【正文】 account for the observed pattern ?Use the remaining causes as you build your causeandeffect diagram and as candidate factors for subsequent diagnostic and confirmation tools (hypothesis tests, regression analysis and designed experiments.) 25 Minitab Follow Along, Part 1: Mechanics of a MultiVari Analysis Open file c:\BoosterData\ (These data are part of a larger study of finish performance we will continue to examine in the next example.) The variables are: ? Panel ID: sequential number of the panel sampled from each paint line. ? Date: day panels were sampled ? Line: which paint line ? AM/PM: morning or afternoon when panels were sampled ? FilmThick: response variable (in inches, nominal ). ? Position: Side of the panel sampled, as it emerges from the paint booth ? Sample: sequential number of the panel (subgroups of size 3). Product characteristic: Paint film thickness on a rectangular panel, front and back side (as defined by orientation of the panel through the paint booth). The panel has no specific orientation in installation (sides are engineered to snapfit correctly regardless of orientation on the long axis of the panel). 26 Families of Variation In this example, there are four potential families of variation we can examine: 1. Unittounit variation (3 consecutive panels sampled each time), which matches shortterm variation 2. Morningtoafternoon variation 3. DaytoDay variation 4. LinetoLine variation Family 4: Lines Family 3: Days Family 2: AM/PM Family 1: Units Number of Measurements Levels 2 2 2 3 24 ? ? ? = 27 Create a MultiVari Chart Using Minitab Commands Single response Stat Quality Tools MultiVari Chart Order of entry matters in this window. To arrange the plot in “standard” form, assign family 1 (panel to panel variation) to factor 1, the next larger time family to factor 2, the next larger time family to factor 3. Reserve factor 4 for a stream family like line. 28 In this example, all boxes should be unchecked to produce the first chart max length min length CTRL E or Stat Quality Tools MultiVari Chart Options Create a MultiVari Chart Using Minitab Commands 29 4 / 1 9 / 9 94 / 1 8 / 9 9PMAMPMAM0 . 0 50 . 0 40 . 0 30 . 0 20 . 0 50 . 0 40 . 0 30 . 0 212D a t e1 2 3 MultiV ari Chart for Film T hicknessF a ct o r 1 : Sa m p l e 。 F a ct o r 2 : A M / PM 。 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。s): ?Gather information on relevant continuous X39。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 X3