IET 603 Quality
Assurance in
Science &
Technology
Travis Fisher
Chapter Outline
3.1 - DESCRIBING VARIATION
3.2 - IMPORTANT DEISCRETE DISTRIBUTIONS
3.3 - IMPORTANT CONTINUOUS DISTRIBUTIONS
3.4 - PROBABILITY PLOTS
3.5 - SOME USEFUL APPROXIMATIONS
Chapter Overview
 To
show how simple tools of descriptive
statistics can be used to express variation
quantitatively in a quality characteristic
when a sample of data on this
characteristic is available.
 To introduce probability distributions and
show how they provide a tool for
modeling or describing the quality
characteristics of a process.
Describing Variation
 No
two units of product produced by a
process are identical.
 Some variation is inevitable.
 Statistics is the science of analyzing data
and drawing conclusions, taking
variations in the data into account.
…Variation
Stem & Leaf Display
A
Stem & Leaf display is one of the most
useful graphical techniques for
summarizing and presenting data.
…Stem & Leaf Display
The Histogram
 Histograms
are a more compact summary
of data than a stem-and-leaf plot.
Constructing a Histogram
 Is
a chart that displays distribution,
center location, and variation of data
by categorizing data.
 Unlike bar graph (commonly used in
Excel), it can show distribution of data.
 Using Minitab a Histogram from the data
below using the following steps.
…Constructing a Histogram
…Constructing a Histogram
…Constructing a Histogram
Shows
distribution
in
comparison
to normal
curve of
same mean
and
standard
deviation.
…Histogram
Box Plot



Boxplot is used to obtain information about the shape,
dispersion, and mid-value of given data.
Spot outliers.
Used to assess the symmetry of the data.
Constructing a Box Plot
 Go



to
Minitab > Graph > Boxplot
Choose the option “Simple”
Select the data column
…Constructing a Box Plot
Box Plot Analysis





The line drawn through the box represents the median of
the data.
The edge above the median represents the first quartile
(Q1), while the edge below represents the third quartile
(Q3). Thus the box portion of the plot represents the
interquartile range (IQR = Q3-Q1), or the middle 50% of
the observations.
The lines extending from the box are called whiskers. The
whiskers extend outward to indicate the lowest and
highest values in the data set (they exclude outliers).
Extreme values, or outliers, are represented by dots. A
value is considered an outlier if it is outside the box
(greater than Q3 or less than Q) by more than 1.5 times
the IQR.
Brush may be used on the graph to find the values of
outliers.
Probability Distributions
A
probability distribution is a mathematical
model that relates the value of the variable
with the probability of occurrence of that value
in the population.
Normality Test

There are various methods to check for Normality. We will discuss one of the
most commonly used methods:
 Probability Plot
 Follow the path in Minitab:
 Minitab > Graph > Probability Plot
 Consider the following data of the number of accidents in a yearly
highway accident report.
Normality Test: Probability Plot
Normality Test: Probability Plot
Normality Test: Probability Plot

P – value = 0.436. Since p – value is greater
than 0.05, the given data is normal.
0.05 is the
alpha value
(alpha risk /
type – I error
the
significance
level).
Generally,
the value
assigned is 5%
unless stated
otherwise or
demanded
by the
process.
Normality Test: Probability Plot

The discrete probability distribution of the number of
successes in a sequence of n independent yes/no
experiments, each of which yields success with probability p.
…Binomial Distributions
References


AuthorStream. (2013). Retrieved from
http://webcache.googleusercontent.com/search?q=cache:MUUMYyOrpp8J:www.aut
horstream.com/Presentation/aSGuest34389-294160-introduction-minitab-education-pptpowerpoint/+minitab+ppt&cd=1&hl=en&ct=clnk&gl=us
Montgomery, D. C. (2009). Introduction to Statistical Quality Control Sixth Edition.
Questions?