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7-statistics-all - ME250 Design and Manufacturing I...

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Statistics and Tolerances ME250 Design and Manufacturing I
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2 Outline Introduction Random variables Normal distribution Absolute and statistical tolerances Summary
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3 Outline Introduction Random variables Normal distribution Absolute and statistical tolerances Summary
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4 What is the correct value? Introduction 2.01” 1.98” 2.03”
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5 Reality: OD will not be exactly the same For each measurement For each products Sources of variations Manufacturing: cutting condition, tool wear, material irregularity.. Measurement: measured location, measured devices.. Environment: temperature, humidity… So what can we do? Specify a dimension with an allowable range, commonly as: Introduction upper lower or nominal tolerance
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6 Given measurements of n sample products… How likely the next OD fall within the target range, say 2.00 ± 0.01? Introduction ??? 2.01 1.98 2.03 2.00 1.99 2.00
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7 Outline Introduction Random variables Normal distribution Absolute and statistical tolerances Summary
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8 Random variable : variable whose value varies for every sample Histogram: frequency plot of sampled values Excel Help: http://office.microsoft.com/en-us/excel/HA102382521033.aspx Random variables 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” sample id 1 2 3 4 5 6 od [in] 2.01 1.98 2.03 2.00 1.99 2.00
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9 Outline Introduction Random variables Normal distribution Absolute and statistical tolerances Summary
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10 What happens to histogram if ? Normal distribution 0 1 2 3 4 1.96 1.98 2.00 2.02 2.04 More OD [in] Frequency n  
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11 Normal distribution Gauss says… 0 1 2 3 4 1.96 1.98 2.00 2.02 2.04 More OD [in] Frequency n   “bell” shape
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12 Normal distribution Gauss says… (simply put) If the values of a random variable x is due to the effects of many other random variables, then the histogram of x with n samples approaches to the normal distribution as Denoted as : mean (“horizontal shift”) : standard deviation (“flatness”) Excel Tip: NORMDIST n   2 2 ( ) 2 1 ( ) 2 x x x x f x e  ( , ) x x N x x x
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13 Normal distribution Example: Which line has the highest mean? Which line has the highest stdev?
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14 Normal distribution Example: Which line has the highest mean? Red , Green , and Blue Which line has the highest stdev? Blue
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