8_CUSUM

8_CUSUM - Spring 2008 EMSE 182, 282, Professor Jim Harris,...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Spring 2008 EMSE 182, 282, Professor Jim Harris, CUSUM and EWMA Charts - 1 CUSUM AND EXPONENTIALLY WEIGHTED MOVING AVENGE CHARTS CUSUM CHARTS Motivation • Slight changes take a long time to detect for X Charts X~N(25,400), then in an X Chart with n=4, if 32 . Ä • X Charts are good for detecting shifts of >1.5 5 • If information of the whole sequence could be compounded,
Background image of page 1

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

View Full DocumentRight Arrow Icon
Spring 2008 EMSE 182, 282, Professor Jim Harris, CUSUM and EWMA Charts - 2 C ( x) ( ( 34 3 4 4œ" 4œ" 33 " œ œ ±± .. . 00 0 ( x ) C " . 0 where C 0 and is the process mean target, then reaction to smaller ! œ . 0 shifts in the process mean would be quicker (compound effect). •This is the basis for the CUSUM or CUMulative SUM Chart - a plot of C vs i. 3 • Note that CUSUM are better (faster or lower ARL) for detecting small shifts and are particularly useful for smaller sample sizes, especially n 1. œ • if the process is in control with mean then the sequence . ! {C } is a random walk with mean 0. 3 • a positive (negative) trend in {C } occurs if the process mean shifts 3 upwards (downwards).
Background image of page 2
Spring 2008 EMSE 182, 282, Professor Jim Harris, CUSUM and EWMA Charts - 3 Assumptions X ~ N ( , ) 3! # .5 • {X } iid. 3 known or well estimated 5 n 1 œ Method • Use a table to track or plot C max{0, x K) C } for upward shifts 3  3 œ Ð . 1 C max{0, K) x C } for downward shifts 33  !3 œÐ . 1 where C C 0. 0 0 œœ K reference value, allowance, or slack value K for detecting a shift in standard deviation units $ .. 2 5 ll # 10 of , i.e. $5 . . . !" ! Äœ • An assignable cause is assumed when C or C H the decision 3 3 interval. H is chosen with ARL in mind but H 5 is recommended. œ 5
Background image of page 3

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

View Full DocumentRight Arrow Icon
Spring 2008 EMSE 182, 282, Professor Jim Harris, CUSUM and EWMA Charts - 4 • Table + S H I F T S SHIFTS Period x x K) C N K) N 33 ! ! 3 3 3  Ð Ð .. + N (N ) tells the run number for positive C (C ) ++ • Example 10, 1, K .5, H 5 .5 ! œœ œ œ  SHIFTS SHIFTS Period x x 10.5 C N 9.5 x C N 1 9.45 1.05 0 0 0.05 0.05 1 2 7.99 2.52 0 0 1.51 1.56 2 3 9.29 1.21 0 0 0.21 1.77 3 4 11.66 1.16 1.16 1 2 3 3 3 + .16 0 0 5 12.16 1.66 2.82 2 2.66 0 0 6 10.18 0.32 2.50 3 0.68 0 0 7 8.04 2.46 0.04 4 1.46 1.46 1 8 11.46 0.96 1.00 5 1.96 0 0 9 9.20 1.30 0. 0 0.30 0.30 1
Background image of page 4
Spring 2008 EMSE 182, 282, Professor Jim Harris, CUSUM and EWMA Charts - 5 • To plot use CUSUM Status Charts
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/02/2010 for the course EMSE 282 taught by Professor Harris during the Spring '07 term at GWU.

Page1 / 17

8_CUSUM - Spring 2008 EMSE 182, 282, Professor Jim Harris,...

This preview shows document pages 1 - 6. Sign up to view the full document.

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