【正文】 ernative Display: Main Effects Plot We want the data means to be displayed。 F a ct o r 3 : D a t e 。 F a ct o r 2 : A M / PM 。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 the study ?Identify the largest process family you will study (facilities? Production lines? Machines? Tools? Shifts?) ?If there are multiple streams ( lines), consider taking only the extreme performers to save effort. ?Determine whether you will sample within units 21 Planning a MultiVari Study, cont. 2. Decide on the time profile of the study ?Find out if units can be sampled consecutively ?Determine what constitutes a short interval ?Determine what constitutes a long interval ?Determine if you can use an interval between short and long term 3. Create the data collection plan (refer to the Data Collection plan format discussed in Week 1.) 22 Planning a MultiVari Study, cont. 4. Collect the samples. 5. Measure the samples 6. Plot the sample data. ?Use StatQuality ToolsMultiVari Chart in Minitab if the data structure permits (see discussion in the next section.) ?Create a plot “by hand” to summarize the information 23 MultiVari Charts Here are three patterns that show how multivari charts can identify different families of variation 1 4 3 6 7 8 9 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 = TimetoTime Variation 9:30 . 1:45 . 5:00 . 1:15 . 1st Shift 2nd Shift Unit No. Time: M e a s u r e m e n t S c a l e Five Sequential Units at Four Time Intervals 1 2 3 4 5 37 38 39U ni t N o.Measurement Scale40 41U n i t t o U n i t V a r i a t i o nTi m e 1 Ti m e 2Fi v e S e qu e nt i a l U ni t s f o P r od uc t a t Tw o I n t e r v a l s i n t he P r od uc t i on R un1 2 3 1 2 3 1 2 39 : 3 0 a . m . 2 : 0 0 p . m . 7 : 4 5 a . m . 1 : 3 0 p . m .A pr . 1 8 A p r . 1 9P c . N o . :Ti m e :Th r e e S e qu e n t i a l U ni t s a t Fo u r Ti m e I nt e r v a l s0 . 0 0 4. 0 0 5 . 0 0 9. 0 1 0 . 0 1 4. 0 2 0 . 0 2 4. 0 2 5 . 0 2 9. 0 3 0 . 0 3 4. 0 3 5 . 0 3 9. 0 4 0 . 0 4 4. 0 5 0 . 0 5 4. 0 5 5 . 0 5 9. 0 6 0 . 0 6 4. 0 1 5 . 0 1 9. 0 4 5 . 0 4 9. 0 7 0 . 0 7 4. 0 7 5 . 0 7 9. 0 6 5 . 0 6 91X2X3XXXXX XXXXXS pe c . Li m i tD a y :X = F r o n t = B a c kW i t h i n U n i t V a r i a t i o n1 2 3 24 Planning a MultiVari Study, cont. 7. Analyze the results ?Look for the most pronounced pattern of variation ?Compare the pattern with the time behavior of causes on your list of hypothetical causes ?Eliminate the causes (for now) that cannot