L9-statistics_and_probability1

# L9-statistics_and_probability1 -...

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Uncertainty in design and manufacturing: Statistics, reliability, and probability VM250, Design and Manufacturing I Mechanical Engineering UM SJTU Joint Institute 1 Primary source: A. John Hart. Includes material from D. Dutta and K. Saitou

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Outline Introduction Random variables Normal distributions Absolute and statistical tolerances Non normal distributions; statistics of failure Reliability of manufacturing sequences Accuracy, repeatability and resolution Summary
Introduction What is the correct value? 2.01” 1.98” 2.03”

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Introduction The dimensions will not be the same each time! For each part For each measurement Sources of variation Manufacturing: machine precision, tool wear, material irregularity, operator, etc. Measurement: accuracy of measurement tool, location of measurement Environment: temperature, humidity, vibration, etc.
Thus we need tolerances! What do we do? Specify a dimension within an allowable range to guarantee * adequate performance of the part or assembly: How do we choose tolerances? 1. Know elementary statistical math (this week) 2. Understand and characterize sources of error 3. Use 1 and 2 to predict the required tolerances 4. Use this and other inputs to choose a manufacturing process and understand its limitations (coming up) *we will never make 100% of the parts functional, but we can be right enough of the time (probability!) to have a successful (profitable, functional, long lasting) product

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Starting to define the statistical guarantee… Given measurements of n sample products… How likely will the next one fall within the target range, say ? ??? 2.00 0.01 2.01” 1.98” 2.03” 2.00” 1.99” 2.00”
Let’s treat the measurements as random variables Random variable : variable whose values are determined by a chance event (a sample) Histogram: a frequency plot of sampled values sample id 1 2 3 4 5 6 od [in] 2.01 1.98 2.03 2.00 1.99 2.00 0 1 2 3 4 1.96 1.98 2.00 2.02 2.04 More OD [in] Frequency 1.99 2.01 x  “bins”

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Sample vs. population When the population is large it is difficult to measure all parts, so we estimate it with a sample .
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## L9-statistics_and_probability1 -...

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