Attributes.ppt

Quality
Improvement
PowerPoint presentation to accompany
Besterfield, Quality Improvement, 9e
Chapter 9- Control
Charts for Attributes

Quality Improvement, 9e
Dale H. Besterfield
© 2013, 2008 by Pearson Higher Education, Inc
Upper Saddle River, New Jersey 07458 • All Rights Reserved
2
Outline
 Attribute
 Control Charts for Nonconforming Units
 Control Charts for Count of Nonconformities
 A Quality Rating System

Dale H. Besterfield
3
Learning Objectives
When you have completed this chapter you should:
 Know limitations of variable control charts and the different
types of attibute charts.
 Know the objectives of the p chart group and the applicable
distribution.
 Be able to construct a:
 Fraction defective chart- fixed subgroup size
 Fraction defective chart-variable subgroup size
 Percent defective chart
 Number defective chart

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4
Learning Objectives cont’d.
When you have completed this chapter you should:
 Know how to minimize the effect of variable
subgroup size.
 Know the applications of the c chart group, the
applicable distribution and two conditions.
 Be able to construct a c chart and a u chart and
know the difference between them.
 Know the three classes of defect severity

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5
 The term Attribute refers to those quality
characteristics that conform to specifications
or do not conform to specifications.
 Attribute are used:
1. Where measurements are not possible.
2. Where measurements can be made but are
not made because of time, cost, or need.
Attribute

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 A nonconformity is a departure of a quality
characteristic from its intended level or state
that occurs with a severity sufficient to cause
an associated product or service not to meet
a specification requirement.
 Defect is concerned with satisfying intended
normal, or reasonably foreseeable, usage
requirement.
Attribute

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 Defect is appropriate for use when evaluation
is in terms of usage.
 Nonconformity is appropriate for conformance
to specifications.
 The term Nonconforming Unit is used to
describe a unit of product or service
containing at least one nonconformity.
Attribute

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 Defective is analogous to defect and is
appropriate for use when unit of product
or service is evaluated in terms of usage
rather than conformance to specifications.
 Limitations of variable control charts:
These charts cannot be used for quality
characteristics which are attributes.
Attribute

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Types of Attribute Charts:
1. Nonconforming Units (based on the
Binomial distribution): p chart, np chart.
2. Nonconformities (based on the Poisson
distribution): c chart, u chart.
Attribute

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 The P Chart is used for data that consist of the
proportion of the number of occurrences of an
event to the total number of occurrences.
 It is used in quality to report the fraction or
percent nonconforming in a product, quality
characteristic, or group of quality characteristics.
The P Chart

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Formula:
 The fraction nonconforming, p, is usually small,
say, 0.10 or less.
 Because the fraction nonconforming is very
small, the subgroup sizes must be quite large
to produce a meaningful chart.
np
p
n

The P Chart

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 It can be used to control one quality
characteristic, as is done with X bar and R chart,
 Or to control a group of quality characteristics of
the same type or of the same part,
 Or to control the entire product.
 It can be established to measure the quality
produced by a work center, by a department, by a
shift, or by an entire plant.
The P Chart

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 It is frequently used to report the
performance of an operator, group of
operators, or management as a means of
evaluating their quality performance.
 The subgroup size of the P chart can be
either variable or constant.
The P Chart

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Objectives of the P Chart:
1. Determine the average quality level: This
information provides the process
capability in terms of attributes.
2. Bring to the attention of management
any changes in the average.
3. Improve the product quality: Ideas for
quality improvement.
The P Chart

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Objectives of the P Chart cont’d:
4. Evaluate the quality performance of
operating and management personnel.
5. Suggest places to use Xbar and R chart:
They are more sensitive to variation.
6. Determine acceptance criteria of a
product before shipment to the customer.
The P Chart

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P-Chart Construction for Constant
Subgroup Size
1. Select the quality characteristic(s):
a) Single quality characteristic.
b) Group of quality characteristics.
c) A part.
d) An entire product.
e) A number of products.
f) It can be established for performance control of an
operator, work center, department, shift, plant, or
corporation
The P Chart

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P Chart Construction for Constant Subgroup Size
cont’d.
2. Determine the subgroup size and method:
 The size of the subgroup is a function of the
proportion nonconforming.
 A minimum size of 50 is suggested as a
starting point.
The P Chart

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cont’d.
3. Collect the data:
 At least 25 subgroups.
 Different sources (Check sheet).
 For each subgroup the proportion
nonconforming is calculated by the formula
P = np/n
The P Chart

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4. Calculate the trial central line and the control
limits:
(1 )
3
(1 )
3
np
p
n
p p
UCL p
n
p p
LCL p
n


 

 


The P Chart

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FIGURE 9-2 A p Chart to Illustrate the Trial Central Line and
Control Limits Using the Data from Table 9-1

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cont’d.
5. Establish the revised central line and control limits.
0
0 0
0
0 0
0
(1
3
(1 )
3
d
new
d
np np
p p
n n
p p
UCL p
n
p p
LCL p
n

 


 

 


The P Chart

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FIGURE 9-3 Continuing Use of the p Chart for Representative
Values of the Proportion Nonconforming, p

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 The P Chart is most effective if it is posted
where operating and quality personnel can
view it.
 The control limits are usually three standard
deviations from the central value. Therefore,
approximately 99% of the plotted points, P,
will fall between the upper and lower control
limits.
The P Chart

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 A P Chart will also indicate long-range
trends in quality, which will help to
evaluate changes in personnel, methods,
equipment, tooling, materials, and
inspection techniques.
 P-chart is based on the binomial
distribution.
The P Chart

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FIGURE 9-4 Various Techniques for Presenting p -Chart Information

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P Chart Construction for Variable Subgroup Size
1. Collect the data.
2. Determine the trial central line and control
limits: Since the subgroup size changes each
day, limits must be calculated for each day.
The P Chart

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FIGURE 9-5 Preliminary Data, Central
Line, and Trial Control Limits
FIGURE 9-5 Preliminary Data, Central Line, and Trial Control Limits

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cont’d.
2. As the subgroup size gets larger, the control
limits are closer together.
3. Establish revised central line and control limits:
The P Chart

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cont’d.
 If Po is known, the process of data collection
and trial control limits is not necessary.
 P is the proportion (fraction) nonconforming
in a single subgroup.
 Pbar is the average proportion (fraction)
nonconforming of many subgroups.
The P Chart

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cont’d.
 Po is the standard or reference value of the
proportion (fraction) nonconforming based
on the best estimate of PBar.
 Φ is the population proportion (fraction)
nonconforming.
The P Chart

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Minimizing the Effect of Variable Subgroup Size
1. Control limits for an average subgroup size: By
using an average subgroup size, one limit can
be calculated and placed on the control chart.
0 0
0
0 0
0
(1
3
(1 )
3
av
av
av
n
n
g
p p
UCL p
n
p p
LCL p
n


 

 

The P Chart

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FIGURE 9-7 Chart for May Data Illustrating Use of an
Average Subgroup Size

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Minimizing the Effect of Variable Subgroup Size cont’d.
Case I: This case occurs when a point (subgroup
fraction nonconforming) falls inside the limits and
its subgroup size is smaller than the average
subgroup size.
Case II: This case occurs when a point (subgroup
fraction nonconforming) falls inside the average
limits and its subgroup size is larger than the
average subgroup size.
The P Chart

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34
Minimizing the Effect of Variable Subgroup Size cont’d.
Case III: This case occurs when a point (subgroup
fraction nonconforming) falls outside the limits and
its subgroup size is larger than the average
subgroup size.
Case IV: This case occurs when a point (subgroup
fraction nonconforming) falls outside limits and its
subgroup size is less than the average subgroup
size.
The P Chart

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FIGURE 9-8 p Chart Illustrating Central Line and Control
Limits for Different Subgroup Sizes

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Number Nonconforming Chart (np):
 The np chart is easier for operating personnel
to understand than the p chart.
 The limitation that this chart has is that the
subgroup size needs to be constant.
The np Chart

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0
0 0 0
Central Line =
Control Limits = 3 (1 )
np
np np p
 
The np Chart

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Number Nonconforming Chart (np):
 If the fraction nonconforming po is unknown,
then it must be determined by collecting
data, calculating trial control limits, and
obtaining the best estimate of po.
The np Chart

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FIGURE 9-9 Number Nonconforming Chart ( np Chart)

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 For an attribute this process is much simpler.
 The process capability is the central line of
the control chart.
 Management is responsible for the capability.
 When the plotted point is outside the control
limit, operating personnel are usually
responsible.
Process Capability

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FIGURE 9-10 Process Capability Explanation and Responsibility

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 The nonconformities chart controls the count
of nonconformities within the product or
service.
 An item is classified as a nonconforming unit
whether it has one or many nonconformities.
 Count of nonconformities (c) chart.
 Count of nonconformities per unit (u) chart.
Control Charts for Count of Non-
conformities

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 Since these charts are based on the Poisson
distribution, two conditions must be met:
1. The average count of nonconformities
must be much less than the total possible
count of nonconformities.
2. The occurrences are independent.
conformities

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Objectives:
1. Determine the average quality level: This
information gives the initial process capability.
2. Bring to the attention of management any
changes in the average.
3. Improve the product quality: Ideas for quality
improvement.
conformities

Dale H. Besterfield
45
Objectives cont’d.:
4. Evaluate the quality performance of
operating and management personnel.
5. Suggest places to use Xbar and R chart.
6. Determine acceptance criteria of a
product before shipment to the customer.
conformities

Dale H. Besterfield
46
C Chart construction:
1. Select the quality characteristic(s):
a) Single quality characteristic.
b) Group of quality characteristics.
c) A part.
d) An entire product.
e) A number of products.
f) It can be established for performance control of
an: operator, work center, department, shift, plant,
or corporation
conformities

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47
C Chart construction cont’d:
2. Determine the subgroup size and method:
3. Collect the data:
 At least 25 subgroups.
 Different sources.
conformities

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c-Chart Construction cont’d:
4. Calculate the trial central line and the control
limits:
3
3
c
c
g
UCL c c
LCL c c

 
 
conformities

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FIGURE 9-11 Control Chart for Count of Nonconformities ( c Chart), Using
Preliminary Data

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5. Establish the revised central line and control
limits
 d
new 0
d
0 0
0 0
c -c
c = c =
g -g
UCL = c + 3 c
LCL = c -3 c
conformities

Dale H. Besterfield
51

Dale H. Besterfield
52
6. Achieve the objectives: The reason for the
control chart is to achieve one or more of the
previously stated objectives.
conformities
C chart construction cont’d:

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Chart for Count of Nonconformities/Unit (u Chart)
3
3
c
c
u u
n n
u
UCL u
n
u
LCL u
n
 
 
 


conformities/Unit

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FIGURE 9-13 u Chart for Errors on Waybills

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Chart for Count of Nonconformities/Unit
(u Chart)
 Scale selected is continuous for the u chart.
For the c chart is discrete.
 Subgroup size for the u chart can vary. For
the c chart is 1.
 The u chart is limited in that we do not
know the location of the nonconformities.
conformities

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Nonconformity Classification:
1. Critical nonconformities: Unsafe conditions for
individuals using, maintaining, or depending upon the
product.
2. Major nonconformities: Result in failure or reduce
materially the usability of the product for its intended
purpose.
3. Minor nonconformities: Reduce materially the usability
of the product for its intended purpose.
A Quality Rating System

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59
Quality Characteristic
Variable Attribute
n>1?
n>=10?
x and MR
no
yes
x and s
x and R
no
yes
Defective Defect
constant
sample
size?
p-chart with
variable sample
size
no
p or
np
yes Sampling
Unit one
c u
yes no
Control Chart Selection

Dale H. Besterfield
Computer Program
 EXCEL/Minitab program files on the
website will solve for:
 p chart
 np chart
 c chart
 U chart
60

Dale H. Besterfield
Homework
 5, 7, 16b, 23
61

Attributes.ppt

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