1. Statistical Thinking and Applications
Chapter 9
Statistical Thinking
and Applications

2. 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

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

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. Importance of Understanding Variation
time
PREDICTABLE ?
UNPREDECTIBLE

6. 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

7. Note to Instructors
The following slides can be used to guide a class demonstration and discussion of the Deming Red Bead experiment using small bags of M&M’s® Chocolate Candies, from a suggestion I found on a TQ newsgroup several years ago. The good output (“red beads”) are the blue M&Ms, with the instructor playing the role of Dr. Deming.

8. We’re Going into Business!!!
We have a new global customer and have to start up several factories. So I need teams of 5 to do the work:
1 production worker
2 inspectors
1 Chief Inspector
1 Recorder

9. Production Setup Take the bag in your left hand.
Tear a 3/4” opening in the right corner.
(only large enough for one piece at a
time)

10. Production Process 1. Production worker produces 10 pieces
and places them on the napkin.
2. Each inspector, independently, counts
the blue ones, and passes to the Chief
Inspector to verify.
3. If Chief Inspector agrees, s/he tells
the recorder, who reports it to me.

11. Be a Quality Worker! Take Pride in Your Work! Do it right the first
time!
Take Pride in
Your Work!
Be a Quality Worker!

12. 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.

13. Statistical Methods Descriptive statistics Statistical inference
Predictive statistics

14. Review of Key Concepts Random variables Probability distributions
Populations and samples
Point estimates
Sampling distributions
Standard error of the mean

15. Important Probability Distributions
Discrete
Binomial
Poisson
Continuous
Normal
Exponential

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. Sampling Methods Simple random sampling Stratified sampling
Systematic sampling
Cluster sampling
Judgment sampling

18. Sampling Error Sampling error (statistical error)
Nonsampling error (systematic error)
Factors to consider:
Sample size
Appropriate sample design

19. Design of Experiments
A test or series of tests to compare two or more methods to determine which is better, or to determine levels of controllable factors to optimize the yield of a process or minimize the variability of a response variable.
Factorial experiment
Analysis of all combinations of factor levels to understand main effects and interactions

20. Excel Descriptive Statistics Tool
Tools…Data Analysis… Descriptive Statistics

22. Excel Histogram Tool
Tools…Data Analysis…Histogram

24. Process Capability
The range over which the natural variation of a process occurs as determined by the system of common causes
Measured by the proportion of output that can be produced within design specifications

25. Types of Capability Studies
Peak performance study - how a process performs under ideal conditions
Process characterization study - how a process performs under actual operating conditions
Component variability study - relative contribution of different sources of variation (e.g., process factors, measurement system)

26. Process Capability Study
Choose a representative machine or process
Define the process conditions
Select a representative operator
Provide the right materials
Specify the gauging or measurement method
Record the measurements
Construct a histogram and compute descriptive statistics: mean and standard deviation
Compare results with specified tolerances

27. Process Capability
specification
natural variation
(a)
(b)
(c)
(d)

28. Process Capability Index
UTL - LTL 6s
Cp =
UTL - m 3s
Cpu =
m - LTL 3s
Cpl =
Cpk = min{
Cpl, Cpu }

29. PROCESS_CAPABILITY.XLS