Attributes Data

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• Attributes Data
• Definition - Attributes are quality
  characteristics for
• which each inspected item can be classified as
• conforming or nonconforming to the specification
• on that quality characteristic
• Types
• Fraction nonconforming
• Number nonconforming
• Number of nonconformities per unit
• Average number of nonconformities per unit

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• Attributes Data
• Are best used where subjective characteristics
  must be checked (presence or absence of nicks,
  for example)
• Tend to emphasize defect reduction as the end
  goal (vs. variability reduction)
• defects (count)
• percentage non-conforming (or percentage)
• defect per unit
• Measurements that depend on counting are called
  attributes measurements.

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Control Chart for Fraction Nonconforming
p-chart where
Fraction nonconforming in the ith sample for i
1, 2, . . . , m
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The p-chart - instructions 1. Obtain a series of
samples of some appropriate size. Convenient
sample sizes are 50 and 100. The sample may
actually be the complete lot if the entire lot
has been checked. Have 20 or more groups if
possible, but not less than 10 groups. 2. Count
the number of defective units (warped, undersize,
oversize, or whatever the characteristics may be
in which you are interested). Calculate the value
of p for each sample.
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The p-chart - instructions 3. Calculate p (the
average percentage defective). This is the
centerline for the p-chart. 4. Calculate upper
and lower control limits for the p-chart.
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• Uses of a p-chart
• Characteristics on which it is difficult or
  impractical to obtain variables measurement.
• Studies of defects produced by machines or
  operators which are directly under the machine
  operators control.
• Direct studies of the amount of dropouts,
  shrinkage, or scrap at specific operations

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• Uses of a p-chart - continued
• Can cover all defects and all characteristics,
• Can be a valuable capability study in itself
• Will also provide a good measure of the
  effectiveness of changes, corrections or
  improvements which have been made as a result of
  other studies

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• p-charts vs. x - R-charts
• The p-chart is less powerful than x and R charts.
  It provides less information
• With the x - R chart, we can study the process
  without regard to the specifications - the
  p-chart requires specs.
• The p-chart cannot tell us whether
  non-conformances are caused by poor centering,
  excessive variability, or out-of-control
  conditions.

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• p-charts vs. x - R-charts
• The p-chart cannot warn of trends or shifts
  unless they are so pronounced that they actually
  resulted in a change in the number of defective
  units produced.

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Number of Nonconformities c - the total number
of nonconformities in a unit
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Number of Nonconformities Statistical Basis -
The number of opportunities for nonconformities
is infinitely large and the probability of
occurrence of a nonconformity at any location is
small and constant. Samples are of a constant
size and the inspection unit is the same for
each sample. X number of nonconformities in
the sample where c expected number of
nonconformities
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