Statistics and ANOVAProduct Development ProcessWe will use statistics to make good design decisions!Let’s consider the Toyota problem.How can we use statistics to make sense of data that we are getting?What kinds of questions can we answer?PowerPoint Presentation>Stat>Basic Statistics>Display Descriptive StatisticsSlide 9Slide 10Slide 11Slide 12Slide 13>Stat>Basic Statistics>Normality TestSlide 15Slide 16Slide 17Slide 18What does this data tell us about our process?Voice of the ProcessThe capability index is defined as:>Stat>Control Charts>Variable Charts for Individuals>IndividualsSlide 23Slide 24Slide 25Slide 26Are the 2 Distributions Different?Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Let’s look at what happened with plain M&M’sWhat do you see with the boxplot?Slide 39Do we see anything that looks unusual?Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Implications for designSlide 48Instructions for Minitab InstallationMinitab on DFS:Statistics and ANOVAME 470Spring 2012PlanningPlanningProduct Development ProcessConceptDevelopmentConceptDevelopmentSystem-LevelDesignSystem-LevelDesignDetailDesignDetailDesignTesting andRefinementTesting andRefinementProductionRamp-UpProductionRamp-UpConcept Development ProcessPerform Economic AnalysisBenchmark Competitive ProductsBuild and Test Models and PrototypesIdentifyCustomerNeedsEstablishTargetSpecificationsGenerateProductConceptsSelectProductConcept(s)Set FinalSpecificationsPlanDownstreamDevelopmentMissionStatementTestProductConcept(s)DevelopmentPlanWe will use statistics to make good design decisions!We will categorize populations by the mean, standard deviation, and use control charts to determine if a process is in control.We may be forced to run experiments to characterize our system. We will use valid statistical tools such as Linear Regression, DOE, and Robust Design methods to help us make those characterizations.Let’s consider the Toyota problem.What was the first clue that there was a problem?Starting in 2003, NHSTA received information regarding reports of accelerator pedals that were operating improperly.How many reports causes the manufacturer to suspect a problem?To issue a recall NHTSA would need to prove that a substantial number of failures attributable to the defect have occurred or is likely to occur in consumers’ use of the vehicle or equipment and that the failures pose an unreasonable risk to motor vehicle safety.ODI conducted a VOQ-based assessment of UA rates on the subject Lexus incomparison to two peer vehicles and concluded the Lexus LS400t vehicles were not overrepresented in the VOQ database.How might we look at two populations and decide this?How can we use statistics to make sense of data that we are getting?•Quiz for the day•What can we say about our M&Ms?What kinds of questions can we answer?•What does the data look like?•What is the mean, the standard deviation?•What are the extreme points?•Is the data normal?•Is there a difference between years? Did one class get more M&Ms than another?•If you were packaging the M&Ms, are you doing a good job?•If you are the designer, what factors might cause the variation?>Stat>Basic Statistics>Display Descriptive StatisticsResults for 2008, 2010, 2011 (From the “Session”)Why would we care about this in design?Assessing Shape: BoxplotBSNOx2.452.402.352.302.252.20Boxplot of BSNOx(Q2), medianQ1Q3largest value excluding outlierssmallest value excluding outliersoutliers are marked as ‘*’Values between 1.5 and 3 times away from the middle 50% of the data are outliers.2011201020081098765YearStackedTotalsIndividual Value Plot of StackedTotals vs Year>Stat>Basic Statistics>Normality TestSelect 2008Anderson-Darling normality test:Used to determine if data follow a normal distribution. If the p-value is lower than the pre-determined level of significance, the data do not follow a normal distribution.Anderson-Darling Normality TestMeasures the area between the fitted line (based on chosen distribution) and the nonparametric step function (based on the plot points). The statistic is a squared distance that is weighted more heavily in the tails of the distribution. AndersonSmaller Anderson-Darling values indicates that the distribution fits the data better.The Anderson-Darling Normality test is defined as: H0: The data follow a normal distribution. Ha: The data do not follow a normal distribution. Another quantitative measure for reporting the result of the normality test is the p-value. A small p-value is an indication that the null hypothesis is false. (Remember: If p is low, H0 must go.)P-values are often used in hypothesis tests, where you either reject or fail to reject a null hypothesis. The p-value represents the probability of making a Type I error, which is rejecting the null hypothesis when it is true. The smaller the p-value, the smaller is the probability that you would be making a mistake by rejecting the null hypothesis. It is customary to call the test statistic (and the data) significant when the null hypothesis H0 is rejected, so we may think of the p-value as the smallest level α at which the data are significant.Note that our p value is quite low, which makes us consider rejecting the fact that the data are normal. However, in assessing the closeness of the points to the straight line, “imagine a fat pencil lying along the line. If all the points are covered by this imaginary pencil, a normal distribution adequately describes the data.” Montgomery, Design and Analysis of Experiments, 6th Edition, p. 39If you are confused about whether or not to consider the data normal, it is always best if you can consult a statistician. The author has observed statisticians feeling quite happy with assuming very fat lines are normal.http://www.statit.com/support/quality_practice_tips/normal_probability_plot_interpre.shtml For more on Normality and the Fat PencilWalter Shewhartwww.york.ac.uk/.../ histstat/people/welcome.htm Developer of Control Charts in the late 1920’sYou did Control Charts in DFM. There the emphasis was on tolerances. Here the emphasis is on determining if a process is in control. If the process is in control, we want to know the capability.What does this data tell us about our process?SPC is a continuous improvement tool which minimizes tampering or unnecessary adjustments (which increase variability) by distinguishing between special cause and common cause sources of