# Statistical Thinking and Applications

Document Sample

```					Chapter 11

Statistical
Thinking and
Applications   1
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.
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
Sources of Variation in
Production Processes
Measurement
Operators     Methods
Materials                                     Instruments

INPUTS        PROCESS            OUTPUTS

Tools                                          Human
Machines    Environment       Inspection
Performance

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
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.
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.
Importance of
Understanding Variation

time
PREDICTABLE

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

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
Production Setup

1. Take the bag in your left hand.

2. Tear a 3/4” opening in the right
corner. (only large enough for
one piece at a time)
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.
Do it right
the first
time!

Take Pride in
Be a Quality Worker!
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.
Statistical Foundations

 Random variables
 Probability distributions

 Populations and samples

 Point estimates

 Sampling distributions

 Standard error of the mean
Important Probability
Distributions
   Discrete
– Binomial
– Poisson
   Continuous
– Normal
– Exponential

17
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.

18
Sampling Methods

 Simple random sampling
 Stratified sampling

 Systematic sampling

 Cluster sampling

 Judgment sampling
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.
Sampling Error

 Sampling error (statistical error)
 Nonsampling error (systematic
error)
 Factors to consider:
– Sample size
– Appropriate sample design
Statistical Methods

 Descriptive statistics
 Statistical inference

 Predictive statistics
Statistical Tools
Excel Tools for Statistics

   Tools…Data Analysis… Descriptive
Statistics
   Tools…Data Analysis…Histogram
Key Idea

One of the biggest mistakes that people make in
using statistical methods is confusing data that
are sampled from a static population (cross-
sectional data) with data sampled from a
dynamic process (time series data).
Enumerative and Analytic
Studies
   Enumerative study – analysis of a
static population
   Analytic study – analysis of a dynamic
time series
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.

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Description: The Scope and Language of Operations Management by James R. Evans.