Class 11 - Control Charts for Attributes3(1 of 2)
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Transcript of Class 11 - Control Charts for Attributes3(1 of 2)
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Introduction
Introduction
Industrial Engineering
Attributes
ControlCharts
Examples
X- bar Control ChartR- Control Chart
S- Control Chart
Out of Control
In Statistical Control
MR Control Chart
Individual Control Chart
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Attributes Control Charts
Introduction
Industrial Engineering
Attributes
ControlCharts
Examples
Attribute data
Data that can be classified into one of several categories or classificationsClassifications such as conforming and nonconforming are commonly used inquality control. Another example of attributes data is the count of defects
Attributes control charts are used for discrete or count data
Fraction nonconforming control charts (p charts) Number nonconforming control charts (np charts) Control charts for nonconformities (c and u control
charts)
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Attributes Control Charts
Introduction
Industrial Engineering
Attributes
ControlCharts
Examples
Fraction Nonconforming
The ratio of the number of nonconforming items in a population to the total numberof items in that population. Control charts for fraction nonconforming are based onthe binomial distribution
Number of Nonconformities
The number of defects per unit inspected or per subgroupNotation
n - number of items examined (lot size, sample size)
m - number of subgroups
p - probability that any one item of interest will be nonconforming. This parameteris often unknown and must be estimated.
p is the sample fraction nonconforming
p is the average fraction nonconforming
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Attributes Control Charts
Introduction
Industrial Engineering
Attributes
ControlCharts
Examples
Development of the p- Control Chart
n = number of units of product selected at random.D = number of nonconforming units from the sample
p = probability of selecting a nonconforming unit from the sample
The sample fraction nonconforming is given as
xn x p p x
n x D P
)1()(
n D p
pn
p p
)1(2
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Attributes Control Charts
Introduction
Industrial Engineering
Attributes
ControlCharts
Examples
If a standard value of p is given, then the control limits for the fractionnonconforming are
n p p
p LCL
pCLn
p p pUCL
)1(3
)1(3
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Attributes Control Charts
Introduction
Industrial Engineering
Attributes
ControlCharts
Examples
If no standard value of p is given, then the control limits for the fractionnonconforming are
Where
n
p p p LCL
pCLn
p p pUCL
)1(3
)1(3
m
p
mn
D p
m
ii
m
ii
11
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Attributes Control Charts
Introduction
Industrial Engineering
Attributes
ControlCharts
Examples
Development of the np- Control Chart
The np chart is a variation of the p chart, with the actual number of nonconformingitems plotted on the chart.
The npchart and the p chart for the same problem will provide identicalinformation.
The average fraction nonconforming p is the only value that must be estimatebefore constructing the control limits
m
p
mn
D p
m
ii
m
ii
11
)1(3
)1(3
p pn pn LCL
pnCL
p pn pnUCL
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Attributes Control Charts
Introduction
Industrial Engineering
AttributesControl Charts
Examples
Example
A process that produces bearing housings is investigated. Ten samples of size100 are selected.
Is this process operating in statistical control?
n = 100, m = 10
Sample # 1 2 3 4 5 6 7 8 9 10# Nonconf. 5 2 3 8 4 1 2 6 3 4
Sample # 1 2 3 4 5 6 7 8 9 10# Nonconf. 5 2 3 8 4 1 2 6 3 4Fraction
Nonconf. 0.05 0.02 0.03 0.08 0.04 0.01 0.02 0.06 0.03 0.04
038.0
1
m
p p
m
ii
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Attributes Control Charts
Introduction
Industrial Engineering
AttributesControl Charts
Examples
Control Limits are:
002.0100
)038.01(038.03038.0
038.0
095.0100
)038.01(038.03038.0
LCL
CL
UCL
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Attributes Control Charts
Introduction
Industrial Engineering
AttributesControl Charts
Examples
A small bank collects data on the number of error in weekly account activities.Over a 12-week period 1000 account activities are randomly selected andexamined for the number that are in error. Use attribute control chart to monitorthe proportion of errors. ( p and np )
The fraction in error for each week must be computed
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Attributes Control Charts
Introduction
Industrial Engineering
AttributesControl Charts
Examples
The average fraction in error must be found
The control limits and centerline for the p chart are
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Attributes Control Charts
Introduction
Industrial Engineering
AttributesControl Charts
Examples
p chart for accounts in error.
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Attributes Control Charts
Introduction
Industrial Engineering
AttributesControl Charts
Examples
np chart for accounts in error.