【正文】 s: ? line pressure into the paint booth ? paint booth temperature. Neither of these factors apparently will account for the differences between front and back panels. Is there any other potential relationship? (Remember that the day to day variation is smaller than the variation within 3 consecutive units.) Take a few minutes to review the main effects plot on the next page and note down some ideas. 53 Illustration (1), cont. P a n e l I DP o s i t i o nA M / P MD a t e121110 9 8 7 6 5 4 3 2 1FrontBackPMAM4/19/994/18/990 . 0 6 50 . 0 6 00 . 0 5 50 . 0 5 00 . 0 4 5ThicknessM a i n Ef f e ct s Pl o t D a t a M e a n s f o r T h i ckn e ssDate T i m e A c tua l ti m e Li n e P r es s ur e ( ps i ) P ai nt B oo th T ( deg F)4/18/ 99 AM 9:30 4/18/ 99 PM 14:0 0 4/19/ 99 AM 7:45 4/19/ 99 PM 13:3 0 54 Answer ?Line pressure moves from low to high on both days, in line with the pattern with the morning to afternoon difference on the main effects plot. ?Higher line pressures might account for more paint delivered to the surfaces in the afternoon vs. the morning. ?The booth temperature does not look like it has any relationship with morning to afternoon differences. 55 Using MultiVari with upstream variables: a second approach ?Use information about the X39。 two levels: April 18 and April 19. 35 Minitab FollowAlong, Part 2, cont. 2 3 2 24 Days Levels Family 4 AM / PM Levels Family 3 2 Number of Consecutive Units (Family 2) Number of Observations Within Units (Family 1) Total measurements ? ? ? = 36 Minitab FollowAlong, Part 2, cont. Open file c:\BoosterData\ You should see these data in the worksheet: Panel ID Date AM/PM Position FilmThick True Time UnitName 1 4/18/99 AM Back 9:30 1 1 4/18/99 AM Front 9:30 1 2 4/18/99 AM Back 9:30 2 2 4/18/99 AM Front 9:30 2 3 4/18/99 AM Back 9:30 3 3 4/18/99 AM Front 9:30 3 4 4/18/99 PM Back 14:00 1 4 4/18/99 PM Front 14:00 1 5 4/18/99 PM Back 14:00 2 5 4/18/99 PM Front 14:00 2 6 4/18/99 PM Back 14:00 3 6 4/18/99 PM Front 14:00 3 7 4/19/99 AM Back 7:45 1 7 4/19/99 AM Front 7:45 1 8 4/19/99 AM Back 7:45 2 8 4/19/99 AM Front 7:45 2 9 4/19/99 AM Back 7:45 3 9 4/19/99 AM Front 7:45 3 10 4/19/99 PM Back 13:30 1 10 4/19/99 PM Front 13:30 1 11 4/19/99 PM Back 13:30 2 11 4/19/99 PM Front 13:30 2 12 4/19/99 PM Back 13:30 3 12 4/19/99 PM Front 13:30 3 37 Minitab FollowAlong, Part 2, cont. Step 6 Plot the sample data Stat Quality Tools MultiVari Chart First version of the multivari chart: Start with the the within unit family as factor 1。R 14 Exercise: Possible Applications of MultiVari Charts in Your Work List the possible sources of variation for a work situation where you are interested in reducing variation Situation: Possible Sources: 15 Exercise 2: MultiVari Display B a ck F r o n t0 . 0 50 . 0 40 . 0 30 . 0 20 . 0 1 Finish Thickness D a y 1 D a y 2AM PM AM PME x a m p l e o f M u l t i v a r i d i sp l a y2 3 1 Panel 1 2 3 1 2 3 1 2 3 1 2 3 Sample, 3 consecutive panels taken at one time. This multivari chart shows four families of variation. We plot measures of film thickness on front and back sides of panels produced on a paint line. 1. Withinpanel variation 2. Unittounit variation 3. Morningtoafternoon variation 4. Daytoday variation 16 Exercise 2: MultiVari Display What can you say about: ?Within panel variation? ?Panel to panel variation? ?AM/PM variation? ?Day to day variation? 17 Exercise 2: MultiVari Display, Answer 1. The difference in film thickness within units is roughly constant across all sampling periods (unit to unit, morning to afternoon and day to day) and neither face dominates. 2. The panel to panel variation is about the same across time of day and days. 3. On each day, the group of samples is relatively higher in the morning than in the afternoon. 4. The range of values on day 1 is about the same as on day 2. 18 Exercise 3: Interpreting a MultiVari Chart Continuous X’s This data was collected on a Folio cutter. It is desirable to reduce variation in cut length. Different speeds and braking methods were run. 2 4 . 9252 5 . 12 5 . 22 5 . 32 5 . 42 5 . 52 5 . 62 5 . 7brake set ting24 34 44 54 64 24 34 44 54 64 24 34 44 54 64 24 34 44 54m a x t h i c k n e s sm i n t h i c k n e s sManual Braking Speed = 300 fps Automatic Braking Speed = 300 fps Manual Braking Speed = 400 fps Automatic Braking Speed = 400 fps max length min length 19 Exercise 3: Interpreting a MultiVari Chart, Answer ?Automatic braking gives consistently lower variation ?When braking manually, 64 lbs. of pressure gives lower variation ?With automatic braking at the speed of 400 fps., the pressure doesn’t affect the variability ?The higher speed (400 fps.) results in reduced variation 20 Planning a MultiVari Study 1. Decide on the scope or domain of