【正文】 r monthly training costs to be? 8 5 0 0 09 0 0 0 09 5 0 0 01 0 0 0 0 01 0 5 0 0 01 1 0 0 0 0Expense ($$)JanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDecMo n thI n d i v i d u a l s C h a r t o f T r a i n i n g E x p e n s e s L a st 2 Ye a r sA v e = 9 7 7 0 0U C L = 1 0 7 4 0 0L C L = 8 8 0 0 0 57 Comparing Specification Limits to Control Limits Unstable ( Not in control ) Stable (In control) Within spec limits Upper Spec Lower Spec Upper Spec Lower Spec UCL LCL UCL LCL Outside spec limits Upper Spec Lower Spec Upper Spec Lower Spec UCL LCL UCL LCL INSTRUCTOR NOTES: Have the students answer the questions. Consider letting them work with their teams. 58 Special Cause Tests 5. E xami ne th e result s.6. L ook at the sess i on w i nd ow .A speci al cause t hat i s s i gnaled by m ore than one test is m arked on thechart only by the l ow est number t est . F or exampl e, T est 8 fail ed at point s30, 31, 32, and 33, but t hos e poi nt s ar e not l abel ed ? ? beca us e t heyal ready fail ed T est s 2, 5, an d/or 6.3331292725232119171513119753Su b g ro u p 16543210Individual ValueOct18Oct4Sep20Sep6Aug23Aug9Jul26Jul12Jun28Jun14May31May17May3Apr19Apr5Mar22Mar8D a t eI C h a r t fo r D o w n tim e66661565652X= 3 . 6 4 53 . 0 SL =5 . 8 3 13 . 0 SL =1 . 4 6 0Number sin d ic a tew h ic hte st s a r evi o la te dTh e s h ift in t h eprocess averageis s ig n a le d inm a n y w a ys . Th ee a r lie st s ig n a l i s ap o in t o u ts id e t h elim its ( Te st 1 ) .Th e n e xt s ig n a lsco m e f r o m T e st s5 a n d 6 . Ye ta n o th e r s ig n a lsh o w s u p a s Te st2 ( e ig h t p o in ts o nsa m e s id e o fce n te r lin e ) .TEST 1. One point more than sigmas from center line.Test Failed at points: 27TEST 2. 8 points in a row on same side of center line.Test Failed at points: 33TEST 5. 2 out of 3 points more than 2 sigmas from center line (on one side of CL).Test Failed at points: 27 28 30 32TEST 6. 4 out of 5 points more than 1 sigma from center line (on one side of CL).Test Fa。 in jail Guilty Example: Court Cases .. 23 Types of Hypothesis Tests Hypothesis Test Purpose ttest Compare two group averages. paired ttest Compare two group averages when data is matched. ANOVA (Analysis Of Variance) Compare two or more group averages. Test for equal variances (Ftest, Bartlett’s test, Levene’s test) Compare two or more group variances. Chisquare test Compare two or more group proportions. 24 Regression: Quantifies the Relationship Between X and Y Regression analysis generates a line that quantifies the relationship between X and Y. 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 X (input) Y (output) Appropriate Data for X or Y In Regression Data Type Minitab Format DiscreteOrdinal ranks 1, 2, ..., 5 Numerical DiscreteCount or Percents of defects, % defective Numerical Continuous Amounts Cycle time Numerical The line, or regression equation, is represented by mathematical equation of a straight line as: Y= bo+ b1X bo = intercept (where the line crosses X= 0) b1 = slope (rise over run, or change in Y per unit increase in X) 25 Confidence and Prediction Intervals 200 250 300165175185195205215225T e m p (F )Seal (g/cm2)Y = 1 0 1 . 6 1 1 + 0 . 3 5 4 2 3 7 XR S q = 8 3 . 3 %R e g r e s s i o n9 5 % C I9 5 % P IR e g r e ssi o n P l o tConfidence Interval ? . = An interval likely to contain the “best fit” line. ? Gives a range of the predicted values for the fitted Y if the regression is repeated again (average). ? Based on a given Xvalue ? For a given confidence Prediction Interval ? . = An interval likely to contain the actual Y values for a given X. ? Gives a range of likely actual values for Y (individual). ? Based on a given Xvalue. ? For a given confidence. 26 Three Factors: Cube Layout ? A cube helps us visualize the experimental space covered by 3 factors ? Each corner represents one of the eight sets of experimental conditions Lower left front corner = Recycled paper, no paper clip, ” (This corner represents all the Low levels: –, –, –) Upper right back corner = Copier paper, paper clip, ” wing (This corner represents all the High levels: +, +, +) Yes Copier Paper clip Paper type Wing Length No Recycled 27 Introduction to MSD 23 Experiment ?We will do an experiment that will take you through each of the steps needed to plan, carry out, and analyze a designed experiment Experiment Design Experiment Analysis 1. Identify responses 2. Identify factors 3. Select design 4. Choose factor levels 5. Randomize runs 6. Conduct experiment and collect data 7. Analyze data 8. Draw conclusions 9. Verify results 28 Focused question: What are reasons why MSDs would fail (be nondurable)? Shaded areas indicate potential causes the team thought were most likely to contribute to the problem Environment Procedures Materials People Nondurable MSDs Causes Effect Raw Material Vendor Abel Vendor Noesting Sizes Vendor Quality Small Large Bad Good Purchasing Agent Management Total Cost Warehouse R