Six Sigma Statistics with EXCEL and MINITAB

Home >
Browse >
Six Sigma Statistics with EXCEL and MINITAB

Six Sigma Statistics with EXCEL and MINITAB

Authors: Issa Bass

Published: June 2007

eISBN: 9780071542685 007154268X | ISBN: 9780071489690

Contents

Preface

Acknowledgments

Chapter 1. Introduction

1.1 Six Sigma Methodology

1.1.1 Define the organization

1.1.2 Measure the organization

1.1.3 Analyze the organization

1.1.4 Improve the organization

1.2 Statistics, Quality Control, and Six Sigma

1.2.1 Poor quality defined as a deviation from engineered standards

1.2.2 Sampling and quality control

1.3 Statistical Definition of Six Sigma

1.3.1 Variability: the source of defects

1.3.2 Evaluation of the process performance

1.3.3 Normal distribution and process capability

Chapter 2. An Overview of Minitab and Microsoft Excel

2.1 Starting with Minitab

2.1.1 Minitab's menus

2.2 An Overview of Data Analysis with Excel

2.2.1 Graphical display of data

2.2.2 Data Analysis add-in

Chapter 3. Basic Tools for Data Collection, Organization and Description

3.1 The Measures of Central Tendency Give a First Perception of Your Data

3.1.1 Arithmetic mean

3.1.2 Geometric mean

3.1.3 Mode

3.1.4 Median

3.2 Measures of Dispersion

3.2.1 Range

3.2.2 Mean deviation

3.2.3 Variance

3.2.4 Standard deviation

3.2.5 Chebycheff's theorem

3.2.6 Coefficient of variation

3.3 The Measures of Association Quantify the Level of Relatedness between Factors

3.3.1 Covariance

3.3.2 Correlation coefficient

3.3.3 Coefficient of determination

3.4 Graphical Representation of Data

3.4.1 Histograms

3.4.2 Stem-and-leaf graphs

3.4.3 Box plots

3.5 Descriptive Statistics—Minitab and Excel Summaries

Chapter 4. Introduction to Basic Probability

4.1 Discrete Probability Distributions

4.1.1 Binomial distribution

4.1.2 Poisson distribution

4.1.3 Poisson distribution, rolled throughput yield, and DPMO

4.1.4 Geometric distribution

4.1.5 Hypergeometric distribution

4.2 Continuous Distributions

4.2.1 Exponential distribution

4.2.2 Normal distribution

4.2.3 The log-normal distribution

Chapter 5. How to Determine, Analyze, and Interpret Your Samples

5.1 How to Collect a Sample

5.1.1 Stratified sampling

5.1.2 Cluster sampling

5.1.3 Systematic sampling

5.2 Sampling Distribution of Means

5.3 Sampling Error

5.4 Central Limit Theorem

5.5 Sampling from a Finite Population

5.6 Sampling Distribution of p

5.7 Estimating the Population Mean with Large Sample Sizes

5.8 Estimating the population Mean with Small Sample Sizes and σ Unknown: t-Distribution

5.9 Chi Square (χ[sup(2)]) Distribution

5.10 Estimating Sample Sizes

5.10.1 Sample size when estimating the mean

5.10.2 Sample size when estimating the population proportion

Chapter 6. Hypothesis Testing

6.1 How to Conduct a Hypothesis Testing

6.1.1 Null hypothesis

6.1.2 Alternate hypothesis

6.1.3 Test statistic

6.1.4 Level of significance or level of risk

6.1.5 Decision rule determination

6.1.6 Decision making

6.2 Testing for a Population Mean

6.2.1 Large sample with known σ

6.2.2 What is the p-value and how is it interpreted?

6.2.3 Small samples with unknown σ

6.3 Hypothesis Testing about Proportions

6.4 Hypothesis Testing about the Variance

6.5 Statistical Inference about Two Populations

6.5.1 Inference about the difference between two means

6.5.2 Small independent samples with equal variances

6.5.3 Testing the hypothesis about two variances

6.6 Testing for Normality of Data

Chapter 7. Statistical Process Control

7.1 How to Build a Control Chart

7.2 The Western Electric (WECO) Rules

7.3 Types of Control Charts

7.3.1 Attribute control charts

7.3.2 Variable control charts

Chapter 8. Process Capability Analysis

8.1 Process Capability with Normal Data

8.1.1 Potential capabilities vs. actual capabilities

8.1.2 Actual process capability indices

8.2 Taguchi's Capability Indices C[sub(PM)] and P[sub(PM)]

8.3 Process Capability and PPM

8.4 Capability Sixpack for Normally Distributed Data

8.5 Process Capability Analysis with Non-Normal Data

8.5.1 Normality assumption and Box-Cox transformation

8.5.2 Process capability using Box-Cox transformation

8.5.3 Process capability using a non-normal distribution

Chapter 9. Analysis of Variance

9.1 ANOVA and Hypothesis Testing

9.2 Completely Randomized Experimental Design (One-Way ANOVA)

9.2.1 Degrees of freedom

9.2.2 Multiple comparison tests

9.3 Randomized Block Design

9.4 Analysis of Means (ANOM)

Chapter 10. Regression Analysis

10.1 Building a Model with Only Two Variables: Simple Linear Regression

10.1.1 Plotting the combination of x and y to visualize the relationship: scatter plot

10.1.2 The regression equation

10.1.3 Least squares method

10.1.4 How far are the results of our analysis from the true values: residual analysis

10.1.5 Standard error of estimate

10.1.6 How strong is the relationship between x and y: correlation coefficient

10.1.7 Coefficient of determination, or what proportion in the variation of y is explained by the changes in x

10.1.8 Testing the validity of the regression line: hypothesis testing for the slope of the regression model

10.1.9 Using the confidence interval to estimate the mean

10.1.10 Fitted line plot

10.2 Building a Model with More than Two Variables: Multiple Regression Analysis

10.2.1 Hypothesis testing for the coefficients

10.2.2 Stepwise regression

Chapter 11. Design of Experiment

11.1 The Factorial Design with Two Factors

11.1.1 How does ANOVA determine if the null hypothesis should be rejected or not?

11.1.2 A mathematical approach

11.2 Factorial Design with More than Two Factors (2[sup(k)])

Chapter 12. The Taguchi Method

12.1 Assessing the Cost of Quality

12.1.1 Cost of conformance

12.1.2 Cost of nonconformance

12.2 Taguchi's Loss Function

12.3 Variability Reduction

12.3.1 Concept design

12.3.2 Parameter design

12.3.3 Tolerance design

Chapter 13. Measurement Systems Analysis–MSA: Is Your Measurement Process Lying to You?

13.1 Variation Due to Precision: Assessing the Spread of the Measurement

13.1.1 Gage repeatability & reproducibility crossed

13.1.2 Gage R&R nested

13.2 Gage Run Chart

13.3 Variations Due to Accuracy

13.3.1 Gage bias

13.3.2 Gage linearity

Chapter 14. Nonparametric Statistics

14.1 The Mann-Whitney U test

14.1.1 The Mann-Whitney U test for small samples

14.1.2 The Mann-Whitney U test for large samples

14.2 The Chi-Square Tests

14.2.1 The chi-square goodness-of-fit test

14.2.2 Contingency analysis: chi-square test of independence

Chapter 15. Pinpointing the Vital Few Root Causes

15.1 Pareto Analysis

15.2 Cause and Effect Analysis

Appendix 1 Binominal Table P(x) =[sub(n)]C[sub(x)] p[sup(x)]q[sup(n–x)]

Appendix 2 Poisson Table P(x) = λ[sup(x)]e[sup(–λ)]/x!

Appendix 3 Normal Z Table

Appendix 4 Student's t Table

Appendix 5 Chi-Square Table

Appendix 6 F Table α = 0.05

Index