Ch6 Control Charts for Attributes

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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

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Control chart for fraction nonconformingP chart
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• ?process?fraction nonconforming p???,???
• ?????????n???,??m?,?

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• ??trial control chart??????

1. ?????,????recheck?
2. ????,????chance???,??????trial control limit?

????????trial control limits??,??????????????patte
rns,???????,pattern????,?????????assignable cause?
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• ?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?

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Example 1
Cardboard cans for frozen orange juice
concentrate.
Nonconforming???e.g. ?side seam?bottom
joint?? Samplen50 cans,m30 ???????????????,????
?,???? ?????

1. Data ????
2. Trial control chart????
3. Sample 15?23 outside control limits.
4. ????,?sample 15?,??????cardboard??????????,??????,
   ???????????sample 23???????????????operator??????
   ??
   ? ???sample 15?23??,??control chart?

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1. ???control chart limits?control chart????
2. 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?
3. ???process???in control,??p0.2150????,??????workf
   orce??????,????management????improve!
4. Management??engineering staff???????,?????????????
   ??????

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1. ???,???????,n50,??24??Data???,Control chart????
   ?
   ?process??????level???,?41 below control
   limit????assignable cause?
2. ????????????

???????

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

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12. ?????(???),?C.C. (???) ? Process is
in control.
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Fraction nonconforming control chart ???

• ??????1. Sample size(n)
• 2. Frequency of
  sampling
• 3. Width of the
  control limits(k)
• (????economic???)

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• Sampling frequency????????control chart?
• ??100 inspection of all process output over
  some
• convenient period of time??????,sample
  size(n)
• ???????,???????sampling frequency
• ????

1. Production rate
2. Rational subgroup

e.g. ??????,??????????shift??,
???????shift?output?subgroup,????
???output?subgroup?
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• Sample size? p ???,????? n ??,???
• ??????????????????,?????
• ???C.C.??sample????????reject????
• ???

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?? I??D??????,????
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?? IIDuncan(1974) n?????,?process
shift???????,???detect ?shift ?????50?
???n ??upper control limit??out of control ??????
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• ??in-control?? p ??,??? n,??C.C.
• ?????0,??????????????
• ???(??????? inspection error ??
• ?, e.g. ????inspector ,??????
• ???)??

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• ?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??????
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• ???????????np control chart.

????,????????????,?? np chart? p chart?????
e.g. Fraction nonconforming orange juice
concentration cans. ???????????,??UCL21,LC
L2, ??????np???UCL?LCL????,???
?out of control?
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• ?sample size???????
• ?????fraction nonconforming?C.C.?,???
• ???????????????100?process
• output,??????????????????,
• ??????variable sample size????

e.g. ????data,???
C.C.????
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?????Average sample size(??????????
sample size?????sample size???????) ?????sampl
e size???????????control
limit?,???exact?control limits?????
??out of control?
e.g. ????
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????variable sample size?C.C.?,runs????
nonrandom patterns????????
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?????standardized C.C.?
?????????standard deviation????
??(continue),data???,C.C.???? ?observation????????
????, Tests for runs?pattern recognition????????
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• ?????????????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. ????????????

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• ???????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?
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• O.C. curve?ARL

(??????)

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

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• 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. ????????????

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

• ? xnonconformities ???Poisson ( c )

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Example 2
Inspection unit100 printed circuit boards. ??26
successive samples of 100 printed circuit
boards. (data ???)?
(???)
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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??????
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• ????,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?
???????
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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????
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• Sample sizen inspection units (e.g. n2.5)

1. Revised chart
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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.
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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.

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Alternative Probability Models for Count Data
(?????Count data???????)
E.g. nonconformities??cluster??
????Jackson(1972), Leavenworth(1976),
Gardiner(1987)?
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• 100??(e.g. ?????)?
• c chart?????C.L.????,u chart??C.L.
• ?n???

• ???????? ? ???u chart,???c chart?
• ??????control chart

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Example 4

• ????

• ????

• inspection unit ?50????

• Data???,control chart????

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• ?????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
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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
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The demerit weights of Class A-100, Class B-50,
Class C-10, and Class D-1 are used fairly widely
in practice.
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D is the total number of demerits in all n
inspection units.
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• ???????
• 1. Two-class??
• 2. ????defect class ?????C.C.

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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.
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• For the u chart, we may generate the OC curve
  from

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

• ??,u?c chart?ineffective !

• ????????C.C.
• the time between successive occurrences
  of defects

• c?u chart?????????????

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Choice Between Attributes and Variables Control
Charts

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

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• 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.?

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

• ????unit??????, ??variable type???
• ?????,????????????units???
• ?,???destructive????????????

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Example 5
? n9
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Sample size on the P chart
? Specification limit is 3-sigma. ? p0.0027
? n79.13(?80)
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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.

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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.

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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

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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
• (???)

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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.
• (???)

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Example 6

• ????

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????(Example 1)
Back
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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
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Back
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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.
Back
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Data for trial control limits, Example 1
sample size n50
Back
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Initial fraction nonconforming control chart for
the data in Example 1
Back
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Revised control limits for the data in Example 1
Back
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Orange juice concentrate can data in samples of
size n50
Back
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Continuation of the fraction nonconforming
control chart, Example 1.
Back
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New control limits on the fraction nonconforming
control chart, Example 1.
Back
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New data for the fraction nonconforming
control chart in Example 1, n50
Back
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Completed fraction nonconforming control chart,
Example 1.
Back
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Back
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Control chart for fraction nonconforming with
variable sample size
Back
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Control chart for fraction nonconforming based
on average sample size
Back
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Back
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Standardize control chart for fraction
nonconforming
Back
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Calculation for construction the OC curve for a
control chart for fraction nonconforming with
n50, LCL0.0303, and UCL0.3697.
Back
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O.C. curve for the fraction nonconforming
control chart
Back
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Data on the number of nonconformities in samples
of 100 printed circuit boards
Back
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Control chart for nonconformities for Example 2
Back
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Continuation of the control chart for
nonconformities, Example 2.
Back
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Pareto analysis of nonconformities for the
printed circuit board process
Back
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Table of defects classified by part number and
defect code
?
?
Back
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Table of defects classified by part number and
defect code(continue)
?
?
Back
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Cause and effect diagram
Back
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Data on number of nonconformities in personal
computers
Back
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A control chart for nonconformities per unit
Back
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Nonconformities per unit control chart with
variable sample size, Example4.
Back
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Calculation of the OC curve for a c chart with
UCL33.22 and LCL6.48
Back
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Actions taken to improve a process
Is the process capable?
Yes
No
Yes
Is the process in control?
No
Back
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Software available in the Journal of Quality
Technology
Back
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Software available in the Journal of Quality
Technology (continued)
Back
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Software available in the Journal of Quality
Technology (continued)
Back
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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
Back
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Fraction nonconforming control chart for Example
6(continue)
Back
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Back
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R chart for Example 6
Back