Unformatted text preview: 1 2 Some (of the many) Uses of Some (of the many) Uses of Probability & Statistics y Games & gambling (e.g. bridge, poker, horse racing) N News media ( h di (perhaps more often misuses) f i ) Politics (e.g. public opinion polls, "lies, damned lies, and statistics") t ti ti ") Law (interpretation of evidence) Fi Finance & insurance (e.g. risk pricing) i ( ik i i ) Social sciences (e.g. economics, psychology) M di i /h lth care (e.g. impact of drugs and other Medicine/health ( i t fd d th interventions) Science & engineering (our focus in ENGG 319) Science & engineering (our focus in ENGG 319) ...
3 What's Engineering All What s "Engineering" All About? About? The "vision" of Engineers Canada: "Canadian engineers provide leadership to advance the quality of life through the creative, responsible and progressive application of engineering principles in a global context." A civil engineer's view (Henry Petroski): engineer s "We have to think and scheme about nature and existing artifacts and figure out how they can be altered existing artifacts and figure out how they can be altered and improved to better achieve the objectives considered beneficial to humankind."
4 The Engineering Method and Statistical Thinking
An engineer is someone who solves problems of interest to society by the efficient application of scientific principles by: Refining existing products or processes Designing new products or processes CEAB s Definition of CEAB's Definition of "Engineering Design Engineering Design" Mastery of probability and statistics helps an engineer to better understand "the world", and thus to develop good designs faster d f t and more economically i ll Good, fast, and cheap (but, remember the "pick any two" caveat)
5 6 The Engineering Method and Statistical Thinking
The fi ld f t ti ti deals ith the ll ti Th field of statistics d l with th collection, presentation, analysis, and use of data to Make decisions S l problems Solve bl g products and processes p Design p
Figure 1.1 The engineering method The Engineering Method and Statistical Thinking The general question statistics helps answer is "What (factor) does what to what (response)?" I.e. what i I h t inputs affect what outputs i what ways t ff t h t t t in h t
7 8 The Engineering Method and Statistical Thinking Thinking Statistical techniques are useful for describing and understanding variability. By variability, we mean successive observations of a system or phenomenon do not produce exactly the same 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. The The goal is to explain which sources contribute most significantly to observed variability
9 Source of Variability (the 5 M s Source of Variability (the 5 "M"s and 1 E ) and 1 "E") Man (human variation in doing tasks) Material Method Machine (or equipment) Measurement E i Environment (a catch-all for everything else) ( h ll f hi l ) 10 The Engineering Method and Statistical Thinking
An engineer is designing a nylon connector to be used in an automotive engine application. The engineer is considering establishing the design specification on wall thickness at 3/32 inch but is somewhat uncertain about the effect of this decision on the connector p ll off force. If the pull-off force is too low, the on the connector pull-off force If the p ll off force is too lo the connector may fail when it is installed in an engine. Eight prototype units are produced and their pull off forces measured prototype units are produced and their pull-off forces measured (in pounds): 12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1. The Engineering Method and Statistical Thinking
Engineering Example Since pull-off force varies or exhibits variability, it is a random variable. A random variable, X, can be model by X=P+H where P i a constant and H a random disturbance. h is t t d d di t b 11 12 The Engineering Method and Statistical Thinking
The dot diagram is a very useful plot for displaying a small body f data b d of d t - say up t about 20 observations. to b t 20 b ti This plot allows us to see easily two features of the data; the location, or the middle, and the scatter or variability. location, or the middle, and the scatter or variability. The engineer considers an alternate design (with a larger wall thickness) and eight prototypes are built and pull-off force measured d The dot diagram can be used to compare the two sets of data The Engineering Method and Statistical Thinking
Engineering Example While the larger wall thickness appears to result in an increased While pull-off force, how sure are we that this is so?
13 14 The Engineering Method and Statistical Thinking Thinking Collecting Engineering Data Collecting Engineering Data
Three basic methods for collecting data: A retrospective study using historical data An observational study (recording new data) A designed experiment, to yield the most useful information with the least effort useful information with the least effort
E.g. to answer a specific question of test some specific hypothesis Enable the impact of each factor to be determined as well as interactions between factors as well as interactions between factors
16 15 Designed Experiments Designed Experiments Figure 1-5 The factorial design for the distillation column
17 18 Designed Experiments Designed Experiments
Whenever data are collected over time it is important to plot Wh d t ll t d ti it i i t tt l t the data over time. Phenomena that might affect the system or process often become more visible in a time-oriented plot or process often become more visible in a time oriented plot and the concept of stability can be better judged. Observing Processes Over Time Observing Processes Over Time Figure 1-6 A four-factorial experiment for the distillation column Figure 1-8 The dot diagram illustrates variation but does Figure 1-8 The dot diagram illustrates variation but does not identify the problem.
19 20 Observing Processes Over Time Observing Processes Over Time Observing Processes Over Time Observing Processes Over Time Figure 1-10 W. Edwards Deming's funnel experiment. g g p Figure 1-9 A time series plot of concentration provides more information than a dot diagram.
21 22 Observing Processes Over Time Observing Processes Over Time Figure 1-11 Adjustments applied to random disturbances g j pp overcontrol the process and increase the deviations from the target. 23 Figure 1-12 Process mean shift is detected at observation g number 57, and one adjustment (a decrease of two units) reduces the deviations from target. 24 Observing Processes Over Time Observing Processes Over Time Observing Processes Over Time Observing Processes Over Time Figure 1-14 Enumerative versus analytic study. Figure 1-13 A control chart for the chemical process concentration data.
25 26 Mechanistic and Empirical Models Mechanistic and Empirical Models
A mechanistic model is built from our underlying knowledge of the basic physical mechanism that relates several variables. Example: Ohm s Law Ohm's Current = voltage/resistance I = E/R I = E/R + H
27 Mechanistic and Empirical Models Mechanistic and Empirical Models An empirical model is built from our engineering and scientific knowledge of the phenomenon, but is not directly developed from our theoretical or first firstprinciples understanding of the underlying mechanism. 28 Mechanistic and Empirical Models Mechanistic and Empirical Models
Suppose we are interested in the number average molecular weight (M ) of a polymer Now we know that M is related to the weight (Mn) of a polymer. Now we know that Mn is related to the viscosity of the material (V), and it also depends on the amount of catalyst (C) and the temperature (T ) in the polymerization reactor when the material is manufactured. The relationship between Mn and these variables is say, where the form of the function f is unknown. One option would be the following (where the E's are unknown Es parameters): Mn = f(V C T) f(V,C,T) 29 30 Mechanistic and Empirical Models Mechanistic and Empirical Models In general, this type of empirical model is called a regression model. g The estimated regression line ( g (based on the least squares method) is given by:
Figure 1-15 Three-dimensional plot of the wire and pull strength data. g
31 32 The Role of Probability The Role of Probability
Probability is a branch of theoretical mathematics Probability is a branch of theoretical mathematics that allows the drawing of conclusions (about samples) given known information (about a samples) given known information (about a population) Probability provides the mathematical framework for statistics (permitting consequences to be derived from assumptions)
Figure 1-16 Plot of the predicted values of pull strength from the empirical model. p
33 Statistics Statistics is a branch of applied mathematics that attempts to make conclusions about populations based on (limited) data on samples
34 35 ...
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