# Quality Progress - May 2017 - 35

```TA B L E   2

One-sided 2-sample
t-test for H 0
µND − µSD < − 2.5 with 97.5% conﬁdence
level or α = 2.5%, and HA: µND − µSD > − 2.5.
Sample

N

Mean

StDev

SE mean

TA B L E   3

TA B L E   4

One-sided 2-sample
t-test for H 0

µND − µSD > 2.5 with 97.5% conﬁdence
level or α = 2.5%, and HA: µND − µSD < 2.5.
Sample

N

Mean

StDev

One two-sided 2-sample t-test,
H0: µND = µSD and HA: µND ≠ µSD with 95%
conﬁdence level.
Sample

N

Mean

StDev

SE mean

SE mean

1

30

18.450

0.350

0.064

2

30

16.100

0.150

0.027

1

30

18.450

0.350

0.064

1

30

18.450

0.350

0.064

2

30

16.100

0.150

0.027

2

30

16.100

0.150

0.027

Difference = mu (1) − mu (2)

Difference = mu (1) − mu (2)

Difference = mu (1) − mu (2)

Estimate for difference: 2.3500

Estimate for difference: 2.3500

Estimate for difference: 2.3500

95% CI for difference: (2.2094, 2.4906)

95% lower bound for difference: 2.2329

95% lower bound for difference: 2.4671

T-test of difference = −2.5 (vs >):
T-value = 69.76; P-value = 0.000;
DF = 39.

T-test of difference = 2.5 (vs <):
T-value = −2.16; P-value = 0.019;
DF = 39.

T-test of difference = 0 (vs not =):
T-value = 33.80; P-value = 0.000;
DF = 39.

DF = degrees of freedom
mu = mean
N = sample size
SE = standard error
StDev = standard deviation

DF = degrees of freedom
mu = mean
N = sample size
SE = standard error
StDev = standard deviation

fully charged, this value can be set as the lower specification limit of the battery life. We can then calculate the Cpk
with a one-sided specification as the ratio between the difference of the mean and the lower specification limit (LSL),
which is 14 hours, to three standard deviations.4
The Cpk results of the designs are shown in Table 1. Cpk for
the new design and the standard design are 4.23 and 4.66,
respectively. These results show the new design is capable
relative to the specifications and as good or even better
than the standard design. The robustness, as measured by
their SNR, is also better for the new design (SNR = 52.71)
than the standard design (SNR = 107.33).
If the LSL were 16, Cpk for the new and standard designs
would be 0.22 and 2.3, respectively. Apparently, the new
design was not capable but still would pass the TOST. In
this example, if the manufacturers had started production,
they would have had a very high percentage of rejected
batches because the new process was simply not capable.
This shows the inherent weakness of the TOST method
when it is applied as a standalone test. It is incorrect to
accept a new design if the test acceptance standards are
not set right in the first place.
This example also shows the sensitivity of the delta.
If it is too wide, it will accept processes that should not
be approved, even if it passes the hypothesis tests. So,

CI = confidence interval
DF = degrees of freedom
mu = mean
N = sample size
NHST = null hypothesis significance test
SE = standard error
StDev = standard deviation

to make a TOST meaningful for the verification of a new
product design, it must always be supplemented with basic
capability tests.
This ensures poor processes are not approved and prevents rejected products, which can cost millions of dollars
per year and lead to product shortages due to an inability
to ship.
REFERENCES
1. Douglas G. Altman and J. Martin Bland, "Absence of Evidence Is Not
Evidence of Absence," British Medical Journal, Aug. 19, 1995, pp.
311-485.
2. Scott Pardo, Equivalence and Noninferiority Test for Quality,
Manufacturing and Test Engineers, CRC Press, 2014.
3. Carmen R. VanVoorhis and Betsy L. Morgan, "Understanding Power
and Rules of Thumb for Determining Sample Sizes," Tutorials in
Quantitative Methods for Psychology, Vol. 3, No. 2, 2007, pp. 43-50.
4. Richard E. Devor, Tsong-how Chang and John W. Sutherland,
Statistical Quality Design and Control: Contemporary Concepts and
Methods, Macmillan Publishing Co., 1992.

Liem Ferryanto is the director of
technical continuous improvement
at Applied Materials in Santa Clara,
CA. He has a doctorate in industrial
statistics from Technische Universität
Kaiserslautern in Germany. Ferryanto is
a senior member of ASQ.

qualityprogress.com ❘ May 2017

QP 35

```
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Seen and Heard
Progress Report
Field Notes
Mind the Gaps
Solid Footing
Are These the Same?
New Tricks for an Old Tool
Innovation Imperative
Experience More
Career Coach
Statistics Spotlight
Standard Issues
Marketplace
Footnotes
Back to Basics
Quality Progress - May 2017 - intro
Quality Progress - May 2017 - cover1
Quality Progress - May 2017 - cover2
Quality Progress - May 2017 - 1
Quality Progress - May 2017 - 2
Quality Progress - May 2017 - 3
Quality Progress - May 2017 - 4
Quality Progress - May 2017 - 5
Quality Progress - May 2017 - Seen and Heard
Quality Progress - May 2017 - Expert Answers
Quality Progress - May 2017 - Progress Report
Quality Progress - May 2017 - Mr. Pareto Head
Quality Progress - May 2017 - 10
Quality Progress - May 2017 - 11
Quality Progress - May 2017 - Field Notes
Quality Progress - May 2017 - 13
Quality Progress - May 2017 - 14
Quality Progress - May 2017 - 15
Quality Progress - May 2017 - Mind the Gaps
Quality Progress - May 2017 - 17
Quality Progress - May 2017 - 18
Quality Progress - May 2017 - 19
Quality Progress - May 2017 - 20
Quality Progress - May 2017 - 21
Quality Progress - May 2017 - 22
Quality Progress - May 2017 - 23
Quality Progress - May 2017 - Solid Footing
Quality Progress - May 2017 - 25
Quality Progress - May 2017 - 26
Quality Progress - May 2017 - 27
Quality Progress - May 2017 - 28
Quality Progress - May 2017 - 29
Quality Progress - May 2017 - Are These the Same?
Quality Progress - May 2017 - 31
Quality Progress - May 2017 - 32
Quality Progress - May 2017 - 33
Quality Progress - May 2017 - 34
Quality Progress - May 2017 - 35
Quality Progress - May 2017 - New Tricks for an Old Tool
Quality Progress - May 2017 - 37
Quality Progress - May 2017 - 38
Quality Progress - May 2017 - 39
Quality Progress - May 2017 - 40
Quality Progress - May 2017 - 41
Quality Progress - May 2017 - 42
Quality Progress - May 2017 - 43
Quality Progress - May 2017 - Innovation Imperative
Quality Progress - May 2017 - 45
Quality Progress - May 2017 - 46
Quality Progress - May 2017 - Career Coach
Quality Progress - May 2017 - 48
Quality Progress - May 2017 - 49
Quality Progress - May 2017 - Statistics Spotlight
Quality Progress - May 2017 - 51
Quality Progress - May 2017 - 52
Quality Progress - May 2017 - 53
Quality Progress - May 2017 - Standard Issues
Quality Progress - May 2017 - 55
Quality Progress - May 2017 - 56
Quality Progress - May 2017 - 57
Quality Progress - May 2017 - Marketplace
Quality Progress - May 2017 - 59
Quality Progress - May 2017 - Footnotes
Quality Progress - May 2017 - 61
Quality Progress - May 2017 - 62
Quality Progress - May 2017 - 63
Quality Progress - May 2017 - Back to Basics
Quality Progress - May 2017 - cover3
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