【正文】 . In order to better understand within piece variation, it is better to plot the data for each piece in a shape corresponding to where in the piece the data are collected. M6 M3 M4 M1 M2 M5 M1 M2 M3 M4 M5 M6 M6 M5 M4 M1 M2 M3 Top consistently higher than bottom or M6 M5 M4 M1 M2 M3 Top consistently higher than bottom, middle higher than edges M1 M2 M3 M4 M5 M6 Understanding Within Piece Variation 48 width Coil L M R 4 Back Front L M R 3 L M R 2 L M R 1 length Thickness Width Length Coil L 1 1 M 1 1 R 1 1 L 2 1 M 2 1 R 2 1 L 3 1 M 3 1 R 3 1 L 4 1 M 4 1 R 4 1 L 1 2 M 1 2 R 1 2 . . . Exercise 4: MultiVari Construction The data shown below is a portion of the data available on the thickness of steel coils. Data has been collected at 12 different locations on each of 12 coils. The plete data set can be found at c:\BoosterData\ 49 Minitab Time Series Plot of Thickness Widths connected 50 1001 0 . 1 51 0 . 2 51 0 . 3 51 0 . 4 5I n d e xThickness1 2 3 4 5 6 7 8 9 10 11 12 coil Exercise 4: Answers 50 1 2 3 4 5 6 7 8 9 10 11 121 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 0 . 1 51 0 . 2 51 0 . 3 51 0 . 4 5C o i lThicknessLMRM u l t i V a r i C h a r t f o r T h i c k n e s s B y W i d t h C o i lL e n g t hW i d t hExercise 4: Answers, cont. 51 Using MultiVari with Upstream Variables Using upstream variables (X39。s are at or near their extreme values You can guide your data collection if you can identify when the X’s are likely to be at or near extreme values: V ari a ble Level W he n y o u are l i kel y t o obse rv e t he l ev elX1 LowX1 Hi g hX2 LowX2 Hi g h. . . . . .56 Illustration (2) ?Your improvement team is studying sealing strength of containers. ?Your preliminary work has identified press temperature and pressure as two continuous variables known to affect sealing strength in other situations. ?In addition, you have identified persistent differences between two presses, A and B with respect to sealing strength, with A producing consistently stronger seals over the past month (on average 4% stronger.). ?Press B has produced more defective seals than A. ?Discussion with operators reveals that press B will run at 175 to 200 degrees (F) and pressure will vary between 36 to 44 psi. These variables are used to verify operation and have not been entered into any database in the past. 57 Illustration (2), cont. The team proposes to sample four containers from press B at four press conditions and then test the strength of the seals (a total of 16 tests). ? Low Temperature: 175 to 180 deg F ? High Temperature: 195 to 200 deg F ? Low Pressure: 3637 psi ? High Pressure: 4344 psi What remendations would you give to the team before they carry out their proposal? 58 Answer 1. It is reasonable to focus on press B since a persistent difference has already been observed between presses A and B. Given limited resources, it makes sense to focus on the variation within press B39。s with patterns of variation in the Y39。 F a ct o r 4 : L i n eL i n e Sa m p l eMultiV ari Chart for Film T hickness?The vertical change in the lines connecting mean symbols shows the average contribution of the factor to the observed variation. ?The largest vertical change matches the dashed lines connecting the squares (the AM to PM variation). The smallest vertical change matches the dotted line connecting the diamonds (the day to day variation). Showing Changes in Average on the MultiVari Chart, cont. 32 Minitab FollowAlong, Part 2 Situation: An improvement team has narrowed down their attention to paint line 1. They are continuing their study of film thickness. Potential list of causes (abbreviated) ? Plant Ambient humidity ? Plant Ambient temperature ? Paintbooth temperature ? Paintbooth humidity ? Line pressure variation for pressors ? Paint viscosity ? Nozzle cleanliness ? Nozzle setting ? Surface contaminants (oxides) on the panels before painting ? Degrees Deviation from vertical (reference angle formed by nozzle tip and surface of panel) ? Temperature in the post paintbooth baking oven 33 Minitab FollowAlong, Part 2, cont. Main Work Step 1: Scope or domain of study ?A single production line in Plant X, on day shift only (paint line runs only on day shift, 6:30 to 2:30 .) Step 2: Time profile: ?Shortterm variation: consecutive units (three panels) ?Longerterm variation: morning and afternoon ?Longterm variation: Day to day, two days chosen to start. 34 Minitab FollowAlong, Part 2, cont. Step 3: a. Location of within unit samples Thickness of paint will be measured in center of front and back panel, as defined by template in QC lab and standard procedure. b. Number of