Chapter 11

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Chapter 11 Statistical Thinking and Applications

• Red bead experiment, random vs. non-random
  variation, probability distribution, sampling,
  statistical methodology

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
• Variation is the enemy of quality

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

• Many sources of uncontrollable variation exist
  (common chance random causes)
• Special (assignable special non-random)
  causes of variation can be recognized and are
  controllable
• 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 (Type I error or
  Producers Risk)
• Attributing to common causes any fault,
  complaint, mistake, breakdown, accident or
  shortage when it actually is due to a special
  cause (Type II error or Consumers Risk)

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 MMs
  Chocolate Candies, from a suggestion I found on a
  TQ newsgroup several years ago. The good output
  (white beads) are the blue MMs, with the
  instructor playing the role of Dr. Deming. -
  James R. Evans

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Were Going into Business!!!
We have a new global customer and have to start
up several factories. The customer wants only
blue MMs. So I need 4 teams of 8 people to do
the work 5 production workers 2 inspectors 1
Chief Inspector / recorder
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Production Process
1. Each production worker reaches into the bag
and take one piece at a time out of the bag. 2.
Production worker produces 10 pieces and places
them on the napkin. 3. Each inspector,
independently, counts the blue ones produced by
each worker, and passes the results (name and
number of blue pieces) to the Chief Inspector to
verify. 4. If Chief Inspector agrees, s/he
records the results by individual and reports
the results to me.
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Second pass

• Reward best performer
• Penalize worst performer
• Remind everyone that customer only wants blue
  MMs
• Exhort workers to do better
• Repeat process

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Third pass

• Again reward best performer
• Again penalize worst performer
• Remind everyone that customer only wants blue
  MMs
• Warn workers their jobs are in jeopardy
• Declare Zero Defects Day
• Repeat process

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Fourth pass

• Fire worst performers
• Put up banners, posters, slogans (see
  next slide)
• Remind everyone that customer only
  wants blue MMs
• Warn that plant closure is possible
• Repeat process

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14
Bad News!

• Results are not good enough
• Customers are not satisfied
• Plant must be closed!

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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.
• Slogans, posters, banners are not the answer

16
Statistical Methods

• Descriptive statistics
• Statistical inference
• Predictive statistics

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Review of Key Concepts

• Random variables
• Probability distributions
• Populations and samples
• Point estimates
• Sampling distributions
• Standard error of the mean

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Important Probability Distributions

• Discrete
• Binomial
• Poisson
• Continuous
• Normal
• Exponential

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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.

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Sampling Methods

• Simple random sampling
• Stratified sampling
• Systematic sampling
• Cluster sampling
• Judgment sampling

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Sampling Error

• Sampling error (statistical error)
• Nonsampling error (systematic error)
• Factors to consider
• Sample size
• Appropriate sample design

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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

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Descriptive Statistics Tool - Microsoft Excel

• ToolsData Analysis Descriptive Statistics

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Descriptive Statistics Results
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Excel Histogram Tool

• ToolsData AnalysisHistogram

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Histogram Frequency Distribution