lecture7 - http/ocw.mit.edu MIT OpenCourseWare 2.830J...

Info iconThis preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
MIT OpenCourseWare ____________ http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: ________________ http://ocw.mit.edu/terms .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1 M anufacturing Control of Manufacturing Processes Subject 2.830/6.780/ESD.63 Spring 2008 Lecture #7 Shewhart SPC & Process Capability February 28, 2008
Background image of page 2
2 M anufacturing Applying Statistics to Manufacturing: The Shewhart Approach Text removed due to copyright restrictions. Please see the Abstract of Shewhart, W. A. “The Applications of Statistics as an Aid in Maintaining Quality of a Manufactured Product.” Journal of the American Statistical Association 20 (December 1925): 546-548.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
3 M anufacturing Applying Statistics to Manufacturing: The Shewhart Approach Text removed due to copyright restrictions. Please see the Abstract of Shewhart, W. A. “The Applications of Statistics as an Aid in Maintaining Quality of a Manufactured Product.” Journal of the American Statistical Association 20 (December 1925): 546-548.
Background image of page 4
4 M anufacturing Applying Statistics to Manufacturing: The Shewhart Approach (circa 1925)* • All Physical Processes Have a Degree of Natural Randomness • A Manufacturing Process is a Random Process if all “Assignable Causes” (identifiable disturbances) are eliminated • A Process is “In Statistical Control” if only “Common Causes” (Purely Random Effects) are present.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5 M anufacturing “In-Control” i i+1 i+2 ... Each Sample is from Same Parent Ti m e
Background image of page 6
6 M anufacturing “Not In-Control” i i+1 i+2 ... The Parent Distribution is Not The Same at Each Sample Ti m e
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
7 M anufacturing “Not In-Control” ... Ti m e Mean Shift Mean Shift + Variance Change Bi-Modal What will appear in “Samples”?
Background image of page 8
8 M anufacturing Xbar and S Charts •S h e w h a r t : –P lo t sequential average of process • Xbar chart • Distribution? – Plot sequential sample standard deviation cha r t • Distribution?
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
9 M anufacturing n measurements at sample j sample interval Δ T A sequential sample of size n Take at intervals T Sample index j Data Sampling and Sequential Averages • Given a sequence of process outputs x i : j j+1 j+2 ...
Background image of page 10
10 M anufacturing x j = 1 n x i i = ( j 1) Δ T + 1 j Δ T + n sample j mean S j 2 = 1 n 1 ( x i i = ( j Δ T j Δ T + n x j ) 2 sample j variance Data Sampling n measurements at sample j sample interval Δ T j j+1 j+2 ...
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
11 M anufacturing n measurements at sample j Subgroups j j+1 j+2 ... • Within Subgroup Statistics xbar j , S j • Between Subgroup Statistics – Average of xbar j – Variance of xbar(j)
Background image of page 12
12 M anufacturing Plot of xbar and S Random Data n=5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 123456789 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 Sample Number 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 1 2 3 4 5 6 7 8 91 0 1 11 2 1 31 4 1 5 1 61 7 1 81 9 2 0 Run number xbar S
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
13 M anufacturing Overall Statistics 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 123456789 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 Sample Number 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 1 2 3 4 5 6 7 8 91 0 1 11 2 1 31 4 1 5 1 61 7 1 81 9 2 0 Run number Grand Mean x = 1 N x j i = 1 N S = 1 N S j i = 1 N Grand Standard Deviation
Background image of page 14
14 M anufacturing
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 16
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/24/2010 for the course MECHE 2.830J taught by Professor Davidhardt during the Spring '08 term at MIT.

Page1 / 69

lecture7 - http/ocw.mit.edu MIT OpenCourseWare 2.830J...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online