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					  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
   variables data.
   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 Data
   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.
Yes/No Data

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?
Counting Data
  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
  examples are:
      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.


Operational Definitions
   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.
Operational Definition
   According to Dr. W. Edwards Deming, an operational
   definition includes:
      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.
Operational Definitions
 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
 invoice contains.
   Select one of the variables below.   Develop an operational
   definition for the variable.

      On-Time Delivery

      Rework in a Department

      Injury at Work

      Customer Complaint

      Invoice Error
Variables Data
   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 mean.
   The equation for the standard deviation is given below.

                       (X  X )
                             n 1

   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.

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