lecture6 - MIT OpenCourseWare http:/ocw.mit.edu _ 2.830J /...

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MIT OpenCourseWare ____________ http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: ________________ http://ocw.mit.edu/terms .
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1 M anufacturing Control of Manufacturing Processes Subject 2.830/6.780/ESD.63 Spring 2008 Lecture #6 Sampling Distributions and Statistical Hypotheses February 26, 2008
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2 M anufacturing Statistics The field of statistics is about reasoning in the face of uncertainty, based on evidence from observed data • Beliefs: – Probability Distribution or Probabilistic model form – Distribution/model parameters • Evidence: – Finite set of observations or data drawn from a population (experimental measurements/observations) • Models: – Seek to explain data wrt a model of their probability
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3 M anufacturing Topics • Sampling Distributions ( χ 2 and Student’s-t) – Uncertainty of Parameter Estimates – Effect of Sample Size – Examples of Inference • Inferences from Distributions – Statistical Hypothesis Testing – Confidence Intervals • Hypothesis Testing • The Shewhart Hypothesis and Basic SPC – Test statistics - xbar and S
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4 M anufacturing Sampling to Determine Parent Probability Distribution • Assume Process Under Study has a Parent Distribution p(x) • Take “ n ” Samples From the Process Output ( x i ) • Look at Sample Statistics (e.g. sample mean and sample variance) • Relationship to Parent • Both are Random Variables • Both Have Their Own Probability Distributions • Inferences about Process via Inferences about the Parent Distribution
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5 M anufacturing Moments of the Population vs. Sample Statistics Mean •V a r i a n c e Standard Deviation Covariance Correlation Coefficient Underlying model or Sample Statistics Population Probability
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6 M anufacturing Sampling and Estimation • Sampling: act of making observations from populations • Random sampling: when each observation is identically and independently distributed (IID) • Statistic: a function of sample data; a value that can be computed from data (contains no unknowns) – Average, median, standard deviation – Statistics are by definition also random variables
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7 M anufacturing Population vs. Sampling Distribution Population (“true”)probability density function) Sample Mean (statistic) n = 20 n = 10 n = 2 Sample Mean Distribution (sampling distribution) n = 1
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8 M anufacturing Sampling and Estimation, cont. •A statistic is a random variable, which itself has a sampling (probability) distribution – I.e., if we take multiple random samples, the value for the statistic will be different for each set of samples, but will be governed by the same sampling distribution • If we know the appropriate sampling distribution, we can reason about the underlying population based on the observed value of a statistic – e.g. we calculate a sample mean from a random sample; in what range do we think the actual (population) mean really sits?
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9 M anufacturing Estimation and Confidence Intervals • Point Estimation:
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This note was uploaded on 09/24/2010 for the course MECHE 2.830J taught by Professor Davidhardt during the Spring '08 term at MIT.

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lecture6 - MIT OpenCourseWare http:/ocw.mit.edu _ 2.830J /...

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