statistics-508 [compatibility mode].pdf
TRANSCRIPT
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Statistics and DOE
David M. Lyth, Ph.D., C.Q.E.Department of Industrial & Manufacturing EngineeringWestern Michigan University
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Managing by facts
“In God we Trust—All others bring data”
ISO9000 AuditorISO9000 Auditor
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Data and Quality
� What are the most pressing problems in our department?
� What do defects cost?What causes most defects?� What causes most defects?
� What is the defect removal rate or quality engineering?
� How many defects are severe?� What is the average cost of repairing a
defect?
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Statistical Thinking
�All work occurs in a system of interconnected processes
�Variation exists in all processes�Variation exists in all processes�Understanding and reducing
variation are the keys to success
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Sources of Variation in Production Processes
Materials Operators Methods MeasurementInstruments
Tools HumanInspectionPerformance
EnvironmentMachines
INPUTS PROCESS OUTPUTS
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Variation
�Many sources of uncontrollable variation exist (common causes)
�Special (assignable) causes of �Special (assignable) causes of variation can be recognized and controlled
�Failure to understand these differences can increase variation in a system
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Problems Created by Variation�Variation increases unpredictability. �Variation reduces capacity utilization. �Variation contributes to a “bullwhip”
effect. effect. �Variation makes it difficult to find root
causes. �Variation makes it difficult to detect
potential problems early.
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Two Fundamental Management Mistakes
1. Treating as a special cause any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to common causesdue to common causes
2. Attributing to common causes any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to a special cause
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Using data
�Managing a process�Understanding a process�Controlling a process� Improving a process
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Collecting data-questions to answer�What is the purpose of collecting data?�What data do I need?�How will I collect it?�How will I analyze it?�How will I analyze it?�What conclusion am I attempting to
draw?�How will I present those conclusions to
achieve my objectives?
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Collection problems� Data accuracy� Representative data� Time series data� False data� False data� Mistaken data� Incorrect data� Unavailable data� Useless data
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Ways to classify data
�Time�Time to failure�Development phase �Team creating defect�Activity producing error�Function of the defect�Severity of the defect
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Possible causes
�Communication – “I didn’t understand what I was supposed to do.”
�Education – “I didn’t know how to do it”Transcription – “I was doing it right, but �Transcription – “I was doing it right, but something went wrong in the process.”
�Oversight – “I just forgot.”
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Statistics
�Descriptive statistics� Inferential statistics�Estimation�Hypothesis testing�ANOVA�Regression
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Data fitting
Goodness of fit test
Χ2 = Σ (fo-fe)2/fe
Ho: Data fits particular distribution
(specify parameters)
H1: Data does not fits particular
distribution (specify parameters)Copyright, Lyth, WMU
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Statistical Methods
�Descriptive statistics�Statistical inference�Predictive statistics�Predictive statistics
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Statistical Foundations
�Random variables�Probability distributions�Populations and samples�Populations and samples�Point estimates�Sampling distributions �Standard error of the mean
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Descriptive statistics
�Measures of central tendency (mean, median, mode)
�Measures of dispersion (variance, standard deviation, range)standard deviation, range)� Histogram� Pie chart� Frequency curve
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Inferential statistics
�Estimation�Hypothesis testing�ANOVA�Regression
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Important Probability Distributions�Discrete
�Binomial�PoissonPoisson
�Continuous�Normal�Exponential
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Central Limit Theorem
� If simple random samples of size n are taken from any population, the probability distribution of sample means will be approximately normal as nbecomes large.
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Statistical Tools
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Sampling Methods
�Simple random sampling�Stratified sampling�Systematic sampling�Systematic sampling�Cluster sampling�Judgment sampling
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Sampling Error
�Sampling error (statistical error)�Nonsampling error (systematic
error)error)�Factors to consider:
�Sample size�Appropriate sample design
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Excel Tools for Statistics
� Tools…Data Analysis… Descriptive Statistics
� Tools…Data Analysis…Histogram
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Enumerative and Analytic Studies�Enumerative study – analysis of a static
population�Analytic study – analysis of a dynamic
time seriestime series
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