7. Product and Process Comparisons

7. Product and Process Comparisons - Detailed Table of Contents [7.]

Introduction [7.1.]
1. What is the scope? [7.1.1.]
2. What assumptions are typically made? [7.1.2.]
3. What are statistical tests? [7.1.3.]
  1. Critical values and p values [7.1.3.1.]
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.]
Comparisons based on data from one process [7.2.]
1. Do the observations come from a particular distribution? [7.2.1.]
  1. Chi-square goodness-of-fit test [7.2.1.1.]
  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.]
  1. Confidence interval approach [7.2.2.1.]
  2. Sample sizes required [7.2.2.2.]
3. Are the data consistent with a nominal standard deviation? [7.2.3.]
  1. Confidence interval approach [7.2.3.1.]
  2. Sample sizes required [7.2.3.2.]
4. Does the proportion of defectives meet requirements? [7.2.4.]
  1. Confidence intervals [7.2.4.1.]
  2. Sample sizes required [7.2.4.2.]
5. Does the defect density meet requirements? [7.2.5.]
6. What intervals contain a fixed percentage of the population values? [7.2.6.]
  1. Approximate intervals that contain most of the population values [7.2.6.1.]
  2. Percentiles [7.2.6.2.]
  3. Tolerance intervals for a normal distribution [7.2.6.3.]
  4. Tolerance intervals based on the largest and smallest observations [7.2.6.4.]
Comparisons based on data from two processes [7.3.]
1. Do two processes have the same mean? [7.3.1.]
  1. Analysis of paired observations [7.3.1.1.]
  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 central tendency? [7.3.5.]
Comparisons based on data from more than two processes [7.4.]
1. How can we compare several populations with unknown distributions (the Kruskal-Wallis test)? [7.4.1.]
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. 1-Way ANOVA overview [7.4.3.1.]
  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.]
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.]
  1. Tukey's method [7.4.7.1.]
  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.]
References [7.5.]