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Besterfield: Quality Control, 8thed.. 2009 Pearson Education, Upper addle !i"er, #$ 0%&'8.

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Quality ControlQuality Control

Chapter 8- ControlChapter 8- Control

Charts for AttributesCharts for AttributesPowerPoint presentation to accompanyPowerPoint presentation to accompany

BestereldBestereld

Quality Control, 8eQuality Control, 8e

PowerPoints created by RosidaPowerPoints created by RosidaCoowarCoowar

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OutlineOutline

Attribute Control Charts for Nonconforming Units

Control Charts for Count of

Nonconformities A Quality Rating System

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earnin! Ob"ecti#esearnin! Ob"ecti#es

When you have completed this chapter you

should:

Kno limitations of variable control charts and

the di!erent types of attribute charts"

Kno the ob#ectives of the p chart group and the

applicable distribution"

$e able to construct a:

%raction defective chart& '(ed subgroup si)e

%raction defective chart&variable subgroup si)e

*ercent defective chart

Number defective chart

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earnin! Ob"ecti#es cont$d%earnin! Ob"ecti#es cont$d%

When you have completed this chapter youshould:

Kno ho to minimi)e the e!ect of variable

subgroup si)e"Kno the applications of the c chart group+ the

applicable distribution and to conditions"

$e able to construct a c chart and a u chartand ,no the di!erence beteen them"

Kno the three classes of defect severity

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-he term Attribute refers to those .ualitycharacteristics that conform to

speci'cations or do not conform to

speci'cations"

Attribute are used:

/" Where measurements are not possible"

0" Where measurements can be made but

are not made because of time+ cost+ or

need"

AttributeAttribute

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A nonconformity is a departure of a.uality characteristic from its intended

level or state that occurs ith a severity

su1cient to cause an associated

product or service not to meet a

speci'cation re.uirement"

2efect is concerned ith satisfying

intended normal+ or reasonably

foreseeable+ usage re.uirement"

AttributeAttribute

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2efect is appropriate for use henevaluation is in terms of usage"

Nonconformity is appropriate for

conformance to speci'cations" -he term Nonconforming Unitis used to

describe a unit of product or service

containing at least one nonconformity"

AttributeAttribute

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2efective is analogous to defect and isappropriate for use hen unit of

product or service is evaluated in terms

of usage rather than conformance to

speci'cations"

3imitations of variable control charts:

-hese charts cannot be used for .uality

characteristics hich are attributes"

AttributeAttribute

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-ypes of Attribute Charts:/" Nonconforming Units 4based on the

$inomial distribution5:pchart+ np

chart"

0" Nonconformities 4based on the

*oisson distribution5: cchart+ uchart"

AttributeAttribute

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-he PChart is used for data that consist ofthe proportion of the number of

occurrences of an event to the total

number of occurrences"

6t is used in .uality to report the fraction or

percent nonconforming in a product+

.uality characteristic+ or group of .uality

characteristics"

&he P Chart&he P Chart

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%ormula:

-he fraction nonconforming+p+ is usually

small+ say+ 7"/7 or less"

$ecause the fraction nonconforming is

very small+ the subgroup si)es must be

.uite large to produce a meaningful

chart"

npp

n=


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6t can be used to control one .ualitycharacteristic+ as is done ith 8 bar and R

chart+

9r to control a group of .uality characteristics

of the same type or of the same part+

9r to control the entire product"

6t can be established to measure the .uality

produced by a or, center+ by a department+

by a shift+ or by an entire plant"


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6t is fre.uently used to report theperformance of an operator+ group of

operators+ or management as a means

of evaluating their .uality performance"

-he subgroup si)e of the Pchart can be

either variable or constant"


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9b#ectives of the PChart:/" 2etermine the average .uality level:

-his information provides the process

capability in terms of attributes"

0" $ring to the attention of management

any changes in the average"

" 6mprove the product .uality: 6deas for

.uality improvement"


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9b#ectives of the PChart cont;d:" Suggest places to use 8 bar and R chart:

-hey are more sensitive to variation"

?" 2etermine acceptance criteria of a

product before shipment to the customer"


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P&Chart Construction for ConstantSubgroup Si)e/" Select the .uality characteristic4s5:

a5 Single .uality characteristic"

b5 @roup of .uality characteristics"c5 A part"

d5 An entire product"

e5 A number of products"

f5 6t can be established for performance control ofan

operator+ or, center+ department+ shift+ plant+or corporation


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PChart Construction for Constant SubgroupSi)e cont;d"

0" 2etermine the subgroup si)e and

method: -he si)e of the subgroup is a function

of the proportion nonconforming"

A minimum si)e of >7 is suggested asa starting point"


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PChart Construction for Constant SubgroupSi)e cont;d"

" Collect the data:

At least 0> subgroups" 2i!erent sources 4Chec, sheet5"

%or each subgroup the proportion

nonconforming is calculated by theformula P np/n


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PChart Construction for Constant Subgroup Si)e

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P Chart Construction for Constant Subgroup Si)econt;d"

>" =stablish the revised central line and control

limits"0

0 00

0 00

(13

(1 )3

d

new

d

np npp p

n n

p pUCL p

np p

LCL pn

= =

= +

=


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-he PChart is most e!ective if it isposted here operating and .uality

personnel can vie it"

-he control limits are usually threestandard deviations from the central

value" -herefore+ appro(imately BB of

the plotted points+ P+ ill fall beteen the

upper and loer control limits"


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A PChart ill also indicate long&rangetrends in .uality+ hich ill help to

evaluate changes in personnel+

methods+ e.uipment+ tooling+

materials+ and inspection techni.ues"

P&chart is based on the binomial

distribution"


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PChart Construction for Dariable SubgroupSi)e

/" Collect the data"

0" 2etermine the trial central line and control

limits: Since the subgroup si)e changes

each day+ limits must be calculated for

each day"


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PChart Construction for Dariable SubgroupSi)e cont;d"

0" As the subgroup si)e gets larger+ the

control limits are closer together"" =stablish revised central line and control

limits:


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PChart Construction for Dariable SubgroupSi)e cont;d"

6f Pois ,non+ the process of data

collection and trial control limits is not

necessary"

Pis the proportion 4fraction5

nonconforming in a single subgroup"

Pis the average proportion 4fraction5

nonconforming of many subgroup"


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PChart Construction for DariableSubgroup Si)e cont;d"

Pois the standard or reference value of

the proportion 4fraction5nonconforming based on the best

estimate of PBar"

E is the population proportion

4fraction5 nonconforming"


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Finimi)ing the =!ect of Dariable Subgroup Si)e

/" Control limits for an average subgroup si)e: $y using an

average subgroup si)e+ one limit can be calculated and

placed on the control chart"

0 0

0

0 0

0

(13

(1 )3

av

av

av

nn

g

p pUCL pn

p pLCL p

n

=

= +

=


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Finimi)ing the =!ect of Dariable Subgroup Si)econt;d"

Case I:-his case occurs hen a point 4subgroup

fraction nonconforming5 falls inside the limits and

its subgroup si)e is smaller than the average

subgroup si)e"

Case II: -his case occurs hen a point 4subgroup

fraction nonconforming5 falls inside the averagelimits and its subgroup si)e is larger than the

average subgroup si)e"


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Finimi)ing the =!ect of Dariable Subgroup Si)econt;d"

Case III:-his case occurs hen a point 4subgroup

fraction nonconforming5 falls outside the limits

and its subgroup si)e is larger than the average

subgroup si)e"

Case IV: -his case occurs hen a point 4subgroup

fraction nonconforming5 falls outside limits andits subgroup si)e is less than the average

subgroup si)e"


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Number Nonconforming Chart 4np5: -he np chart is easier for operating

personnel to understand than thep

chart"

-he limitation that this chart has is that

the subgroup si)e needs to be constant"

&he np Chart&he np Chart

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0

0 0 0

Central Line =

Control Limits = 3 (1 )

np

np np p


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Number Nonconforming Chart 4np5: 6f the fraction nonconformingpois

un,non+ then it must be determine by

collecting data+ calculating trial control

limits+ and obtaining the best estimate

ofpo"


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%or an attribute this process is much simpler"

-he process capability is the central line of

the control chart"

Fanagement is responsible for the

capability"

When the plotted point is outside the control

limit+ operating personnel are usually

responsible"

Process CapabilityProcess Capability

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-he nonconformities chart controls the

count of nonconformities ithin the product

or service"

An item is classi'ed as a nonconforming

unit hether it has one or many

nonconformities"

Count of nonconformities 4c5 chart"

Count of nonconformities per unit 4u5 chart"

Control Charts for Count ofControl Charts for Count of

'on-conformities'on-conformities

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Since these charts are based on the

*oisson distribution+ to conditions

must be met:

/" -he average count of nonconformities

must be much less than the total

possible count of nonconformities"

0" -he occurrences are independent"

Control Charts for Count of Non&Control Charts for Count of Non&

conformitiesconformities

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9b#ectives:

/" 2etermine the average .uality level: -his

information gives the initial processcapability"

0" $ring to the attention of management any

changes in the average"

" 6mprove the product .uality: 6deas for

.uality improvement"



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9b#ectives cont;d":

" Suggest places to use 8 bar and R

chart"

?" 2etermine acceptance criteria of a

product before shipment to the

customer"



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C Chart construction:

/" Select the .uality characteristic4s5:

a5 Single .uality characteristic"

b5 @roup of .uality characteristics"

c5 A part"

d5 An entire product"

e5

A number of products"f5 6t can be established for performance control of

an: operator+ or, center+ department+ shift+

plant+ or corporation



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C Chart construction cont;d:

0" 2etermine the subgroup si)e and

method:" Collect the data:

At least 0> subgroups"

2i!erent sources"



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>" =stablish the revised central line and

control limits

dnew 0

d

0 0

0 0

c - c

c = c = g - g

UCL = c ! c

LCL = c - ! c



C chart construction cont;d:

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?" Achieve the ob#ectives: -he reason forthe control chart is to achieve one or

more of the previously stated ob#ectives"



C chart construction cont;d:

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Chart for Count of NonconformitiesGUnit 4u

Chart5

3

3

ccu u

n n

uUCL u

n

uLCL u

n

= =

= +

=


'on-conformities()nit'on-conformities()nit

l h f f

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Chart for Count of NonconformitiesGUnit

4uChart5

Scale selected is continuous for the uchart" %or the cchart is discrete"

Subgroup si)e for the uchart can vary" %or

the cchart is /"

-he uchart is limited in that e do not

,no the location of the nonconformities"



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Nonconformity Classi'cation:

/" Critical nonconformities: Unsafe conditions for

individuals using+ maintaining+ or depending

upon the product"

0" Fa#or nonconformities: Result in failure or reducematerially the usability of the product for its

intended purpose"

" Finor nonconformities: Reduce materially the

usability of the product for its intended purpose"

A Quality Ratin! *ystemA Quality Ratin! *ystem

Control Charts forControl Charts for

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0 0 0 0

2 2 20 0 0 0

0 0

0 0

, 9,3 1

9 3 1

9 3 1

9 3 1

33

c c ma ma mi mi

c ma mi

c ma mi

c ma mi

u c ma mi

u

u

D w u w u w u

when w w and w are and

D u u u

D u u u

u u u

UCL DLCL D

= + +

= + +

= + +

= + +

= +

=

Control Charts forControl Charts for+emerits()nit+emerits()nit

l h l iC t l Ch t * l ti

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Quality Characteristic

*aria+le (ttri+ute

n-

n/-0

and 1!no

yes

and s

and !no

yes

efecti"e efect

constantsa3ple

si4e

p5chart 6ith"aria+le sa3ple

si4e

no

p or

np

yesconstant

sa3plin)

unit

c u

yes no

Control Chart *electionControl Chart *election

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