1. Statistical Thinking and Applications
Chapter 10
Statistical Thinking and Applications

2. Key Idea
Raw data collected from the field do not provide the information necessary for quality control or improvement. Data must be organized, analyzed, and interpreted. Statistics provide an efficient and effective way of obtaining meaningful information from data, allowing managers and workers to control and improve processes.

3. Principles of Statistical Thinking
All work occurs in a system of interconnected processes
Variation exists in all processes
Understanding and reducing variation are the keys to success

4. Variation
Many sources of uncontrollable variation exist (common causes)
Special (assignable) causes of variation can be recognized and controlled
Failure to understand these differences can increase variation in a system

5. Sources of Variation in Production Processes
Measurement
Instruments
Operators
Methods
Materials
INPUTS
PROCESS
OUTPUTS
Tools
Human
Inspection
Performance
Machines
Environment

6. Key Idea
A system governed only by common causes is called a stable system. Understanding a stable system and the differences between special and common causes of variation is essential for managing any system.

7. Problems Created by Variation
Variation increases unpredictability.
Variation reduces capacity utilization.
Variation contributes to a “bullwhip” effect.
Variation makes it difficult to find root causes.
Variation makes it difficult to detect potential problems early.

8. Two Fundamental Management Mistakes
Treating as a special cause any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to common causes
Attributing to common causes any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to a special cause

9. Deming’s Red Bead Experiment – Round 1

10. Control Chart of Results

11. Lessons Learned Quality is made at the top.
Rigid procedures are not enough.
People are not always the main source of variability.
Numerical goals are often meaningless.
Inspection is expensive and does not improve quality.

12. Statistical Foundations
Random variables
Probability distributions
Populations and samples
Point estimates
Sampling distributions
Standard error of the mean

13. Important Probability Distributions
Discrete
Binomial
Poisson
Continuous
Normal
Exponential

14. Key Idea
A good sampling plan should select a sample at the lowest cost that will provide the best possible representation of the population, consistent with the objectives of precision and reliability that have been determined for the study.

15. Histogram

16. 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 n becomes large.

17. Example

18. Confidence Intervals

19. Hypothesis Testing Formulate the hypotheses to test.
Select a level of significance that defines the risk of drawing an incorrect conclusion about the assumed hypothesis that is actually true.
Determine a decision rule on which to base a conclusion.
Collect data and calculate a test statistic.
Apply the decision rule to the test statistic and draw a conclusion.

20. Enumerative and Analytic Studies
Enumerative study – analysis of a static population
Analytic study – analysis of a dynamic time series

21. Design of Experiments
A designed experiment is a test or series of tests that enables the experimenter to compare two or more methods to determine which is better, or determine levels of controllable factors to optimize the yield of a process or minimize the variability of a response variable.
DOE is an increasingly important tool for Six Sigma.

22. Main Effects
Measures the difference that a change in a factor level has on the response. E.g., what is the effect of increasing the launch angle?
Main effect = average response at high level – average response at low level

23. Interactions
An interaction is when the effect of changing one factor depends on the levels of the other factors.
Response
Factor 2 at level 1
Factor 2 at level 2
Factor 1

24. Analysis of Variance
ANOVA is a methodology for drawing conclusions about equality of means of multiple populations.
ANOVA tests the hypothesis that the means of all populations are equal against the alternative hypothesis that at least one mean differs from the others.

25. Regression and Correlation
Regression analysis is a tool for building statistical models that characterize relationships between a dependent variable and one or more independent variables, all of which are numerical.
Correlation is a measure of a linear relationship between two variables, X and Y, and is measured by the (population) correlation coefficient.

26. Example: Voltmeter Calibration

27. Regression Line and Equation