Class 11 - Control Charts for Attributes3(1 of 2)

8/11/2019 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


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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Introduction


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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Introduction


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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Introduction


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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Introduction


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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Introduction


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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Introduction


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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Introduction



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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Introduction



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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Introduction



Examples

The average fraction in error must be found

The control limits and centerline for the p chart are


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Introduction



Examples

p chart for accounts in error.


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Introduction



Examples

np chart for accounts in error.

Class 11 - Control Charts for Attributes3(1 of 2)

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