# Quality Progress - September 2017 - 53

```"the supervisor tells you a sample of 50 widgets was measured and found to have a mean length of 22.4 mm, and the
processes is known to have a standard deviation of 0.4. The
process mean is known to be 22.5. Use a Z-test to determine
if we have evidence the mean has changed using an alpha
of 0.05."
The problem is solvable with the given information. In real
life, however, I have yet to have a supervisor ever tell me the
process standard deviation, the correct test to use or the
desired alpha.
In the real world, we must generally determine the process standard deviation on our own or select a statistical
test that does not require us to know the process standard
deviation. Although the example is not realistic, it still serves
as a method for teaching basic concepts. After those are
understood, the model can be changed to become more
complex and realistic.
Simple models are not only useful for textbooks and
teaching statistics. A statistician planning a design of
experiments (DoE) may need to use a simple model for
explaining what a DoE is, for example, and how it works
when working together with subject matter experts (SME)
who have no knowledge of DoEs.
The ﬂight time of a paper helicopter can be used to illustrate the response variable, and the various dimensions of the
helicopter can be used for communicating the concepts of
factors and levels. It would be easier to plan the DoE after the
SMEs understand what a DoE is based on the simple model.

Models and the world

Statistics are often used to create a mathematical model of
the real world for the purpose of making a decision.
An insurance company, for example, may perform a
statistical analysis to determine whether age, gender, type
of vehicle and location have an inﬂuence on the rate of
automobile accidents. An engineer may perform a DoE to
identify the factors and their levels to improve the output of
a manufacturing process.
The DoE results in a mathematical model that represents
the actual process. The model may not match the process
exactly due to variation under production conditions. If
the DoE was properly carried out, however, the model can
be used to identify the settings required for an increased
output.

Knowing the limitations

Simplified models of a complex world can be useful for
explaining nonintuitive concepts in an easier-to-comprehend

manner and gaining on understanding of actual phenomena to make
more-informed decisions.
When using models, we would do
well to remember George E.P. Box
and Norman R. Draper's warning:
"Essentially, all models are wrong."
Although all models may be wrong,
hope is not lost because Box and
Draper also reassure us: "Some are
useful."4
The trick is to know when the
model is useful as well as the limitations of the model.
REFERENCES
1. Douglas C. Giancoli, Physics: Principles
With Applications, fifth edition, Prentice
Hall, 1998.
2. Phil Plait, "A Sunday Morning Brain
Teaser for You," Slate, June 26, 2016.
3. John Lawson and John Erjavec, Modern
Statistics for Engineering and Quality
Improvement, Wadsworth Group, 2001.
4. George E.P. Box and Norman R. Draper,
Empirical Model-Building and Response
Surfaces, John Wiley & Sons Inc., 1987.

Matthew Barsalou is
a statistical problem
resolution Master Black
Belt (MBB) at BorgWarner
Turbo Systems
Engineering GmbH in
Kirchheimbolanden,
Germany. He has a
master's degree in business administration and
engineering from Wilhelm Büchner Hochschule
in Darmstadt, Germany, and a master's degree in
liberal studies from Fort Hays State University in
Hays, KS. Barsalou is an ASQ senior member and
holds several certifications.

qualityprogress.com ❘ September 2017

QP 53

```
http://www.qualityprogress.com

# Table of Contents for the Digital Edition of Quality Progress - September 2017

Seen and Heard
Progress Report
Mr. Pareto Head
Career Coach
Expert Answers
Field Notes
Data Disruption
The Deal With Big Data
Better Intelligence
A Study in Measurement
Innovation Imperative
Statistics Spotlight
Standard Issues
ASQ's 2017 Quality Resource Guide
Marketplace
Footnotes
Back to Basics
Quality Progress - September 2017 - Intro
Quality Progress - September 2017 - cover1
Quality Progress - September 2017 - cover2
Quality Progress - September 2017 - 1
Quality Progress - September 2017 - 2
Quality Progress - September 2017 - 3
Quality Progress - September 2017 - 4
Quality Progress - September 2017 - 5
Quality Progress - September 2017 - Seen and Heard
Quality Progress - September 2017 - 7
Quality Progress - September 2017 - Progress Report
Quality Progress - September 2017 - 9
Quality Progress - September 2017 - Mr. Pareto Head
Quality Progress - September 2017 - 11
Quality Progress - September 2017 - Career Coach
Quality Progress - September 2017 - 13
Quality Progress - September 2017 - 14
Quality Progress - September 2017 - Expert Answers
Quality Progress - September 2017 - Field Notes
Quality Progress - September 2017 - 17
Quality Progress - September 2017 - 18
Quality Progress - September 2017 - 19
Quality Progress - September 2017 - Data Disruption
Quality Progress - September 2017 - 21
Quality Progress - September 2017 - 22
Quality Progress - September 2017 - 23
Quality Progress - September 2017 - 24
Quality Progress - September 2017 - 25
Quality Progress - September 2017 - The Deal With Big Data
Quality Progress - September 2017 - 27
Quality Progress - September 2017 - 28
Quality Progress - September 2017 - 29
Quality Progress - September 2017 - 30
Quality Progress - September 2017 - 31
Quality Progress - September 2017 - 32
Quality Progress - September 2017 - 33
Quality Progress - September 2017 - Better Intelligence
Quality Progress - September 2017 - 35
Quality Progress - September 2017 - 36
Quality Progress - September 2017 - 37
Quality Progress - September 2017 - 38
Quality Progress - September 2017 - 39
Quality Progress - September 2017 - 40
Quality Progress - September 2017 - 41
Quality Progress - September 2017 - A Study in Measurement
Quality Progress - September 2017 - 43
Quality Progress - September 2017 - 44
Quality Progress - September 2017 - 45
Quality Progress - September 2017 - 46
Quality Progress - September 2017 - 47
Quality Progress - September 2017 - Innovation Imperative
Quality Progress - September 2017 - 49
Quality Progress - September 2017 - 50
Quality Progress - September 2017 - Statistics Spotlight
Quality Progress - September 2017 - 52
Quality Progress - September 2017 - 53
Quality Progress - September 2017 - Standard Issues
Quality Progress - September 2017 - 55
Quality Progress - September 2017 - 56
Quality Progress - September 2017 - 57
Quality Progress - September 2017 - ASQ's 2017 Quality Resource Guide
Quality Progress - September 2017 - 59
Quality Progress - September 2017 - 60
Quality Progress - September 2017 - 61
Quality Progress - September 2017 - 62
Quality Progress - September 2017 - 63
Quality Progress - September 2017 - 64
Quality Progress - September 2017 - 65
Quality Progress - September 2017 - 66
Quality Progress - September 2017 - 67
Quality Progress - September 2017 - Marketplace
Quality Progress - September 2017 - 69
Quality Progress - September 2017 - Footnotes
Quality Progress - September 2017 - 71
Quality Progress - September 2017 - Back to Basics
Quality Progress - September 2017 - cover3
Quality Progress - September 2017 - cover4
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