PTTE 434
Quality Organization &
Management Lecture 7
Ch 11: Statistical Tools for Analyzing
Data (Process Control Charts)
Chapter Overview
 Statistical Fundamentals
 Process Control Charts
 Some Control Chart Concepts
 Process Capability
 Other Statistical Techniques in Quality
Management
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Some useful URLs on Control Charts
 Stat Soft Quality Control Charts:
http://www.statsoft.com/textbook/stquacon.html
 Free Quality. Org (Many free tools)
http://www.freequality.org
(Please Note: These tools are supported by MS Excel and Access
and download best when MS Internet Explorer is used.)
 Wikipidia on Control Charts
http://en.wikipedia.org/wiki/Control_chart
 Six Sigma on Control Charts
http://www.isixsigma.com/st/control_charts/
 Univariant and Multivariant Control Charts
http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc3.htm
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Process Control Charts
Slide 1 of 37
 Process Charts


Tools for monitoring process variation.
The figure on the following slide shows a
process control chart. It has an upper limit,
a center line, and a lower limit.
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Process Control Charts
Slide 2 of 37
Control Chart (Figure 10.3 in the Textbook)
The UCL, CL, and
LCL are computed
statistically
Upper Control
Limit (UCL)
Each point represents
data that are plotted
sequentially
Center
Line (CL)
Lower Control
Limit (LCL)
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Process Control Charts
Slide 3 of 37
 Variables and Attributes

To select the proper process chart, we must
differentiate between variables and attributes.



A variable is a continuous measurement such
as weight, height, or volume.
An attribute is the result of a binomial process
that results in an either-or-situation.
The most common types of variable and attribute
charts are shown in the following slide.
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Process Control Charts
Slide 4 of 37
Variables and Attributes
Variables
Attributes
X (process population average)
P (proportion defective)
X-bar (mean for average)
np (number defective)
R (range)
C (number conforming)
MR (moving range)
nonconforming)
U (number
S (standard deviation)
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Process Control Charts
Slide 5 of 37
Central Requirements for Properly Using
Process Charts
1. You must understand the generic process for implementing
process charts.
2. You must know how to interpret process charts.
3. You need to know when different process charts are used.
4. You need to know how to compute limits for the different types
of process charts.
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Process Control Charts
Slide 6 of 37
A Generalized Procedure for
Developing Process Charts


Identify critical operations in the process
where inspection might be needed. These are
operations in which, if the operation is
performed improperly, the product will be
negatively affected.
Identify critical product characteristics. These
are the attributes of the product that will result
in either good or poor function of the product.
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Process Control Charts
Slide 7 of 37
 A Generalized Procedure for Developing Process
Charts (continued)
 Determine whether the critical product characteristic
is a variable or an attribute.


Select the appropriate process control chart from
among the many types of control charts. This
decision process and types of charts available are
discussed later.
Establish the control limits and use the chart to
continually improve.
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Process Control Charts
Slide 8 of 37
 A Generalized Procedure for Developing
Process Charts (continued)

Update the limits when changes have been
made to the process.
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Process Control Charts
Slide 9 of 37
 Understanding Control Charts

A process chart is nothing more than an
application of hypothesis testing where the
null hypothesis is that the product meets
requirements.


An X-bar chart is a variables chart that
monitors average measurement.
An example of how to best understand control
charts is provided under the heading
“Understanding Control Charts” in the
textbook.
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Process Control Charts
Slide 10 of 37
 X-bar and R Charts

The X-bar chart is a process chart used to monitor the
average of the characteristics being measured. To set
up an X-bar chart select samples from the process for
the characteristic being measured. Then form the
samples into rational subgroups. Next, find the average
value of each sample by dividing the sums of the
measurements by the sample size and plot the value
on the process control X-bar chart.
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Process Control Charts
Slide 11 of 37
 X-bar and R Charts (continued)

The R chart is used to monitor the variability or
dispersion of the process. It is used in conjunction
with the X-bar chart when the process characteristic
is variable. To develop an R chart, collect samples
from the process and organize them into subgroups,
usually of three to six items. Next, compute the
range, R, by taking the difference of the high value in
the subgroup minus the low value. Then plot the R
values on the R chart.
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Process Control Charts
Slide 12 of 37
X-bar and R Charts
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Process Control Charts
Slide 13 of 37
 Interpreting Control Charts


Before introducing other types of process charts, we
discuss the interpretation of the charts.
The figures in the next several slides show different
signals for concern that are sent by a control chart, as
in the second and third boxes. When a point is found
to be outside of the control limits, we call this an “out of
control” situation. When a process is out of control, the
variation is probably not longer random.
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Process Control Charts
Slide 14 of 37
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Process Control Charts
Slide 15 of 37
Control Chart Evidence for Investigation
(Figure 10.10 in the textbook)
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Process Control Charts
Slide 16 of 37
Control Chart Evidence for Investigation
(Figure 10.10 in the textbook)
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Process Control Charts
Slide 17 of 37
Control Chart Evidence for Investigation
(Figure 10.10 in the textbook)
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Process Control Charts
Slide 18 of 37
 Implications of a Process Out of Control



If a process loses control and becomes
nonrandom, the process should be stopped
immediately.
In many modern process industries where
just-in-time is used, this will result in the
stoppage of several work stations.
The team of workers who are to address the
problem should use a structured problem
solving process.
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Process Control Charts
Slide 19 of 37
 X and Moving Range (MR) Charts for
Population Data


At times, it may not be possible to draw
samples. This may occur because a process
is so slow that only one or two units per day
are produced.
If you have a variable measurement that you
want to monitor, the X and MR charts might be
the thing for you.
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Process Control Charts
Slide 20 of 37
 X and Moving Range (MR) Charts for
Population Data (continued)



X chart. A chart used to monitor the mean of a
process for population values.
MR chart. A chart for plotting variables when
samples are not possible.
If data are not normally distributed, other
charts are available.
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Process Control Charts
Slide 21 of 37
 g and h Charts


A g chart is used when data are geometrically
distributed, and h charts are useful when data are
hypergeometrically distributed.
The next slide presents pictures of geometric and
hypergeometric distributions. If you develop a
histogram of your data, and it appears like either of
these distributions, you may want to use either an h or
a g chart instead of an X chart.
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Process Control Charts
Slide 22 of 37
h and g Distributions (Figure 10.12 in the textbook)
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Process Control Charts
Slide 23 of 37
 Control Charts for Attributes


We now shift to charts for attributes. These charts deal
with binomial and Poisson processes that are not
measurements.
We will now be thinking in terms of defects and
defectives rather than diameters or widths.


A defect is an irregularity or problem with a larger
unit.
A defective is a unit that, as a whole, is not
acceptable or does not meet specifications.
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Process Control Charts
Slide 24 of 37
 p Charts for Proportion Defective



The p chart is a process chart that is used to graph the
proportion of items in a sample that are defective
(nonconforming to specifications)
p charts are effectively used to determine when there
has been a shift in the proportion defective for a
particular product or service.
Typical applications of the p chart include things like
late deliveries, incomplete orders, and clerical errors
on written forms.
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Process Control Charts
Slide 25 of 37
 np Charts


The np chart is a graph of the number of
defectives (or nonconforming units) in a
subgroup. The np chart requires that the
sample size of each subgroup be the same
each time a sample is drawn.
When subgroup sizes are equal, either the p
or np chart can be used. They are essentially
the same chart.
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Process Control Charts
Slide 26 of 37
 np Charts (continued)

Some people find the np chart easier to use
because it reflects integer numbers rather than
proportions. The uses for the np chart are
essentially the same as the uses for the p
chart.
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Process Control Charts
Slide 27 of 37
 c and u Charts

The c chart is a graph of the number of
defects (nonconformities) per unit. The units
must be of the same sample space; this
includes size, height, length, volume and so
on. This means that the “area of opportunity”
for finding defects must be the same for each
unit. Several individual unites can comprise
the sample but they will be grouped as if they
are one unit of a larger size.
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Process Control Charts
Slide 28 of 37
 c and u Charts (continued)

Like other process charts, the c chart is used
to detect nonrandom events in the life of a
production process. Typical applications of
the c chart include number of flaws in an auto
finish, number of flaws in a standard typed
letter, and number of incorrect responses on a
standardized test
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Process Control Charts
Slide 29 of 37
 c and u Charts (continued)


The u chart is a graph of the average number of
defects per unit. This is contrasted with the c chart,
which shows the actual number of defects per
standardized unit.
The u chart allows for the units sampled to be different
sizes, areas, heights and so on, and allows for different
numbers of units in each sample space. The uses for
the u chart are the same as the c chart.
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Process Control Charts
Slide 30 of 37
 Other Control Charts

s Chart. The s (standard deviation) chart is
used in place of the R chart when a more
sensitive chart is desired. These charts are
commonly used in semiconductor production
where process dispersion is watched very
closely.
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Process Control Charts
Slide 31 of 37
 Other Control Charts (continued)


Moving Average Chart. The moving average
chart is an interesting chart that is used for
monitoring variables and measurement on a
continuous scale.
The chart uses past information to predict
what the next process outcome will be. Using
this chart, we can adjust a process in
anticipation of its going out of control.
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Process Control Charts
Slide 32 of 37
 Other Control Charts (continued)

Cusum Chart. The cumulative sum, or cusum,
chart is used to identify slight but sustained
shifts in a universe where there is no
independence between observations.
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Process Control Charts
Slide 33 of 37
Summary of Chart Formulas (Table 10.2 in the textbook)
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Process Control Charts
Slide 34 of 37
 Some Control Chart Concepts

Choosing the Correct Control Chart

Obviously, it is key to choose the correct control
chart. Figure 10.19 in the textbook shows a
decision tree for the basic control charts. This
flow chart helps to show when certain charts
should be selected for use.
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Process Control Charts
Slide 35 of 37
 Some Control Chart Concepts (continued)

Corrective Action. When a process is out of control,
corrective action is needed. Correction action steps
are similar to continuous improvement processes.
They are
 Carefully identify the problem.


Form the correct team to evaluate and solve the
problem.
Use structured brainstorming along with fishbone
diagrams or affinity diagrams to identify causes of
the problem.
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Process Control Charts
Slide 36 of 37
 Some Control Chart Concepts (continued)

Corrective Action (continued)
 Brainstorm to identify potential solutions to
problems.




Eliminate the cause.
Restart the process.
Document the problem, root causes, and
solutions.
Communicate the results of the process to all
personnel so that this process becomes
reinforced and ingrained in the operations.
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Process Control Charts
Slide 37 of 37
 Some Control Chart Concepts (continued)

How Do We Use Control Charts to Continuously
Improve?
 One of the goals of the control chart user is to
reduce variation. Over time, as processes are
improved, control limits are recomputed to show
improvements in stability. As upper and lower

control limits get closer and closer together, the
process improving.
The focus of control charts should be on
continuous improvement and they should be
updated only when there is a change in the
process.
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Process Capability
Slide 1 of 4
 Process Stability and Capability



Once a process is stable, the next emphasis is to
ensure that the process is capable.
Process capability refers to the ability of a process to
produce a product that meets specifications.
Six-sigma program such as those pioneered by
Motorola Corporation result in highly capable
processes.
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Process Capability
Slide 2 of 4
Six-Sigma Quality (Figure 10.21 in the textbook)
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Process Capability
Slide 3 of 4
 Process Versus Sampling Distribution

To understand process capability we must first
understand the differences between population and
sampling distributions.



Population distributions are distributions with
all the items or observations of interest to a
decision maker.
A population is defined as a collection of all
the items or observations of interest to a
decision maker.
A sample is subset of the population.
Sampling distributions are distributions that
reflect the distributions of sample means.
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Process Capability
Slide 4 of 4
 The Difference Between Capability and
Stability?


Once again, a process is capable if individual
products consistently meet specifications.
A process is stable if only common variation is
present in the process.
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Determine
characteristic
to be charted.
Is the data
variable?
YES
How to choose the correct control chart
NO
NO
Non-conforming
units? (% bad
parts)
Nonconformities?
(I.e., discrepancies
per part.)
YES
YES
NO
NO
Constant
sample size?
YES
Use X - MR chart.
Use np or
p chart.
NO
Use
m
chart.
YES
YES
Is it homogeneous,
or not conducive to
subgroup sampling?
(e.g., chemical
bath, paint
batch, etc.)
Is sample
space
constant?
Use
p chart.
Can subgroup
averages be
conveniently
computed?
Use
c or m
chart.
Use
median
chart.
NO
YES
Next slide.
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How to choose the correct control chart
(from previous page)
Can subgroup
averages be
conveniently
computed?
NO
Use
median
chart.
YES
NO
Is the subgroup
size < 9?
Use
X - R chart
.
YES
Can s be calculated
for each group?
NO
Use
X - R chart
.
YES
Use
X - s chart
.
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