Quality Progress - July 2015 - (Page 64)
BACK TO BASICS
BY JOSEPH PAUL MITCHELL
Hypothesis test provides unbiased, statistics-based solutions
HYPOTHESIS TESTING IS one of many
Handbook.1 The p-value is a conditional
Six Sigma tools and techniques used for
Steel tubing is processed in a tempering
probability: In other words, if the UTS of
process improvement. Recently, it was part
oven. Following the tempering process,
tubes processed in January are the same
of a manufacturer's define, measure, ana-
one tube per load is randomly selected and
as February, what is the likelihood of
lyze, improve and control (DMAIC) inves-
tensile tested. The mechanical property
observing this same data versus observing
tigation concerning a suspected variance
chosen for investigation was ultimate ten-
data that are significantly different?
of mechanical properties in steel tubing. In
sile strength (UTS)-the maximum stress
A statistical software program using an
this case, the product's population standard
the tube can withstand before it fractures.
Anderson-Darling test-used to see whether
deviation was unknown, and consequently,
a two-sample t-test was used.
In January, a total of 80 loads were
a sample of data came from a population
processed without straightening issues.
with a specific distribution2-indicated
Data showed the mean UTS for January
normal data sets for January and February.
was 210.7 kilopounds per square inch
Statistical software calculations showed
The investigation took place at an organi-
(KSI) (see Online Figure 1, which can be
(see Online Tables 1 and 2): p-value = 0.000.
zation that fabricates steel tubing for com-
found on this column's webpage at www.
mercial or industrial applications.
qualityprogress.com). Management was
esis was rejected. The result suggested a
Manufacturing specifications for steel
unsure if the mean UTS for February (see
change in UTS had occurred: It increased.
tubing ensure the material will form during
Online Figure 2) had changed because no
the fabrication process. In February, opera-
control charts or other statistical process
tors of equipment that straighten and form
control charts were used for monitoring
The results from hypothesis testing
tubing complained that the material was
the tempering oven.
prompted investigation of the tempering
difficult to form, resulting in less-efficient
The current quality system was pass/
Based on the p-value, the null hypoth-
oven, and the inspection confirmed a heat-
production due to constant equipment
fail-the UTS specification was 200 KSI
ing element was failing and needed to be
(+/- 25). This type of quality practice is
replaced. Due to this condition, the oven
known as lot-acceptance sampling, and it
was unable to reach the correct tempering
variation in material properties. During the
does not evaluate the quality of the load
temperature, and consequently, the tubing
measurement phase of DMAIC, a process
and only provides a basis for conclud-
did not receive proper heat treatment.
map was constructed. Based on the steps
ing all parts are acceptable for further
shown, a key input variable was determined
One possible cause of the problem was a
to be the tempering process-the last heat
Management realized a significant
Hypothesis testing is a valuable tool
for determining whether the difference
between two means is greater than what
treatment the material undergoes prior to
change in UTS may contribute to straight-
straightening and forming operations.
test steps /
opposed to emotions and unsubstantiated
Based on the changes in UTS, hypoth-
would be expected from chance.
This allows for an unbiased decision
based on statistics and probability, as
Null hypothesis: (H0: µ = 211 KSI).
H0: After tempering, mean UTS did
Alternative hypothesis: (Ha: ≠ 211 KSI).
H1: After tempering, mean UTS did change.
Level of significance.
α = 0.05
KSI = kilopounds per square inch
64 QP * www.qualityprogress.com
esis testing was proposed. Hypothesis
testing requires only a few steps: a null
hypothesis, alternative hypothesis, level of
significance and p-value. Table 1 shows the
hypothesis test used in this scenario.
"The significance level is the probability of making the mistake of rejecting the
null hypothesis when it is in fact true,"
states The Certified Quality Engineer
1. Connie M. Borror, ed., The Certified Quality Engineer Handbook, third edition, ASQ Quality Press, 2009.
2. "Anderson-Darling Normality Test," iSixSigma.com, http://
JOSEPH PAUL MITCHELL is a metallurgist at True Temper Sports Inc. in
Amory, MS. He earned his MBA from
Lawrence Technological University
in Southfield, MI. A member of ASQ,
Mitchell is an ASQ-certified quality
Table of Contents for the Digital Edition of Quality Progress - July 2015
Mr. Pareto Head
Open to Change
Turning on the Light Bulb
What‘s Your Theory?
Measure for Measure
Quality in the First Person
ASQ's Continuing Education and Professional Development Directory
One Good Idea
Back to Basics
Quality Progress - July 2015