15
2
Quality Analysis and Improvement
Tools/Techniques Used in This Book
This chapter gives a brief denition/description of each of the quality
analysis and improvement tools/techniques used in the case studies pre-
sented in this book. Because this is not a statistics textbook, in-depth cov-
erage of each of these tools or techniques is beyond the scope of the book.
However, a useful reference is provided for the interested reader for each
tool and technique.
2.1 Confidence Interval Estimation
Condence interval estimation is a technique to estimate a population
parameter (such as population proportion) using sample data. The estimate
is calculated for a given condence level and is expressed as an interval.
The higher the condence level is, the less precise the interval estimate. See
Montgomery and Runger (2011) for an excellent introduction to condence
interval estimation.
An application of this technique to Six Sigma is illustrated using Minitab
®
in Chapter 3.
2.2 Hypothesis Testing
Hypothesis testing is a technique to test whether there is enough statisti-
cal evidence to reject a claim. Typically, the claim is expressed as the “null
hypothesis,” and an “alternative hypothesis” is considered to verify which of
these two hypotheses is true. These two hypotheses are mutually exclusive (if
one is true, the other one is not) and collectively exhaustive (no other hypoth-
esis is possible). Hypothesis testing is explained in detail in Montgomery
and Runger (2011).
An application of this technique to Six Sigma is illustrated using Minitab
®
in Chapter 4.
16 Six Sigma Case Studies with Minitab
®
2.3 Chi-Square Analysis
Chi-square analysis is a type of hypothesis testing where a sample statistic
(called chi-square value) used in the test is assumed to follow a chi-square
distribution. This technique is explained in detail in Black (2011).
Applications of this technique to Six Sigma are illustrated using Minitab
®
in Chapters 4 and 15.
2.4 Process Capability Analysis
If USL is the upper specication limit for a process, LSL is the lower speci-
cation limit for a process, µ is the process mean, and σ is the process
standard deviation, the following process capability ratios can measure
process performance:
First-generation process capability ratio,
=
C
USL LSL
p
Second-generation process capability ratio with respect to LSL,
=
µ−
σ
C
LSL
3
pl
Second-generation process capability ratio with respect to USL,
=
−µ
σ
C
USL
3
pu
Second-generation process capability ratio,
=CC
C
MINIMUMof{ ,}
pk pl pu
The higher the C
p
and C
pk
values are, the better the process is. See Ryan
(2011) for further explanation of these ratios.
An application of the process capability ratios to Six Sigma is illustrated
using Minitab
®
in Chapter 6.
17Quality Analysis and Improvement Tools/Techniques Used in This Book
2.5 Binary Logistic Regression
Binary logistic regression is a technique used to predict the outcome of a
binary categorical variable with exactly two possible outcomes (e.g., Yes or
No for whether a product is defective). This technique is explained in detail
in Black (2011).
An application of this technique to Six Sigma is illustrated using Minitab
®
in Chapter 7.
2.6 Item Analysis
Item analysis is used to check whether there is a correlation among categori-
cal responses to multiple questions in a customer survey. See Boslaugh (2012)
for an excellent introduction to item analysis. An application of this tech-
nique to Six Sigma is illustrated using Minitab
®
in Chapter 8.
2.7 Cluster Analysis
Cluster analysis helps group customers into various clusters, using coordi-
nate systems and Euclidean distances. See Boslaugh (2012) for a thorough
introduction to cluster analysis.
An application of this technique to Six Sigma is illustrated using Minitab
®
in Chapter 8.
2.8 Mixture Design and Analysis of Experiments
Mixture design and analysis of experiments is a technique used to opti-
mize the proportion of each of the components of a mixture such as a fuel
mixture or a juice blend. This technique is explained in detail in Perry and
Bacon (2006).
An application of this technique to Six Sigma is illustrated using Minitab
®
in Chapter 9.

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