Statistics-508 [Compatibility Mode].pdf

Statistics and DOE

David M. Lyth, Ph.D., C.Q.E.Department of Industrial & Manufacturing EngineeringWestern Michigan University

Managing by facts

“In God we Trust—All others bring data”

ISO9000 AuditorISO9000 Auditor

Copyright, Lyth, WMU

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?


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


Sources of Variation in Production Processes

Materials Operators Methods MeasurementInstruments

Tools HumanInspectionPerformance

EnvironmentMachines

INPUTS PROCESS OUTPUTS


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


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.


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


Using data

�Managing a process�Understanding a process�Controlling a process� Improving a process


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?


Collection problems� Data accuracy� Representative data� Time series data� False data� False data� Mistaken data� Incorrect data� Unavailable data� Useless data


Ways to classify data

�Time�Time to failure�Development phase �Team creating defect�Activity producing error�Function of the defect�Severity of the defect


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.”


Statistics

�Descriptive statistics� Inferential statistics�Estimation�Hypothesis testing�ANOVA�Regression


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

Statistical Methods

�Descriptive statistics�Statistical inference�Predictive statistics�Predictive statistics


Statistical Foundations

�Random variables�Probability distributions�Populations and samples�Populations and samples�Point estimates�Sampling distributions �Standard error of the mean


Descriptive statistics

�Measures of central tendency (mean, median, mode)

�Measures of dispersion (variance, standard deviation, range)standard deviation, range)� Histogram� Pie chart� Frequency curve


Inferential statistics

�Estimation�Hypothesis testing�ANOVA�Regression


Important Probability Distributions�Discrete

�Binomial�PoissonPoisson

�Continuous�Normal�Exponential


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.


Statistical Tools


Sampling Methods

�Simple random sampling�Stratified sampling�Systematic sampling�Systematic sampling�Cluster sampling�Judgment sampling


Sampling Error

�Sampling error (statistical error)�Nonsampling error (systematic

error)error)�Factors to consider:

�Sample size�Appropriate sample design


Excel Tools for Statistics

� Tools…Data Analysis… Descriptive Statistics

� Tools…Data Analysis…Histogram


Enumerative and Analytic Studies�Enumerative study – analysis of a static

population�Analytic study – analysis of a dynamic

time seriestime series


Documents

Statistics-508 [Compatibility Mode].pdf