【正文】 s output. 2. The team should record the time of day and information about press conditions (including shift and operators) that might provide additional clues. 3. When the team grabs samples at the low or high temperatures, it should also record the pressure at the same time. Similarly, when they grab samples at the low or high pressures, they should record the temperature. 4. Jumping right to observations on temperature and pressure may miss other signals that might be revealed by a more plete multivari analysis that considered within unit variation, unit to unit variation, subgroup to subgroup variation and longterm variation. Also, there may be other families of variation (related to geometry of units within the press, for example) relevant to the study. 5. Has the team verified the performance of the temperature and pressure gauges? 59 Summary Multivari analysis is a method that helps you depose total variation into ponent families. By means of a multivari graph, you seek to match patterns in the variation with potential causes. You use the method to narrow down potential causes and find clues as you build a useful causal theory. 60 Reflection Consider how you might apply Multivari analysis to your project. What questions do you have now about this method? 。s to guide your sampling approach ?Seek to observe the process when the X39。s. 52 Illustration (1) Suppose the team in the paint thickness example had been able to record a pair of continuous X39。s at the same time you gather product samples and measure output characteristics ?Associate changes in X39。s) as well as output measures (Y39。 here we select the two time families as factors 2 and 3 38 Minitab FollowAlong, Part 2, cont. Unless you check the first box, Minitab will only display the means of the first three factors. 39 Minitab FollowAlong, Part 2, cont. 4 / 1 9 / 9 94 / 1 8 / 9 9PMAMPMAM0 . 0 80 . 0 70 . 0 60 . 0 50 . 0 4D a t eFilmThicknesB a c k F r o n tM u l t i V a ri C h a rt f o r F i l mT h i ckn e s By Po si t i o n D a t eA M / P MP o si t i o n40 Minitab FollowAlong, Part 2, cont. 4 / 1 9 / 9 94 / 1 8 / 9 9PMAMPMAM0 . 0 80 . 0 70 . 0 60 . 0 50 . 0 4D a t eFilmThicknes123M u l t i V a ri C h a rt f o r F i l mT h i ckn e s By U n i t N a me D a t eA M / P MU n i t N a m e41 Alternative Display: Main Effects Plot We want the data means to be displayed。 two levels, AM and PM. ? Family 4: Longterm variation (day to day)。 F a ct o r 3 : D a t e 。 F a ct o r 4 : L I n eL i n e Sa m p l eChart Appearance Minitab plots the three samples in sequence left to right for line 1, 4/18/99 AM. The square shows the average of these three reading. The diamond is the average of all the readings within one day and line. 30 CrtlE or Stat Quality Tools MultiVari Charts… In the options window, connect the means for factors 13. Some people find it easier to see the relative contribution of the different families when the means are connected. Showing Changes in Average on the MultiVari Chart 31 4 / 1 8 / 9 9 4 / 1 9 / 9 9AMPMAMPM0 . 0 20 . 0 30 . 0 40 . 0 50 . 0 20 . 0 30 . 0 40 . 0 521D a t e1 2 3 F a ct o r 1 : Sa m p l e 。 F a ct o r 2 : A M / PM 。Process Door Versus Data Door 2 ANALYZE Goal ?Identify root causes and confirm them with data Output ?A theory that has been tested and confirmed IMPROVE 3 You Are Here Develop a focused problem statement Process Door Versus Data Door Organize potential causes Hypothesis Testing and Regression Analysis Design of Experiments and Response Surface ? Green Belt Materials—Process Analysis ?Activity Flow Charts ?Deployment Flow ?Charts ?Value Stream Maps ? Data Door: ?Stratified Time and Frequency Plots ?Scatter Plots Bridge Material ? MultiVari Analysis 4 Goals ?Know how to interpret a multivari analysis ?Be able to use multivari to gather information on potential causes 5 The Focus of Analyze Y = f (X1, X2, X3, ..., Xn) X1, X3, X5 Identification Verification Quantification What vital few process and input variables (Xs) affect critical to quality process performance or output measures (Ys)? 6 Process or Data Door? Process Door Data Door ?To understand the drivers of variation in the process ?To tackle quality problems and waste ?To understand the root cause of differences between outputs ?To improve the understanding of process flow ?To tackle cycle time problems ?To identify opportunities to reduce process costs Stratification Scatter Diagrams MultiVari Analysis Detailed Process Map Value Added Analysis Cycle Time Analysis It is remended to go through both doors to make sure that potential causes are not overlooked. MultiVari Analysis 8 What is the Tool? MultiVari analysis helps you see patterns of variation in response variable(s) that you can correlate with potential causal variables. The specific