Ch6 Control Charts for Attributes

- ??????Attribute control charts
- 1. Control chart for fraction

nonconformingP chart - 2. Control chart for nonconformingc chart
- 3. Control chart for nonconformities per

unitu chart

Control chart for fraction nonconformingP chart

- ?process?fraction nonconforming p???,???
- ?????????n???,??m?,?

- ??trial control chart??????

- ?????,????recheck?
- ????,????chance???,??????trial control limit?

????????trial control limits??,??????????????patte

rns,???????,pattern????,?????????assignable cause?

- ?p???????,????trial control limits?
- ??process?true p????,?????????
- standard?p?,????out of control?signal??,
- ??????process?out of control at the target p

- but in control at some other value of p?

Example 1

Cardboard cans for frozen orange juice

concentrate.

Nonconforming???e.g. ?side seam?bottom

joint?? Samplen50 cans,m30 ???????????????,????

?,???? ?????

- Data ????
- Trial control chart????
- Sample 15?23 outside control limits.
- ????,?sample 15?,??????cardboard??????????,??????,

???????????sample 23???????????????operator??????

??

? ???sample 15?23??,??control chart?

- ???control chart limits?control chart????
- Sample 21 exceed??control limit,??????????????assi

gnable causes,????????,?????control

chart????future samples???,(???????control

chart?maximum run5,????nonrandom?pattern),???????

?process?in control at the level

p0.2150,??control chart???monitor current

procedure? - ???process???in control,??p0.2150????,??????workf

orce??????,????management????improve! - Management??engineering staff???????,?????????????

??????

- ???,???????,n50,??24??Data???,Control chart????

?

?process??????level???,?41 below control

limit????assignable cause? - ????????????

???????

- ?????data??C.C. ,????
- (?LCLlt0?,???LCL0)
- ? The process is in control at this new

level.

12. ?????(???),?C.C. (???) ? Process is

in control.

Fraction nonconforming control chart ???

- ??????1. Sample size(n)
- 2. Frequency of

sampling - 3. Width of the

control limits(k) - (????economic???)

- Sampling frequency????????control chart?
- ??100 inspection of all process output over

some - convenient period of time??????,sample

size(n) - ???????,???????sampling frequency
- ????

- Production rate
- Rational subgroup

e.g. ??????,??????????shift??,

???????shift?output?subgroup,????

???output?subgroup?

- Sample size? p ???,????? n ??,???
- ??????????????????,?????
- ???C.C.??sample????????reject????
- ???

?? I??D??????,????

?? IIDuncan(1974) n?????,?process

shift???????,???detect ?shift ?????50?

???n ??upper control limit??out of control ??????

(No Transcript)

- ??in-control?? p ??,??? n,??C.C.
- ?????0,??????????????
- ???(??????? inspection error ??
- ?, e.g. ????inspector ,??????
- ???)??

- ?P chart???????3-sigma limit?

??fraction nonconforming control

chart?????????????fraction nonconforming

data? i.e. 1. P(nonconforming unit)constant

2. Successive units of production are

independent. ?nonconforming units?cluster???(???c

orrelation)?????????,???P chart??????

- ???????????np control chart.

????,????????????,?? np chart? p chart?????

e.g. Fraction nonconforming orange juice

concentration cans. ???????????,??UCL21,LC

L2, ??????np???UCL?LCL????,???

?out of control?

- ?sample size???????
- ?????fraction nonconforming?C.C.?,???
- ???????????????100?process
- output,??????????????????,
- ??????variable sample size????

e.g. ????data,???

C.C.????

?????Average sample size(??????????

sample size?????sample size???????) ?????sampl

e size???????????control

limit?,???exact?control limits?????

??out of control?

e.g. ????

????variable sample size?C.C.?,runs????

nonrandom patterns????????

?????standardized C.C.?

?????????standard deviation????

??(continue),data???,C.C.???? ?observation????????

????, Tests for runs?pattern recognition????????

- ?????????????standardize control
- chart???,????variable control limits(?
- ???)??????,?????standardize
- C.C.?quality engineers use?

- ?length of the production run???,????
- ?standardize control chart?

- Fraction nonconforming?C.C.????????
- ????
- e.g. 1. ????pay period??????????
- ?????
- 2. ????????????

- ???????fraction nonconforming C.C.??
- ???variable sample size????

e.g. ????,?????????aerospace

company?????(????????? ????issues

purchase order),??? purchase

order????????, ?incorrect part numbers,

incorrect delivery dates, incorrect

prices or terms, wrong supplier numbers?

- O.C. curve?ARL

(??????)

- ??Binomial dist. ?c.d.f.???
- ?p??(e.g. plt0.1),n?,??Poisson approximation?
- ?p??,n?,??normal approximation?

(No Transcript)

- Nonconformities(Defects)?C.C.

a. ??nonconforming item??????

nonconformities(defects)? b. ????nonconformities?i

tem??? ???nonconforming item(????

defect?????,e.g. PC????? ??)?

1. c charttotal number of nonconformities in a

unit. 2. u chartaverage number of

nonconformities per unit.

- ??????,c or u chart??p chart????
- e.g. 1. ?100??????,????????
- 2. ????????????

- c chart(control chart for nonconformities)

1. The number of opportunities or potential

location for nonconformities are infinite

large. 2. The probability of occurrence of a

nonconformities at any location be small and

constant. (?Poisson

Postulates) 3. ????sample?????inspection

unit. ? nonconformities?????type,?????class?nonc

onformities?????????

(Rmk?independent?Poisson,????Poisson?)

- Inspection unit?????????????????
- e.g. single unit of product?5 units (or 10

units)of product.

- ? xnonconformities ???Poisson ( c )

Example 2

Inspection unit100 printed circuit boards. ??26

successive samples of 100 printed circuit

boards. (data ???)?

(???)

1. Sample 6?20?limits??, Sample 6 ? new

inspector examined the board,????

??board???????nonconformities?

Sample 20 ? ??????,????????

2. ???????,??C.C. revised,?????sample 20

?(???)???process?in control,???board?

nonconformities??????? ? ????management

action??improve??????

- ????,c chart?p chart????(????
- nonconformities?????)?

e.g. ???,for defect data 500 boards?data?

Pareto chart???,???,?????60

?defect?????????solder cold joints

??,????,??isolate?eliminate wave

soldering process???,??process yield?

???????

1. ??????defects attributable to a

few(???two)defect types,???????nonconformities

follow a Pareto distribution?

- 2. ???,?printed circuit board???type
- nonconformities????
- ??40???????20?solder cold joints????part

0001285??? - ??board??????????

3. ?cause effect diagram?????,????????????solde

r process,????????designed experiment?variables?op

timize wave soldering????

- Sample sizen inspection units (e.g. n2.5)

1. Revised chart

2. ?u chart

If we find c total nonconformities in a sample of

n inspection units, then the average number of

nonconformities per inspection unit is

Note that c is a Poisson random variable.

Example 3

- PC???

- 1?PC 1?inspection unit

- Sample size 5?inspection units

- ??20?samples(???)?

- ??lack of statistical control,?u???(???)?

- ??Management must take action to improve the
- process.

Alternative Probability Models for Count Data

(?????Count data???????)

E.g. nonconformities??cluster??

????Jackson(1972), Leavenworth(1976),

Gardiner(1987)?

- 100??(e.g. ?????)?
- c chart?????C.L.????,u chart??C.L.
- ?n???

- ???????? ? ???u chart,???c chart?
- ??????control chart

Example 4

- ????

- ????

- inspection unit ?50????

- Data???,control chart????

- ?????defects?

- ?defects??severity?????weights?

Class A DefectsVery Serious 1. Completely unfit

for service 2. Cannot be easily corrected in the

field 3. Cause personal injury or property damage

Class B DefectsSerious 1. Suffer a Class A

operating failure 2. Will certainly have reduced

life or increase maintenance cost

Class C DefectsModerately Serious 1. Fail in

service 2. Possibly have reduced life or

increased maintenance costs 3. A major defect in

finish appearance, or quality of work

Class D DefectsMinor Minor defects in

finish, appearance, or quality of work

The demerit weights of Class A-100, Class B-50,

Class C-10, and Class D-1 are used fairly widely

in practice.

D is the total number of demerits in all n

inspection units.

- ???????
- 1. Two-class??
- 2. ????defect class ?????C.C.

We will generate the O.C. curve for the c chart

in Example 2

Inspection unit100 printed circuit boards. ??26

successive samples of 100 printed circuit boards.

- For the u chart, we may generate the OC curve

from

????

- Dealing With Low-Defect levels(PPM range?1000)

- ??,u?c chart?ineffective !

- ????????C.C.
- the time between successive occurrences

of defects

- c?u chart?????????????

Choice Between Attributes and Variables Control

Charts

- ?quality characteristic??????(?color
- of the item),???attribute C.C.?

- Attribute C.C.????,????quality characteristic
- ?????nonconforming???,?variable C.C.??
- multivariate C.C.?????????

- Variable C.C.????Attribute C.C.??????,?
- ?????out of control????

- ?process-capability????,???????variable
- C.C.?

(No Transcript)

- ??????process shift level,??Variable C.C.??
- ?sample size?Attribute C.C.??

- ????unit??????, ??variable type???
- ?????,????????????units???
- ?,???destructive????????????

Example 5

? n9

Sample size on the P chart

? Specification limit is 3-sigma. ? p0.0027

? n79.13(?80)

Guidelines for Implementing Control Charts

1. Choosing the proper type of control charts.

2. Determining which process characteristics to

control.

3. Determining where the charts should be

implemented in the process.

4. Taking actions to improve processes as the

result of SPC/control chart analysis.

5. Selecting data-collection systems and computer

software.

- Remember, control charts are not just for

process - surveillance they should be used as an

active, on- - line method for reduction of process

variability.

Choosing the Proper Type of Control Chart

- A new process is coming on stream, or a new

product is - being manufactured by an existing process.

- The process has being in operation for some

time, but it - is chronically in trouble or unable to hold

the specified - tolerances.

- The process is in trouble, and the control

charts can be - useful or diagnostic purposes(troubleshooting

).

- Destructive testing(or other expensive testing

procedures) - is required.

B. Attributes Charts(p charts, c charts, and u

charts)

C. Control Charts for Individuals

- inconvenient or impossible to obtain more than

one - measurement per sample, or repeat

measurements

- automated testing and inspection

- available very slowly

Determining Which Characteristics to Control and

Where to Put the Control Charts

- At the beginning of a control charts program,

control - charts should be applied to any product

characteristics - or manufacturing operations believed to be

important.

Action Taken to Improve Process

- Process improvement is the primary objective of

- statistical process control.
- 1. Statistical control
- 2. Capability
- (???)

Selection of Data-Collection Systems and Computer

Software

- There are several sources of free software. In

addition to - the packages available on various personal

computer - bulletin boards, the Journal of Quality

Technology has - published computer programs in either BASIC

or - FORTRAN since 1969.
- (???)

Example 6

- ????

????(Example 1)

Back

The Poisson postulates

The Poisson distribution can be derived from a

set of basic assumptions, sometimes called the

Poisson postulates. These assumptions relate to

the physical properties of the process under

consideration. While, generally speaking, the

assumptions are not very easy to verify, they do

provide an experimenter with a set of guidelines

for considering whether the Poisson will provide

a reasonable model. For a more complete treatment

of the Poisson postulates, see the classic text

by Feller(1968)or Barr and Zehna(1983).

Back

Back

The postulates may also be interpreted as

describing the Behavior of objects spatially(for

example, movement of insects), giving the

Poisson application in spatial Distributions.

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Data for trial control limits, Example 1

sample size n50

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Initial fraction nonconforming control chart for

the data in Example 1

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Revised control limits for the data in Example 1

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Orange juice concentrate can data in samples of

size n50

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Continuation of the fraction nonconforming

control chart, Example 1.

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New control limits on the fraction nonconforming

control chart, Example 1.

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New data for the fraction nonconforming

control chart in Example 1, n50

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Completed fraction nonconforming control chart,

Example 1.

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Control chart for fraction nonconforming with

variable sample size

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Control chart for fraction nonconforming based

on average sample size

Back

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Standardize control chart for fraction

nonconforming

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Calculation for construction the OC curve for a

control chart for fraction nonconforming with

n50, LCL0.0303, and UCL0.3697.

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O.C. curve for the fraction nonconforming

control chart

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Data on the number of nonconformities in samples

of 100 printed circuit boards

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Control chart for nonconformities for Example 2

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Continuation of the control chart for

nonconformities, Example 2.

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Pareto analysis of nonconformities for the

printed circuit board process

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Table of defects classified by part number and

defect code

?

?

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Table of defects classified by part number and

defect code(continue)

?

?

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Cause and effect diagram

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Data on number of nonconformities in personal

computers

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A control chart for nonconformities per unit

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Nonconformities per unit control chart with

variable sample size, Example4.

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Calculation of the OC curve for a c chart with

UCL33.22 and LCL6.48

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Actions taken to improve a process

Is the process capable?

Yes

No

Yes

Is the process in control?

No

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Software available in the Journal of Quality

Technology

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Software available in the Journal of Quality

Technology (continued)

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Software available in the Journal of Quality

Technology (continued)

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Fraction nonconforming control chart for Example 6

???p0.05?process?100 samples(??200?) ??100

samples (??200?)???C.C.?limits

?????50 samples

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Fraction nonconforming control chart for Example

6(continue)

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R chart for Example 6

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