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UT Dallas CS 6313 - ch01

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Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.Chapter 1The Role of Statistics in EngineeringApplied Statistics and Probability for EngineersSixth EditionDouglas C. Montgomery George C. RungerCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.An engineer is someone who solves problems of interest to society with the efficient application of scientific principles by:• Refining existing products• Designing new products or processesWhat Engineers Do?2Sec 1-1 The Engineering Method & Statistical ThinkingCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.The Creative ProcessFigure 1-1 The engineering method3Sec 1-1 The Engineering Method & Statistical ThinkingCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.The field of statistics deals with the collection, presentation, analysis, and use of data to:• Make decisions• Solve problems• Design products and processesIt is the science of data.Statistics Supports The Creative Process4Sec 1-1 The Engineering Method & Statistical ThinkingCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.• Statistical techniques are useful to describe and understand variability.• By variability, we mean successive observations of a system or phenomenon do not produce exactly the same result.• Statistics gives us a framework for describing this variability and for learning about potential sources of variability.Variability5Sec 1-1 The Engineering Method & Statistical ThinkingCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.Eight prototype units are produced and their pull-off forces are measured (in pounds): 12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1. All of the prototypes do not have the same pull-off force. We can see the variability in the above measurements – note the “average” is 13.0.The dot diagram is a very useful plot for displaying a small body of data - say up to about 20 observations. This plot allows us to see easily two features of the data; the location, or the middle, and the scatter or variability.An Engineering Example of Variability6Sec 1-1 The Engineering Method & Statistical ThinkingFigure 1-2 Dot diagram of the pull-off force data.Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.Three basic methods of collecting data:– A retrospective study using historical data• Data collected in the past for other purposes.– An observational study• Data, presently collected, by a passive observer.– A designed experiment• Data collected in response to process input changes.Basic Methods of Collecting Data7Sec 1-2.1 Collecting Engineering DataCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.Hypothesis Tests8Hypothesis Test• A statement about a process behavior value.• May be comparison between two values.• Data is gathered to support or refuse the claim.One-sample hypothesis test:• Example: Ford avg mpg = 30 vsFord avg mpg < 30Two-sample hypothesis test:• Example: Ford avg mpg – Chevy avg mpg = 0 vsFord avg mpg – Chevy avg mpg > 0Sec 1-2.4 Designed ExperimentsCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.Factorial Experiment & Example9Example:Consider a petroleum distillation column:• Output is acetone concentration• Inputs (factors) are:1. Reboil temperature2. Condensate temperature3. Reflux rate• Output changes as the inputs are changed by experimenter.Sec 1.2.4 Designed ExperimentsAn experiment design which uses every possible combination of the factor levels to form a basic experiment with “k” different settings for the process. This type of experiment is called a factorial experiment.Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.Factorial Experiment Example10Sec 1-2.4 Designed ExperimentsTable 1-1 The Designed Experiment (Factorial Design) for the Distillation Column• Each factor is set at 2 reasonable levels (-1 and +1)• 8 (23) runs are made, at every combination of factors, to observe acetone output.• Resultant data is used to create a mathematical model of the process representing cause and effect.Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.Fractional Factorial Experiment11• Factor experiments can get too large. For example, 8 factors will require 28= 256 experimental runs of the distillation column.• Certain combinations of factor levels can be deleted from the experiments without degrading the resultant model.• The result is called a fractional factorial experiment.Sec 1-2.4 Designed ExperimentsCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.Fractional Factorial Experiment - ExampleFigure 1-3 A fractional factorial experiment for the distillation column (one-half fraction) 24/ 2 = 8 circled settings.12Sec 1-2.4 Designed ExperimentsCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.13An Experiment in VariationW. Edwards Deming, a famous industrial statistician & contributor to the Japanese quality revolution, conducted a illustrative experiment on process over-control or tampering.Let’s look at his apparatus and experimental procedure.Sec 1-2.5 Observing Processes Over TimeCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.Sec 1-2.5 Observing Processes Over Time 14Deming’s Experimental Set-upMarbles were dropped through a funnel onto a target and the location where the marble struck the target wasrecorded.Variation was caused by several factors:Marble placement in funnel & release dynamics, vibration, aircurrents, measurement errors.Figure 1-4 Deming’s Funnel experimentCopyright © 2014 John Wiley & Sons, Inc. All rights reserved.Deming’s Experimental Procedure• The funnel was aligned with the center of the target. Marbles were dropped. The distance from the strike point to the target center was measured and recorded.• Strategy 1: The funnel was not moved. Then the process was repeated.• Strategy 2: The funnel was moved an equal distance in the opposite direction to compensate for the error. He continued to make this type of adjustment after each marble was dropped. Then the process was repeated.Sec 1-2.5 Observing Processes Over Time 15Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.Deming’s Experimental Procedure• When both strategies were completed, he noticed the variability of the distance from the target for strategy 2 was approximately twice as large than for strategy 1.• The deviations from the target is increased due to the


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UT Dallas CS 6313 - ch01

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