Types of Data
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Control charts give us a picture of our process over time. This
picture tells us when to leave our process alone (i.e., the
process is in control) or when to look for a problem (i.e., an
assignable cause is present).
There are many different types of control charts. However, you
can group control charts into two major categories. The type of
data being charted distinguishes these two categories. There
are two types of data you can have: attributes data and
Both these types of data are introduced in this module. With
attributes data, there is a need to develop specific descriptions.
These descriptions, which are called operational definitions, are
also introduced in this module.
For variables data, the standard deviation is an important
measurement as well as the average. Both of these terms are
explored in more detail below.
In this module you will learn:
1. What attributes data are.
2. What an operational definition is.
3. What variables data are.
4. What the average and standard deviation are.
It is important to know what type of data you will collect so you
can determine what type of control chart to construct.
Different charts will give different information. Attributes charts
include p, np, c and u charts. Variables charts include Xbar-R
charts, Xbar-s charts, individuals charts and moving average
and moving range charts.
Attributes control charts are based on attributes data. These
types of data are often referred to as discrete data. There are
two kinds of attributes data: yes/no type of data and counting
data. p and np control charts are used with yes/no type data; c
and u charts are used with counting type data. The two types
of attributes data are described below.
For one item, there are only two possible outcomes:
either it passes or it fails some preset specification.
Each item inspected is either defective (i.e., it does
not meet the specifications) or is not defective (i.e.,
it meets specifications). Examples of the yes/no
attributes data are:
mail delivery: is it on time or not on time?
phone answered: is it answered or not answered?
invoice correct: is it correct or not correct?
stock item: is it in stock or not in stock?
cycle count: is it correct or not correct?
product : in-spec or out of spec?
supplier: material received on-time or not on-time?
With counting data, you count the number of defects. A
defect occurs when something does not meet a preset
specification. It does not mean that the item itself is
defective. For example, a television set can have a
scratched cabinet (a defect) but still work properly. When
looking at counting data, you end up with whole numbers
such as 0, 1, 2, 3; you can't have half of a defect.
To be considered counting data, the opportunity for defects
to occur must be large; the actual number that occurs must
be small. For example, the opportunity for customer
complaints to occur is large. However, the number that
actually occurs is small. Thus, the number of customer
complaints is an example of counting type data. Other
number of mistakes in picking
number of items shipped incorrectly
number of accidents for delivery trucks
For your organization, what are some examples of yes/no type
data and counting type data. List your responses below.
When working with attributes data, you have to have a clear
understanding of whether the item you are looking at is
defective or not (yes/no type data) or whether it should be
counted as a defect (counting type data). In order to know
whether a shipment was on time or to count the number of on-
time shipments, you have to have a definition of what "on time"
means. Is "on time" anywhere from 1:55 p.m. to 2:05 p.m.,
anytime before 2:00 p.m., or anytime between 2:00 p.m. and
2:15 p.m.? This clear understanding of a quality expectation is
called an operational definition.
According to Dr. W. Edwards Deming, an operational
a written statement (and/or a series of examples) of criteria or
guidelines to be applied to an object or to a group.
a test of the object or group for conformance with the guidelines
that includes specifics such as how to sample, how to test, and
how to measure.
a decision: yes, the object or the group did meet the
guidelines; no, the object or group did not meet the
guidelines; or the number of times the object or group did not
meet the guidelines.
Using an invoice error example, the written
statement may read "An invoice error is an
incorrect shipping amount or a wrong
price." The test could be to:
compare every invoice to the packing list to
check for incorrect shipping amounts and,
compare every invoice to a price schedule to
check for wrong prices.
Based on these guidelines and a test for
conformance with these guidelines, you
could make a decision as to whether an
invoice is defective or how many defects an
Select one of the variables below. Develop an operational
definition for the variable.
Rework in a Department
Injury at Work
Variables control charts are based on variables data. Variables
data consist of observations made from a continuum.
That is, the observation can be measured to any decimal place
you want if your measurement system allows it.
Some examples of variables data are contact time with a
customer, sales dollars, amount of time to make a delivery,
height, weight, and costs.
For your organization, what are some examples of variables
data? Record your answers below.
Average and Standard Deviation
In dealing with variables data, the average and standard
deviation are very important parameters. One must understand
what is meant by these terms.
The average (also called the mean) is probably well understood
by most. It represents a "typical" value. For example, the
average temperature for the day based on the past is often
given on weather reports. It represents a typical temperature
for the time of year.
The average is calculated by adding up the results you have and
dividing by the number of results. For example, suppose the
last five customer complaints took 5, 6, 2, 3, and 8 days to
close. The average is determined by adding up these five
numbers and dividing by 5. The average is denoted by and in
this case is;
X 5 6 2 3 8 24 4.8
n 5 5
Average and Standard Deviation
While the average is understood by most, few understand the
standard deviation, denoted by the letter s.
The standard deviation can be thought of as an average
distance (the standard) that each individual point is away from
The equation for the standard deviation is given below.
(X X )
We will be using control charts to estimate what our process
average is and what the process standard deviation is. For
these two numbers to have any meaning, the process must be
in statistical control.
Control charts can be divided into two major categories:
attribute control charts and variable control charts.
Attribute control charts are based on attribute data. There
are two types of attributes data: yes/no type and counting
data. Yes/no type attributes data have only two possible
outcomes: either the item is defective or it is not defective.
With counting type attributes data, the number of defects
is counted. With attributes data, there is the need for
operational definitions. Operational definitions are used to
determine what constitutes a defective item or a defect.
Variable control charts are based on variables data.
Variables data are data from a continuum. The basic
probability distribution underlying the calculation of control
limits for variables data is the normal distribution.