Lean six sigma process improvement tools and techniques by donna summers chapter 17

Statistics
Chapter 17

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• Statistics, the collection, tabulation,
analysis, interpretation, and presentation
of numerical data, provide a viable method
of supporting or clarifying a topic under
discussion.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• Statistical information should illuminate the
user’s understanding of the issue or
problem at hand.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• A population is a collection of all possible
elements, values, or items associated with
a situation.
– A population can contain a finite number of
things or it may be nearly infinite. Limitations
may be placed on a collection of items to
define the population.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• A sample is a subset of elements or
measurements taken from a population.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.

Statistics
• Descriptive or deductive statistics describe
a population or complete group of data.
When describing a population using
deductive statistics, the investigator must
study each entity within the population. This
provides a great deal of information about the
population, product, or process, but gathering
the information is time-consuming.
• Inductive statistics deal with a limited
amount of data or a representative sample of
the population.
Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• Measurement error is considered to be
the difference between a value measured
and the true value. The error that occurs is
one either of accuracy or of precision.
• Accuracy refers to how far from the actual
or real value the measurement is.
• Precision is the ability to repeat a series
of measurements and get the same value

each time.
Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• A frequency diagram shows the number
of times each of the measured values
occurred when the data were collected.
This diagram can be created either from
measurements taken from a process or
from data taken from the occurrences of
events.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• To create a frequency diagram:
• 1. Collect the data. Record the measurements or counts of the
characteristics of interest.
• 2. Count the number of times each measurement or count occurs.
• 3. Construct the diagram by placing the counts or measured values on

the x axis and the frequency or number of occurrences on the y axis. The
x axis must contain each possible measurement value from the lowest to
the highest, even if a particular value does not have any corresponding
measurements. A bar is drawn on the diagram to depict each of the
values and the number of times the value occurred in the data collected.
• 4. Interpret the frequency diagram. Study the diagrams you create and
think about the diagram’s shape, size, and location in terms of the
desired target specification.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• Histograms
– Similar to frequency diagrams.
• The most notable difference between the two is
that on a histogram the data are grouped into cells.
Each cell contains a range of values.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.

Statistics
• To create a histogram:
– Step 1: Collect the data and construct a tally sheet
– Step 2: Calculate the range
– Step 3: Create the cells by determining the cell
intervals, midpoints, and boundaries
– Step 4: Label the axes
– Step 5: Post the values
– Step 6: Interpret the histogram

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• Analysis of Histograms
– Shape, spread, and location are the
characteristics used to describe a distribution

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics

– Shape: refers to the form that the values of
the measurable characteristics take on
when plotted or graphed.
– Shape is based on the distributions symmetry,
skewness, and kurtosis

– Spread: the distance between the highest
and lowest values
– Location: Where is the distribution in relation
to the target?
Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• Measures of Central Tendency
– Mean
– The mean of a series of measurements is determined
by adding the values together and then dividing this
sum by the total number of values.

– Median
– The median is the value that divides an ordered series
of numbers so that there is an equal number of values
on either side of the center, or median, value.

– Mode

– The mode is the most frequently occurring number in a
group of values.
Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• Measures of Dispersion
– Range
• The range is the difference between the highest
value in a series of values or sample and the
lowest value in that same series.

– Standard Deviation
• The standard deviation shows the dispersion of
the data within the distribution.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• The Central Limit Theorem
– The central limit theorem states that a group

of sample averages tends to be normally
distributed; as the sample size n increases,
this tendency toward normality improves.
– The central limit theorem enables conclusions
to be drawn from the sample data and applied
to a population.

Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.


Statistics
• To Find the Area under the Normal Curve:

Xi  X
Z
standard normal value
s
X i individual X value of interest
X average
s standard deviation
Lean Six Sigma: Process Improvement Tools and Techniques
Donna C. Summers

© 2011 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.