ch.4 - control charts for attributes.ppt

8/19/2019 Ch.4 - Control Charts for Attributes.ppt

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Topic 4.0

Control Chart forAttributes


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Introduction

Many quality characteristics cannot beconveniently represented numerically.

In such cases, each item inspected is

classied as either conforming ornonconforming to the specications onthat quality characteristic.

uality characteristics of this type are

called attributes. !"amples are nonfunctional semiconductor

chips, #arped connectin$ rods, etc,.


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When to use a control

chart? Controlling ongoing processes by finding and correcting

problems as they occur.

Determining whether a process is stable (in statistical

control).

Analyzing patterns of process variation from special

causes (non-routine events) or common causes (built intothe process).

Determining whether the quality improvement proect

should aim to prevent specific problems or to ma!e

fundamental changes to the process.


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"ariables control charts "ariable data are measured on a continuousscale.

#$ample% time& weight& distance or temperature canbe measured in fractions or decimals.

Attributes control charts Attribute data are counted and cannot havefractions or decimals. Attribute data arise when youare determining only the presence or absence ofsomething& such as%

o success or failureo accept or reecto correct or not correct.

#$ample& a report can have four errors or fiveerrors& but it cannot have four and a half errors.


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Advantages of attribute

control charts Allowing for quic! summaries& that is& the engineermay simply classify products as acceptable or

unacceptable& based on various quality criteria.

'hus& attribute charts sometimes bypass the needfor e$pensive& precise devices and time-consuming

measurement procedures.

ore easily understood by managers that unfamiliar

with quality control procedures.


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Defect vs. Defective

Defect* + a single nonconforming quality

characteristic.

Defective* + items having one or more

defects.


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Choice Between

Attributes

and Variables Control

Charts

#ach has its own advantages and disadvantages Attributes data is easy to collect and several

characteristics may be collected per unit.

"ariables data can be more informative sincespecific information about the process mean andvariance is obtained directly.

"ariables control charts provide an indication ofimpending trouble (corrective action may be ta!en

before any defectives are produced). Attributes control charts will not react unless the

process has already changed (more nonconformingitems may be produced.


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Advantages of attributecontrol charts Allowing for quic! summaries& that is& the engineer

may simply classify products as acceptable or

unacceptable& based on various quality criteria.

'hus& attribute charts sometimes bypass the needfor e$pensive& precise devices and time-consuming

measurement procedures.

ore easily understood by managers that unfamiliar

with quality control procedures.


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p charts: proportion of units nonconforming.

np charts: number of units nonconforming.

c charts: count of nonconformities.

u charts: count of nonconformities per unit.

Control Charts for Variables Data

X and R charts: for sample averages and ranges.

Md and R charts: for sample medians and ranges.

X and s charts: for sample means and standard deviations.

X charts: for individual measures; uses moving ranges.

Types of Control Charts

Control Charts for Attributes Data


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Type of Attribute Charts

p charts This chart sho#s the fraction of nonconformin$ or defective

product produced by a manufacturin$ process. It is also called the control chart for fraction nonconformin$.np charts

This chart sho#s the number of nonconformin$. Almost thesame as the p chart.c charts This sho#s the number of defects or nonconformities

produced by a manufacturin$ process.u charts This chart sho#s the nonconformities per unit produced by a

manufacturin$ process.


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p charts

• ,n this chart& we plot the percent of

defectives (per batch& per day& per machine&

etc.).


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p-Chart construction forconstant subgroup size %elect the quality characteristics. &etermine the sub$roup si'e and method Collect the data. Calculate the trial central line and control

limits. !stablish the revised central line and

control limits. Achieve the ob(ective.


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Forula

raction nonconforming%

p (np)/n

0here&

p proportion or fraction nc in the sample

or subgroup&

n number in the sample or subgroup& np number nc in the sample or subgroup.


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Calculate the trial central line andcontrol limits

'he formula%

average of p for many subgroups

Where, n number inspected in a subgroup

n

p p pUCL

)1(3

−+=

n

p p p LCL

)1(3

−−=

∑∑=

nnp p


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%ub)$roup

*umber

*umberInspected

n

np p

1 300 12 0.040

2 300 3 0.010

3 300 9 0.030

4 300 4 0.013

5 300 0 0.0

6 300 6 0.020

7 300 6 0.020

8 300 1 0.003

19 300 16 0.053

25 300 2 0.007

Total 7500 138

018.07500

138===

∑∑

n

np p

0.0005.0

300

)018.01(018.03018.0

=−=

−−= LCL

041.0

300

)018.01(018.03018.0

=

−+=UCL

*e$ative value of +C+ is possible in a theoriticalresult, but not in practical proportion of nc never

ne$ative-.


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p Chart

p-bar

1C1

2C1

3ubgroup

p

4 56 54 76 74

6

6.65

6.67

6.68

6.69

6.648


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!stablish the revised central lineand control limits

Determine the standard or reference value for

the proportion nc& po.

#here npd number nc in the discarded

sub$roups nd number inspected in the discarded

sub$roups

∑∑

−−=

d

d

newnnnpnp p


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!"!#CI$!%

3hows data for the result inspection

operation bottel from au a!mur

Company 3dn :hd. ;aving 76 subgroup

each another 566 bottel. Define%i) Average zero defect

ii) 1ine for limit control upper ang loer

iii)


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SUBGROUP NONCONFORMING (np) SUBGROUP NONCONFORMING (np)

1 14 11 8

2 10 12 12

3 12 13 9

4 13 14 10

5 9 15 11

6 11 16 10

7 10 17 8

8 12 18 12

9 13 19 10

10 10 20 16


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np Chart

'he np chart is almost the same as the p chart.

Central line npo

,f po is un!nown& it must be determined bycollecting data& calculating 2C1& 1C1.

)1(3 ooo pnpnpUCL −+=

)1(3 ooo pnpnp LCL −−=


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!&aple


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$epintas lalu'$epintas lalu'

;ati > itu !adang!ala perlu ua di!etu! ia dgn

uian& agar ia terdidi! ut! tida! sentiasa

selesa pada ?!esu!aan? tapi uga selesa dgn

?!esa!itan?... @adi senyumlahB wahai saudara!u& walau

su!a walau du!a !erana yg su!a itu

anugerah dan yg duka itu tarbiyyah dari,1A;, buat hambanya yg di!asihi.


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!nd (f $ession

'han! ou and

%!*/M

http://../Documents/Raihan%20-%20Senyum.flvhttp://../Documents/Raihan%20-%20Senyum.flv


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c Chart

'he procedures for c chart are the same a sthose for the p chart.

,f count of nonconformities& co& is un!nown& it

must be found by collecting data& calculating2C1 E 1C1.

average count of nonconformities

ccUCL 3+= cc LCL 3−=

g

cc =


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!&aple 64.525

141===

g

cc

76.1264.5364.5 =+=UCL

048.1

64.5364.5

=−=

−= LCL


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c-Chart

6

4

56

54

76

74

5 7 8 9 4 F G H I 56 55 57 58 59 54 5F 5G 5H 5I 76 75 77 78 79 74

ubgroup !umber

C o u n t o f ! o n c o n f o r m i t i e s

c

2C1

c-bar

1C1


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#evised

Jut-of-control% sample no. 4& 55& 78.

23.4

325

141420141=

−

−−−=

−

−=

d

d new

g g

ccc

40.1023.4323.43 =+=+= oo ccUCL

094.123.4323.43 =−=−=−= oo cc LCL


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u Chart

The u chart is mathematically equivalentto the c chart.

ncu =

∑∑=

ncu

n

uuUCL 3+=

n

uu LCL 3−=


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!&aple20.1

2823

3389===

∑

∑n

cu


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or @anuary 86%

09.111012030 ===

ncu Jan

51.1

110

20.1320.130 =+= JanUCL

89.0110

20.1320.130 =−= Jan LCL


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)onconfority Classi*cation

Critical nonconformities ,ndicate hazardous or unsafe conditions.

aor nonconformities ailure

inor nonconformities


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Control Charts for +ariables vs. Charts for Attributes

3ometimes& the quality control engineer has

a choice between variable control charts and

attribute control charts.