteria for Rejection Test Statistic H 2 2 X2 gt X2 0 0390 0 aZmrl 0r 2 2 2 2 H1 039 039 X0 lt KHz27H Z Z 2 H0 O0 X2 X2 X2 n1S 2 2 0 lt 17man 0 2 H1 039 lt 0390 0390 H0 2 03902 2 2 X3 gt XZM H1 039 gt 0390 2 Z 2 H0 0391 0392 F0 gtFzz2n171n271 0 F S1 2 2 0 2 H1 01 at 0392 F0 lt FirmZmlrl zil S2 H0 612 03922 S22 F gtF 7 7 F 2 2 0 ml ml 1 0 S2 H1 61 lt 0392 1 H0 612 03922 S12 F0gtFzzn71n71 F0 2 2 v 1 v 2 2 H1 01 gt 0392 S2 Lastmodified II Febmary 2003 Page 5 of 7 Equation Sheet for MEGR 3282 SPC amp Metrology Variables control charts n 0 given Quality Characteristic Center Line Control Limits 9 I u i A 039 R 0 M1DpU1QU S 90 MlBpM1Bp n 0 not given unknown f f fiAjiar i R F UCLLL LCLL S M1BSM1amp Attributes control charts Quality Characteristic Center Line Control Limits plp Fractlon nonconformmg p g1ven P p i 3 7 il i Fractlon nonconformmg p not g1ven p p i 3 7 Number nonconforming p given quotP np 3 np 1 p Number nonconforming p not given 7 np i 3 np 1 Nonconformities c given 0 c 34 Nonconformities c not given 5 c 3J5 Average number of nonconformltles E E i 3 1 per un n Lastmodified II Febmary 2003 Page 6 Of 7 Equation Sheet for MEGR 3282 SPC amp Metrology Con dence Interval for PCR A X2 A X2 PCR 1 1 3 PCR 3 PCR 2 1 n 1 n 1 Hypothesis Testing from PCR a 010 a 005 Sample Size n PCRhigh C PCRhigh C PCRlow PCRlow PCRlow PCRlow 10 1 88 1 27 226 137 20 1 53 1 20 173 126 30 1 41 1 16 155 121 40 1 34 114 1 46 1 18 50 1 30 1 13 140 1 16 60 1 27 1 11 136 1 15 70 1 25 110 1 33 1 14 80 1 23 110 1 30 1 13 90 1 21 1 10 128 1 12 100 120 109 126 111 Lastmodified II Febmary 2003 Page 7 of 7


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