2010 MS-5 SPC-11(NS)

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PIQC Institute of Quality

ATTRIBUTE CONTROL

CHARTS

Types of Data

ATTRIBUTE DATA give you counts representing the presence orabsence of a characteristic or defect.

ese counts are ase on t e occurrence o screte events, e.g.,

true/false statements

Accepted or rejected

Passed or fail

An attribute is not numerically measured; its either there or its not.

quality characteristic produced by the process, e.g.,

Diameter of a shaft

Temperature of Oven

Pressure of Steam, etc.

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Nonconforming Defect Defective

Types of Data

Attribute Control Charts

Data

Attribute

Data

Defectives/

UnitsDefects

n fixed n varies n fixed n varies

np Chart p Chart

c Chart u Chart

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Constructing p Chart

Attribute

Unit of measure

Defectives (defected units)

Sample Size

Varying (inconsistent)

Data Collection Frequencyhourly, daily, weekly, etc.


Suppose you work in a plant that manufactures printed

circuit boards with various wave solder machine, which

passes the boards over a surface of liquid solder.

Soldered boards are then connected to test stations,

which test the circuits and classify the boards as either

conforming or nonconforming. Following table contains

records of the daily numbers of rejected circuit boards for

a 30 days period.

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Day Tested (ni) Rejects Proportion

1 286 14

2 281 22


16 297 15

17 283 14

18 321 13

Example 9.1 Step 1: Collect data

4 313 19

5 293 21

6 305 18

7 322 16

8 316 16

9 293 21

19 317 10

20 307 21

21 317 19

22 323 23

23 304 15

24 304 12

10 287 14

11 307 15

12 328 16

13 296 21

14 296 9

15 317 25

25 324 19

26 289 17

27 299 15

28 318 13

29 313 19

30 289 12


1 286 14 0.049

2 281 22 0.078


16 297 15 0.051

17 283 14 0.049

Example 9.1Step 2: Calculate the Fractions for each value

3 310 9 0.029

4 313 19 0.061

5 293 21 0.072

6 305 18 0.059

7 322 16 0.050

8 316 16 0.051

18 321 13 0.040

19 317 10 0.032

20 307 21 0.068

21 317 19 0.060

22 323 23 0.071

23 304 15 0.049

.

10 287 14 0.049

11 307 15 0.049

12 328 16 0.049

13 296 21 0.071

14 296 9 0.030

15 317 25 0.079

.

25 324 19 0.059

26 289 17 0.059

27 299 15 0.050

28 318 13 0.041

29 313 19 0.061

30 289 12 0.042

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Example 9.1

Step 3: Calculate the Central Limit

==

n

pp

Step 4: Calculate the control limits

Example 9.1

=

+=ni

pppUCL

)1(3

== pCL

=

=ni

pppLCL

)1(3

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Constructing the p Chart

Step 5: Plot the p Chart

0. 3

0. 2

roportion

P C hart for Rejects

P=0.1685

3.0SL=0.3324

20100

0. 1

0. 0

Sample Number

-3.0SL=0.004728


printed circuit boards with various wave solder

machine, which passes the boards over a surface of

liquid solder. Soldered boards are then connected to

test stations, which test the circuits and classify the

boards as either conforming or nonconforming.

Following table contains records of the daily

numbers of rejected circuit boards for a 30 days

period.

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Step 1

Choose Stat >

Control Charts >

Attributes Charts >

P.


Ste 2

In Variables, enter

Rejects.

In Subgroup sizes,

enterSampled.

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Step 3

Select tests for special

causes


What is your analysis of

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Constructing np Chart

Attribute

Unit of measure

Defectives (defected units)

Sample Size

Constant



Suppose you work in a department, where items are

routed through successions of different processes. In

order to keep track of an items progress is to attach

paperwork, also known as travelers. To monitor the

quality of such paperwork; periodic samples of 100

travelers are examined for errors, where a

nonconforming document is defined to be one that

contains at least one error. Following table shows datafrom 25 daily samples of 100 drawn from completed

travelers prior to initiating production.

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Day Sample Size Nonconforming Doc

1 100 10

Example 9.2 Step 1: Collect data

Day Sample Size Nonconforming Doc

14 100 21

3 100 10

4 100 11

5 100 6

6 100 7

7 100 12

8 100 10

16 100 12

17 100 11

18 100 6

19 100 10

20 100 10

21 100 11

9 100 6

10 100 11

11 100 9

12 100 14

13 100 16

22 100 11

23 100 11

24 100 6

25 100 9

100


Step 2: Calculate the Central Limit

==

kn

Xipn

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Step 3: Calculate the control limits

)1(3 ppnpnUCL +=

)1(3 ppnpnLCL =


Suppose you work in a department,

w ere ems are rou e roug

successions of different processes. In

order to keep track of an items

progress is to attach paperwork, also

known as travelers. To monitor the

quality of such paperwork; periodic

samples of 100 travelers are

examined for errors, where a

to be one that contains at least one

error. Following table shows data

from 25 daily samples of 100 drawn

from completed travelers prior to

initiating production.

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Step 1

Choose Stat >

Control Charts >

Attributes Charts >

NP.


Ste 2

In Variables, enter

Rejects.

In Subgroup sizes,

enterSampled.

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Step 3


causes


Analyze the results.

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Exercise np Chart

The following tablecontains the number of

accidents on the work

site across 40 operating

Number of Accidents

Un

it

March-

June

July to

Oct

Nov to

Feb

1 2 1 2

Number of Accidents

Un

it

March-

June

July to

Oct

Nov to

Feb

21 3 4 1

divisions of a certain

company.3 2 4 0

4 1 2 4

5 1 3 1

6 1 1 1

7 4 8 8

8 0 0 0

9 2 1 2

10 1 0 2

11 3 2 0

23 1 4 1

24 3 1 2

25 1 4 4

26 1 0 0

27 1 0 0

28 1 0 0

29 0 0 0

30 0 0 0

31 0 0 12

12 2 6 3

13 0 3 1

14 0 0 0

15 1 0 1

16 2 2 4

17 0 3 2

18 0 0 3

19 2 0 4

20 2 6 7

32 1 0 1

33 2 3 2

34 0 0 0

35 0 2 3

36 0 0 0

37 0 0 0

38 0 0 0

39 0 1 0

40 1 1 1

ANSWER

=n

Any special cause variation?

______________________________________________

______________________________________________

______________________________________________

onc us on:

______________________________________________

______________________________________________

______________________________________________

______________________________________________

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Constructing c Chart

Attribute

Unit of measure

Defects (e.g., no. of defects in a unit)

Sample Size

Constant



One measure of software quality is the error rate per

1000 lines of code. With the abbreviation k for the word

thousand, a block of 1000 lines of computer code is

often abbreviated as KLOC (K lines of code). Following

table show the defects per KLOC obtained from daily

test logs in a software company. Plot a c chart for this

case.

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Constructing c Chart Step 1: Record the dataDay Number of Errors per C 1000

Lines of Code (KLOC), Ci

1 6

2 7

Day Number of Errors per C 1000

Lines of Code (KLOC), Ci

16 3

17 2

4 6

5 8

6 6

7 5

8 8

9 1

19 0

20 1

21 2

22 5

23 1

24 7

10 6

11 212 5

13 5

14 4

15 3

25 7

26 127 5

28 5

29 8

30 8

Constructing the c Chart

Step 2: Calculate the the average, UCL and LCL

csubgroupsofno.total

defectstotalCenterline

subgroupperdefectsofnumberc

==

=

cc

c

3LCL

3cUCL

=

+=

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Constructing the c Chartk

==

=

k

C

c ii

1

==

== cc 3LCL

Constructing the c Chart

Step 3: Plot the c Chart

15

10

leCount

C Chart for No. of Defects

1

=

1.0SL=7.966

2.0SL=10.33

3.0SL=12.70

109876543210

5

0

Sample Number

Sam

.

-1.0SL=3.234

-2.0SL=0.8671-3.0SL=0.000

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Constructing c ChartOne measure of software quality

s e error ra e per nes o

code. With the abbreviation k for

the word thousand, a block of

1000 lines of computer code is

often abbreviated as KLOC (K

lines of code). Following table

show the defects per KLOC

obtained from daily test logs in a

.

for this case.


Step 1

Choose Stat >

Control Charts >

Attributes Charts >

c.

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Step 2

In Variables, enter

Blemish.


Step 3

Define the control limits

for standard deviations

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PIQC Institute of Quality 2

Constructing c ChartStep 4


causes


What is your analysis of

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Exercise c Chart

Off-color flaws in aspirins are caused by extremely small

amounts of iron that change color when wet aspirin

material comes into contact with the sides of drying

containers. At Dow Chemical plant, out of every batch of

aspirin, a 250-lb sample is taken and the number of off-

color flaws is counted. Following table shows the number

of flaws per 250-lb sample obtained over a 25-days

period.

Sample

Number

Number of Flaws

1 46

C Chart Step 1: Collect data

Sample

Number

Number of Flaws

14 49

3 56

4 57

5 37

6 51

7 47

8 34

16 59

17 53

18 61

19 63

20 42

21 45

9 30

10 44

11 47

12 51

13 46

22 43

23 42

24 39

25 38

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ANSWER


______________________________________________

______________________________________________

______________________________________________

onc us on:

____________________________________________________________________________________________

______________________________________________

______________________________________________

Constructing u Chart

Attribute

Unit of measure

Defects (e.g., no. of defects in a unit)

Sample Size

Varying Data Collection Frequency

hourly, daily, weekly, etc.

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The software error rate per 1000 lines of code (i.e., per

KLOC) were obtained from daily test logs for the purpose

of tracking error rates. Suppose that the programming

department decides to speed up the daily error counting

process by simply counting the numbers of errors in

finished software modules. Since the module may

consist of any number of lines of code, the reported error

rates must be converted to a per unit or per KLOC

basis before charting.


ksubgroupsnformitieTotalNoncou

sin=

tsspect onunnum ero nota .

in

uuUCL 3+=

inuUCL 3=

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Step 1

Choose Stat >

Control Charts >

Attributes Charts >

u.

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Constructing u ChartSte 2

In Variables, enter

Defects.

In Subgroup sizes,

enterSample.


Step 3


causes

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Analyze the results.

Exercise u Chart

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ANSWER


______________________________________________

______________________________________________

______________________________________________

onc us on:

____________________________________________________________________________________________

______________________________________________

______________________________________________

ACCURACY & PRECISION

54

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ACCURACY & PRECISION

55PIQC Institute Of Quality

(A) Most of the da ta we re on ta rget,with very little variation from it.

(C) Even when most of the da ta w ereclose toge ther, they were located off

the target b y a significa nt am ount.

(B) Although some d ata were ontarget , ma ny ot hers were dispe rsed

awa y from the target.

(D) The da ta we re off targe t andwidely dispersed

Is Process within Specification Limits?

Capable

56

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Process capability is the natural variation in aprocess that results from common causes.

Chapter 08 Process Capability

Process capability

A process is in Statistical Control when

When special causes have been identified andeliminated.

stable.

Mostly the assumption for process capability isthat data is normally distributed.

Estimating Process Variation


When subgroup are formed, Control chart data can.

For normally distributed data, R chart and s chartcan be used to calculate the standard deviation.

Where, R bar is the average of the ranges of all subgroups.

Assumption: Data is normally distributed

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Estimating Process Variation


For normally distributed data, R chart and s chartcan e use o ca cu a e e s an ar ev a on.

Where, S bar is the average standard deviation of the std deviations of allsubgroups.

Assumption: Data is normally distributed

Example, you have 100 readings for a particular process.

Process Capability

Process capabil ityis the natural variation in a


process that results from common causes.

Cp= (USL LSL)

6Where:

USL = upper spec. limitLSL = lower spec. limit

= standard deviation of the process

= An estimate of process standard deviation based on the samplestandard deviation, s)

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Process Capability

USL LSL is the allowable process spread

6 is the actual process spread

6 is the estimated process spread

Cp < 1.0 not capable

Cp = 1.0 Marginally capableCp > 1.0 capable

Capability Indexes

Process capabil ityis the natural variation in aprocess that results from common causes.


When Cp = 1, the natural variation is the sameas the design specification width

When Cp < 1, a significant percentage ofoutput will not conform to the specifications

Cp > 1, indicates good capability

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One-sided capability indices that consider off- centered processes

Cpu = (USL )/3

C = LSL /3


Cpk = Min (Cpl, Cpu) orwhere

)(

|2

)(|

LSLUSL

uLSLUSL

k

+

=

ppk CkC )1( =

USL = upper spec. limit

LSL = lower spec. limit

= the mean performance of the process

= standard deviation of the process (or an estimate based on thesample standard deviation, s)

A controlled process shows an overall mean of 2.50 and


Example

an average range o . . amp es o s ze were useto construct the control charts.

d2= 2.059

Part A: What are extreme values?

Part B:If specifications are 2.60 0.25, What is the process capability?

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Overall mean = 2.50

R bar = 0.42


Sample size = 4

Part A:

d2= 2.059,

= R/d2= 0.42/2.059 = 0.20.

x reme va ues = ean

Thus, the observed extreme values are 2.50

3(.020), or 1.90to 3.10.

Part B:

Specifications are 2.60 0.25


Example

LSL = 2.35

USL = 2.85

Target = 2.60

Apply the formula, Cp is less than 1 so not a capable process.

Example 8.3

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In an automobile company, a lot of 500 shafts has been received from a

vendor. The QC inspector at the receiving has taken a sample of 50pieces and measured the diameter of each of the 50 pieces. The

recorded readings of the 50 pieces are given below. The required

Exercise

Item: Sha ft Parameter Diameter

Lot size: 500 Sam ple size: 50

Standard: 145 +/ - 3

Dimensions (mm):

spec ca ons o e s a are mm w a + - mm o erance.

Calculate the Process Capability (Cp, Cpk) of the supplier.

148 145 143 142 140 149 150 143 148 150

148 145 147 148 141 147 144 142 149 146

145 144 145 148 143 141 145 143 147 145145 144 146 149 145 142 143 142 146 143

143 145 144 142 142 141 142 141 145 142

ANSWER

=

Cp =

Cpk =

Conclusion:

_____________________________________________

_____________________________________________

68PIQC Institute Of Quality

__________________________________________________________________________________________

_____________________________________________

_____________________________________________

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