FME461 Engineering Design II Dr.Hussein Jama Hussein.jama@uobi.ac.ke Office 414 Lecture: Mon 8am -10am Tutorial Tue 3pm - 5pm 11/18/2018

Statistical Considerations 11/18/2018

Introduction Engineering design considerations This lecture is based on Shigley Ch 20 20 - 1 Random Variables 20 – 2 Mean, variance & Std Deviation 20 – 3 Probability distributions Normal Weibull 20 - 4 Probability of error 20 – 5 Linear Regression 11/18/2018

Engineering Design is an iterative process that has as its primary objective the synthesis of machines in which the critical problems are based upon material sciences and engineering mechanics sciences. This synthesis involves the creative conception of mechanisms, and optimization with respect to performance, reliability and cost. 11/18/2018

Engineering design Machine design does not encompass the entire field of mechanical engineering. Design where the critical problems involve the thermal/fluid sciences fall under the broader category of “mechanical engineering design.” The primary objective of machine design is synthesis, or creation, not analysis. Analysis is a tool that serves as a means toward an end. 11/18/2018

Design Process 11/18/2018

Design steps Often the first step in which a designer becomes involved, and may not involve intense iteration. In this phase, we deal with the entire machine: Define function Identify constraints involving cost, size, etc. Develop alternative conceptions of mechanism/process combinations that can satisfy the constraints Perform supporting analyses (thermodynamic, heat transfer, fluid mechanics, kinematics, force, stress, life, cost, compatibility with special constraints) Select the best mechanism Document the design 11/18/2018

Design steps- prelim Concept 1 Two longitudinal members, one trans-verse split-end cross member, small transverse member in transmission tunnel, rear transverse member similar to original, gauge reduction. Concept 6 Two integrated, split transverse cross members, rear transverse member similar to original, reduced sheet thickness in cross members. 11/18/2018

Intermediate step Generally occurs after preliminary design, but the two phases may overlap. Intermediate design always involves iterations. In this phase, we deal with individual components of the machine: Identify components Define component functions Identify constraints involving cost, size, etc. Develop tentative conceptions of the components mechanism/process combinations using good form synthesis principles Perform supporting analyses (including analyses at each critical point in each component), FMEA, C& E Select the best component designs Document component designs; prepare a layout drawing 11/18/2018

Detail Design Phase Subsequent to intermediate phase. In this phase, we deal with individual components of the machine and the machine as a whole: Select manufacturing and assembly processes Specify dimensions and tolerances Prepare component detail drawings Prepare assembly drawings 11/18/2018

Ass 2 - requirements General consideration of similar machines Availability Cost Designs Weakness/strengths Design , details in the appendix Analysis Drawings 11/18/2018

Statistics – engineering design Engineering statistics is the study of how best to… Collect engineering data Summarize or describe engineering data Draw formal inferences and practical conclusions on the basis of engineering data all the while recognizing the reality of variation 11/18/2018

Use of statistics in engineering Design of experiments (DOE) use statistical techniques to test and construct model of engineering components and systems. Quality control and process control use statistics as a tool to manage conformance to specifications of manufacturing processes and their products. Time and method engineering use statistics to study repetitive operations in manufacturing in order to set standards and find optimum (in some sense) manufacturing procedures. 11/18/2018

Collection of quantitative data (Measurement) If you can’t measure, you can’t do statistics… or engineering for that matter! Issues: Validity Precision Accuracy 11/18/2018

Statistics FME471 11/18/2018

Precision and Accuracy Accurate, Not Precise Not Accurate Not Precise Precise, Not Accurate Accurate and Precise 11/18/2018

NO! Statistical thinking Statistical methods are used to help us describe and understand variability. By variability, we mean that successive observations of a system or phenomenon do not produce exactly the same result. Are these gears produced exactly the same size? NO! 11/18/2018

Sources of variability Environment Method Man Material Machine 11/18/2018

Example An engineer is developing a rubber compound for use in O-rings. The engineer uses the standard rubber compound to produce eight O-rings in a development laboratory and measures the tensile strength of each specimen. The tensile strengths (MPa) of the eight O-rings are 103,104,102, 105, 102, 106, 101, and 100. 11/18/2018

Variability There is variability in the tensile strength measurements. The variability may even arise from the measurement errors Tensile Strength can be modeled as a random variable. Tests on the initial specimens show that the average tensile strength is 102 MPa. The engineer thinks that this may be too low for the intended applications. He decides to consider a modified formulation of rubber in which a Teflon additive is included. 11/18/2018

Random sampling Assume that X is a measurable quantity related to a product (tensile strength of rubber). We model X as a random variable Occur frequently in engineering applications Random sampling Obtain samples from a population All outcomes must be equally likely to be sampled Replacement necessary for small populations Meaningful statistics can be obtained from samples 11/18/2018

Point estimation The probability density function f(x) of the random variable X is assumed to be known. Generally it is taken as Gaussian distribution basing on the central limit theorem. Our purpose is to estimate certain parameters of f(x), (mean, variance) from observation of the samples. 11/18/2018

Sample mean M is a point estimator of m S is a point estimator of s Sample variance: M is a point estimator of m S is a point estimator of s 11/18/2018

Normal Distribution Mean and standard deviation to describe the sample or population 11/18/2018

Example 11/18/2018

Solution 11/18/2018

Weibull distribution 11/18/2018

Example 2 11/18/2018

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