1 1 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 Designing new products or processes 1 1 The Engineering Method and Statistical Thinking The engineering or scientific method is the approach to formulating and solving these problems The steps in the engineering method are as follows 1 Develop a clear and concise description of the problem 2 Identify at least tentatively the important factors that affect this problem or that may play a role in its solution 3 Propose a model for the problem using scientific or engineering knowledge of the phenomenon being studied State any limitations or assumptions of the model 4 Conduct appropriate experiments and collect data to test or validate the tentative model or conclusions made in steps 2 and 3 5 Refine the model on the basis of the observed data 1 1 The Engineering Method and Statistical Thinking 7 Conduct an appropriate experiment to confirm that the proposed solution to the problem is both effective and efficient 8 Draw conclusions or make recommendations based on the problem solution 1 1 The Engineering Method and Statistical Thinking 1 1 The Engineering Method and Statistical Thinking Steps 2 4 in Fig 1 1 are enclosed in a box indicating that several cycles or iterations of these steps may be required to obtain the final solution Consequently engineers must know how to efficiently plan experiments collect data analyze and interpret the data and understand how the observed data are related to the model they have proposed for the problem under study The field of statistics deals with the collection presentation analysis and use of data to make decisions solve problems and design products and processes 1 1 The Engineering Method and Statistical Thinking Because many aspects of engineering practice involve working with data obviously some knowledge of statistics is important to any engineer Specifically statistical techniques can be a powerful aid in designing new products and systems improving existing designs and designing developing and improving production processes 1 1 The Engineering Method and Statistical Thinking The field of statistics deals with the collection presentation analysis and use of data to Make decisions Solve problems Design products and processes 1 1 The Engineering Method and Statistical 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 result Statistics gives us a framework for describing this variability and for learning about potential sources of variability 1 1 The Engineering Method and Statistical Thinking statistical thinking can give us a useful way to incorporate this variability into our decision making processes For example consider the gasoline mileage performance of your car Do you always get exactly the same mileage performance on every tank of fuel Of course not This observed variability in gasoline mileage depends on many factors such as the type of driving that has occurred most recently city versus highway the changes in condition of the vehicle over time which could include factors such as tire inflation engine compression or valve wear the brand and or octane number of the gasoline used or possibly even the weather conditions that have been recently experienced These factors represent potential sources of variability in 1 1 The Engineering Method and Statistical Thinking Engineering Example 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 pull off force If the pull off force is too low the connector may fail when it is installed in an engine Eight 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 1 1 The Engineering Method and Statistical Thinking Engineering Example 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 1 1 The Engineering Method and Statistical Thinking Engineering Example The engineer considers an alternate design and eight prototypes are built and pull off force measured The dot diagram can be used to compare two sets of data Figure 1 3 Dot diagram of pull off force for two wall thicknesses 1 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 where is a constant and a random disturbance 1 1 The Engineering Method and Statistical Thinking The need for statistical thinking arises often in the solution of engineering problems Consider the engineer designing the connector From testing the prototypes he knows that the average pulloff force is 13 0 pounds However he thinks that this may be too low for the intended application so he decides to consider an alternative design with a greater wall thickness 1 8 inch Eight prototypes of this design are built and the observed pull off force measurements are 12 9 13 7 12 8 13 9 14 2 13 2 13 5 and 13 1 The average is 13 4 This display gives the impression that increasing the wall thickness has led to an increase in pull off force 1 1 The Engineering Method and Statistical Thinking How do we know that another sample of prototypes will not give different results Is a sample of eight prototypes adequate to give reliable results What risks are associated with this decision That increasing the thickness of the part and its cost really has no effect on the pull off force 1 1 The Engineering Method and Statistical Thinking 1 1 The Engineering Method and Statistical Thinking Often physical laws such as Ohm s law and the ideal gas law are applied to help design products and processes We are familiar with this reasoning from general laws to specific cases But it is also important to reason from a specific set of measurements to more general cases to answer the previous questions This reasoning is from a sample such as the eight connectors to a population such as the connectors that will