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Ch 3 Distributions

# Ch 3 Distributions - IND E 321 Quality Control Instructor...

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1 IND E 321: Quality Control Instructor: Linda Ng Boyle Dept of ISE, U. Washington Chapter 3: Modeling Process Quality

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2 Chapter 3 Chapter 3 : Modeling Process Quality Describing Variation Probability Distribution (Discrete versus Continuous) Probability Plots
3 Chapter 3: Describing Variation How do we show how much variation there is in anything we do? Descriptive Statistics Graphical displays Numerical summaries Why do we need both?

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4 Chapter 3: Modeling Process Quality Easier for people to visualize Easier to show what is going on to non- technical people (factory workers, managers, inspectors, consumers) Easier to see unusual observations Good to provide concise data
5 Coffee machine example Coffee machine : need to make sure your machine is filling each cup of coffee with 8 fluid ounces (or 240 ml).

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6 Coffee machine example Every day for 20 days, 5 samples from the coffee machine is weighed. Day Average weight (ml) Day Average weight (ml) 1 242 11 205 2 219 12 210 3 220 13 214 4 239 14 221 5 244 15 238 6 243 16 218 7 220 17 239 8 222 18 233 9 239 19 209 10 209 20 212
7 Stem and Leaf Plot Stem ( leading digits ) Leaf Frequency 20 21 22 23 24 For the coffee example, use two leading digits; frequency should sum up to the number of days (i.e., 20 days) Board discussion

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8 Ordered Stem and Leaf Stem Leaf Frequency 20 21 22 23 24 The leafs should be in numerical order within each stem Board discussion
9 Ordered Stem and Leaf Advantage of ordering the data Immediately see what the smallest number is Can determine: Mean, mode and median 50 th percentile = sample median Median = 220.5 First quartile (lower quartile) = 213 Third quartile (upper quartile) = 239

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10 Time series plot (run chart)
11 Frequency Distributions and Histograms Histogram 0 1 2 3 4 5 6 209 219 229 239 249 Bin Frequency Coffee Weight Bins

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12 Stem & Leaf and Histograms If you have a large dataset, histogram is better → more compact summary of data Data should be divided into meaningful intervals (range of data) Of equal width For histograms, these intervals can be called bins, cells, class intervals Do not want data divided into too many or too few intervals.
13 Histograms Histograms Rule of thumb for segmenting the bins sample your in datapoints of number the is where n n Examples Coffee example had 20 samples = > 4.47 ~ 5 bins If you had 40 samples => 6.32 ~ 6 to 7 bins

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14 Numerical Summary of Data Important summary statistics for distribution of data can include: Sample mean, Sample variance, s 2 Sample standard deviation, s Sample median, M x
15 Numerical Summary of Coffee Data 2 : Deviation Standard s s = n x x i = 1 ) ( 2 2 - - = n x x s i Mean Variance

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16 Coffee machine example Every day for 20 days, 5 samples from the coffee machine is weighed.
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