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7. Product and Process Comparisons
7. Product and Process Comparisons
7.
Product and Process
Comparisons
This chapter presents the background and specific analysis techniques needed to
compare the performance of one or more processes against known standards or one
another.
1.
Introduction
Scope
2.
Comparisons: One Process
Comparing to a Distribution
1.
2.
Assumptions
2.
Comparing to a Nominal
Mean
3.
Statistical Tests
4.
Confidence Intervals
3.
Comparing to Nominal
Variability
5.
Equivalence of Tests and Intervals
4.
Fraction Defective
6.
Outliers
5.
Defect Density
7.
Trends
6.
Location of Population
Values
3.
Comparisons: Two Processes
Means: Normal Data
4.
Comparisons: Three +
Processes
Comparing Populations
2.
Variability: Normal Data
1.
3.
Fraction Defective
2.
Comparing Variances
4.
Failure Rates
3.
Comparing Means
5.
Means: General Case
4.
Variance Components
5.
Comparing Categorical
Datasets
6.
Comparing Fraction
Defectives
7.
Multiple Comparisons
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1.
1.
7. Product and Process Comparisons
Detailed table of contents
References for Chapter 7
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7. Product and Process Comparisons
7.
Product and Process Comparisons -
Detailed Table of Contents [7.]
1.
Introduction
[7.1.]
What is the scope?
[7.1.1.]
1.
2.
What assumptions are typically made?
[7.1.2.]
3.
What are statistical tests?
[7.1.3.]
Critical values and p values
[7.1.3.1.]
1.
4.
What are confidence intervals?
[7.1.4.]
5.
What is the relationship between a test and a confidence interval?
[7.1.5.]
6.
What are outliers in the data?
[7.1.6.]
7.
What are trends in sequential process or product data?
[7.1.7.]
2.
Comparisons based on data from one process
[7.2.]
Do the observations come from a particular distribution?
[7.2.1.]
Chi-square goodness-of-fit test
[7.2.1.1.]
1.
1.
2.
Kolmogorov- Smirnov test
[7.2.1.2.]
3.
Anderson-Darling and Shapiro-Wilk tests
[7.2.1.3.]
2.
Are the data consistent with the assumed process mean?
[7.2.2.]
Confidence interval approach
[7.2.2.1.]
1.
2.
Sample sizes required
[7.2.2.2.]
3.
Are the data consistent with a nominal standard deviation?
[7.2.3.]
Confidence interval approach
[7.2.3.1.]
1.
2.
Sample sizes required
[7.2.3.2.]
4.
Does the proportion of defectives meet requirements?
[7.2.4.]
Confidence intervals for large sample sizes
[7.2.4.1.]
1.
2.
Confidence intervals for small sample sizes
[7.2.4.2.]
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7. Product and Process Comparisons
3.
Does the defect density meet requirements?
[7.2.5.]
Sample sizes required
[7.2.4.3.]
5.
6.
What intervals contain a fixed percentage of the population values?
[7.2.6.]
Approximate intervals that contain most of the population values
[7.2.6.1.]
1.
2.
Percentiles
[7.2.6.2.]
3.
Tolerance intervals for a normal distribution
[7.2.6.3.]
4.
Two-sided tolerance intervals using EXCEL
[7.2.6.4.]
5.
Tolerance intervals based on the largest and smallest observations
[7.2.6.5.]
3.
Comparisons based on data from two processes
[7.3.]
Do two processes have the same mean?
[7.3.1.]
Analysis of paired observations
[7.3.1.1.]
1.
1.
2.
Confidence intervals for differences between means
[7.3.1.2.]
2.
Do two processes have the same standard deviation?
[7.3.2.]
3.
How can we determine whether two processes produce the same proportion of
defectives?
[7.3.3.]
4.
Assuming the observations are failure times, are the failure rates (or Mean Times To
Failure) for two distributions the same?
[7.3.4.]
5.
Do two arbitrary processes have the same mean?
[7.3.5.]
4.
Comparisons based on data from more than two processes
[7.4.]
How can we compare several populations with unknown distributions (the
Kruskal-Wallis test)?
[7.4.1.]
1.
2.
Assuming the observations are normal, do the processes have the same
variance?
[7.4.2.]
3.
Are the means equal?
[7.4.3.]
1-Way ANOVA overview
[7.4.3.1.]
1.
2.
The 1-way ANOVA model and assumptions
[7.4.3.2.]
3.
The ANOVA table and tests of hypotheses about means
[7.4.3.3.]
4.
1-Way ANOVA calculations
[7.4.3.4.]
5.
Confidence intervals for the difference of treatment means
[7.4.3.5.]
6.
Assessing the response from any factor combination
[7.4.3.6.]
7.
The two-way ANOVA
[7.4.3.7.]
8.
Models and calculations for the two-way ANOVA
[7.4.3.8.]
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7. Product and Process Comparisons
4.
What are variance components?
[7.4.4.]
5.
How can we compare the results of classifying according to several
categories?
[7.4.5.]
6.
Do all the processes have the same proportion of defects?
[7.4.6.]
7.
How can we make multiple comparisons?
[7.4.7.]
Tukey's method
[7.4.7.1.]
1.
2.
Scheffe's method
[7.4.7.2.]
3.
Bonferroni's method
[7.4.7.3.]
4.
Comparing multiple proportions: The Marascuillo procedure
[7.4.7.4.]
5.
References
[7.5.]
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