Ch4 Methods and Philosophy of SPC

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Ch4 Methods and Philosophy of SPC

• Statistical Process Control(SPC)
• 1. Powerful collection of problem-solving
  tools.
• 2. Reduce variability to achieve process
  stability improve capability.
• 3. Build an environment in which all
  individuals in an organization desire
• continuous improvement in quality and
  productivity.

• Seven major tools(The magnificent seven)
• 1. Histogram or stem-and-leaf display.
  2. Check sheet.
• 3. Pareto chart. 4. Cause and
  effect diagram.
• 5. Defect concentration diagram. 6.
  Scatter diagram.
• 7. Control chart.

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• In any production process, regardless of how
  well designed
• or carefully maintained it is, a certain amount
  of inherent or
• natural variability will always exist. This
  natural variability
• or background noise is the cumulative effect
  of many
• small, essential unavoidable causes.
• A process that is operating with only chance
  cause of
• variation present is said to be in
  statistical control.

• A process that is operating in the presence of
  assignable
• cause is said to be out of control.
• e.g. improperly adjusted or controlled
  machines,operator
• errors, or defective raw material.

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• SPC?????Elimination of variability in the
  process.
• 1. ???? assignable causes of process shift.
• 2. ??Control chart???on-line process-control
  
• technique,???detect process shift,????
• ????????????process capability,?
• ?????????????

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Control chart

• Shewhart control charts

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• Typical control chart
• Points plot within the control limits no
  nonrandom pattern process is in control, no
  action is necessary.
• A point plots outside of the control limits or
  random pattern exists process is out of
  control, investigation and correction action
  are required to eliminate the assignable cause.

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• A point plotting within the control limits is
  equivalent to
• failing to reject the hypothesis of statistical
  control.
• A point plotting outside the control limits is
  equivalent
• to rejecting the hypothesis of statistical
  control.
• Type I error of the control chart the process
  is out of
• control when it is really in control.
• Type II error of the control chart the process
  is in control
• when it is really out of control.
• Operating-characteristic cure an indication of
  the ability
• of the control chart to detect process shifts
  of different
• magnitudes.

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• ????

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Control chart ??????
??

• ?????????? control state?????

• Routine?attentive???control chart???
• assignable causes,???? causes ???
• variability?improve process?

• Control chart??detect assignable causes,
• management?operator and engineering
• action??eliminate??causes?

• ????

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Control chart ???????
(1)Variable control charts
variable????????????,??? ( i ) measure of
central tendency ( ii) measure of
variability ?????????
(2)Attributes control charts
attribute?????????????,??????? ( i )
conforming(non-defective) ( ii)
non-conforming(defective)
e.g. P chart(control chart for fraction non-
conforming), c chart, u chart.
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Design of the control chart
(1)Selection of the sample size
(2)Control limits
(3)Frequency of sampling
?????????economic??? e.g. 1. Cost of sampling
2. Losses from allowing excessive amounts of
defective product to be produced
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Choice of control limits
(1)k?? ? Type I error??
Type II error??
(2)k3, 3-sigma control limit(U.S.A.???????.)
prob. of type I error 0.0027, if
normality is assumed. ? An incorrect
out of control signal will be generated in
only 27 out of 10,000 points.
???????????,????probability limit??
(???)
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(???0.001 limits,?warning limits?0.025limits)
??????Warning limits?control limits??,? ??process?
??out of control.
Solution ? ?????????????
??sampling frequency?????
3-sigma limit???action limits,??????
3-sigma??,?????assignable cause,??
???????corrective action?

• ????

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Sample size and sampling frequency
(1)Larger samples easier to detect small shift in
the process.
????
(2)?detecting shifts??? --- large sample very
frequently ????economically feasible.

• Small samples at short intervals(current
  industry favor)

• Large samples at longer intervals.

• ????high volume manufacturing process???
• assignable causes??????,????????
• small samples at short intervals??????

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• ????Automatic sensing?measurement technology
• (e.g. microcomputers)??? ? ????????unit
• ??????tested!

• ???,The probability of detecting a shift from
  74.0000
• mm to 74.0100 mm increases as the sample
  size n increases.
• ??????the size of the shift????n????

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(3)?????????sample size ?sampling frequency
???--- Average run length(ARL)
the average number of points that
must be plotted
before a point indicate an out of control
condition.
E.g. Shewhart control chart?
?? p ??????Control limit???
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• ?????process??control??,???370???
• ??????out of control????

• ?sampling frequency????,??????370??
• ?????false alarm.

• ??n5,?process?mean?shift?74.015mm(i.e.
• process ?out of control),?????O.C. curve?

? ????,???shift?detect?shift??2???
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??improve??shift????
1. ??sample size n. e.g. n10?,?O.C.
curve?, p 0.9 ?
ARL1.11,ATS1.11 hours 2. Sampling more
frequency e.g. ??????????,????1????detect.
????shift???1??,?????detect??shift, ???????Design?
??
Design 1 Sample size n 5 Sampling
frequencyevery half hour
Design 2 Sample size n 10 Sampling
frequencyevery hour
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Rational subgroups???????
Using chart to detect changes in the
process mean ?Assignable causes???
(1)?differences between subgroups????????
(2)??assignable cause??difference within a
subgroup ????????
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Rational subgroups?????
(1)Each sample consists of units that were
produced at the same time (or as
chosely as possible)(snapshot).
---????detect process shift(???minimize within
sample variability?maximize between
sample variability ?????????standard
deviation????)
(2)Each sample consists of units of product that
are representive of all units that
have been product since the last sample was
taken. ?? each subgroup is a random sample
of all process output over the sampling
interval. ---?control chart
????????? All units of product
that have been product since the last sample.

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????
1. ?process shift to an out of control state and
then back in control between
samples,?????(1) ??????shift,????????(2)?
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???5? ????
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Patterns on Control Charts
DefnA run is defined as a sequence of the same
type, the number of the sequence is
called its length.
e.g. A sequence of increasing (decreasing)points
is called a run up(down).
??A run of length 8 or more points has a very low
probability of occurrence in a random sample of
points. ? ???out of control????
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• ??????????? operator fatigue, raw material
  deliveries, heat, or stress build up and so
  forth,??process?????out of control,???????????????
  ??variability,????

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The Western Electric Handbook(1956)suggests a set
of decision rules for detecting nonrandom
patterns on control charts. Specifically, it
suggests concluding that the process is out of
control if either
1. One point plots outside the 3-sigma control
limits.
2. Two out of three consecutive points plot
beyond the 2-sigma warning limits.
3. Four out of five consecutive points plot at a
distance of 1-sigma or beyond from the
center line.
4. Eight consecutive points plot on one side of
the center line.
These rules apply to one side of the center
line at a time.
Sensitizing rules
5. An unusual or nonrandom pattern in the data.
6. One or more points near a warning or control
limit.
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??? ???4???? 1-sigma limit. ???Western
Electric zone rules,??
nonrandom?pattern, ?process is out of
control.
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The rest of the Magnificent Seven
1. Histogram
2. Check sheet
3. Pareto chart
4. Cause and effect diagram
5. Defect concentration diagram
6. Scatter diagram
7. Control chart
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A check sheet to record defects on tank use in
an aerospace application

• ??????????tank,
• ???summarizing the data
• monthly!

• Time-oriented summary???
• ??????trend or patterns.

• ???trial run??the check
• sheet layout and design.

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• The Pareto chart does not identify the most
  important defects,
• but only these that occur most frequently.

Pareto chart of the tank defect data
Frequency distribution (histogram) of attribute
data arranged by category
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Example of Pareto charts Electronic assembly
process
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Non-manufacturing applications of
quality-improvement method. e.g. ???????Pareto
charts
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Cause and effect diagram for the tank defect
problem
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Cause and effect diagram
1. Define the problem or effect to be analyzed.
2. Form the team to perform the analysis. Often
the team will uncover potential causes through
brainstorming. 3. Draw the effect box and the
center line. 4. Specify the major potential
cause categories and join them as boxes connected
to the center line. 5. Identify the possible
causes and classify them into the categories in
steps 4. Create new categories,it necessary. 6.
Rank order the causes to identify those that seem
most likely to impact the problem. 7. Take
corrective action.
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Defect concentration diagram ???
1. Surface-finish defects on a refrigerator.
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2. Defect concentration diagram for the tank.
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A scatter diagram
Identify potential relationship. Not necessary
imply causality!
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4-6 SPC???(???)

• ????????????????,????????
• ?,???????????
• 1. brittle copper (????)
• 2. copper voids (????)
• 3. Long flow time (????????,?????
• ????????,????????)
• ??????????Improvement Team
• 1. Plating Tank Operator
• 2. ??????????
• 3. Quality engineer

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• ?????Magnificent seven ?

• ????????????????????? miss delivery
  target ,????????????????flow time.
• ??operator???,????????????flow
• time???????????????????????(downtime)???
• ??Cause and Effect Analysis
• 1. ?????????Controller downtime?11????
• 2. ????Check sheet??????(logbook)?,?
• ?????????????????Check sheet?
• 3. ??4-6?????(????6??)?

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• Pareto analysis

• ?Pareto analysis?,???????colorimeter???
• ????????

• ?????????????Control charts?monitor
• Copper concentration,??????????????
• ?Copper concentration,?????? ?

chart
R chart (maximum-minimum)Jan. 3. ? Tolerance
Diagram (?????????????,? Tolerance
Diagram?????specification limits??control
limits,??observation?????,?????!)???? ??Jan.
3.?????,??????????
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• 2??,?manufacturing engineering??colorimeter?
• controller ,????????cooper concentration?
• variation?pre-shutdown?level?

• ???controller?downtime?60????20,?
• ?process???????production rate?

• ???????????????????,??defect
• ??????1.brittle copper2.copper voids.

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• ??????????????identify controllable input
• variables into the process.

1. ??---Minimize ??????? 2. ??Table
4-1?16runs, ??5???factorsCopper
concentration?Sodium hydroxide
concentration?Formaldehyde concentration?
Temperature?Oxygen? 3.??????????????????
?? 4.????????????level??,???????
?1/10?

• ????SPC???,????????????,??
• ????????,??????toward??near-zero-
• defect?capability?

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4-7 SPC???(????)

• ??????????SPC????????????
• 1. ?????,?????????????
• 2. ?????,??improve?system????
• ??1. ???---PC assembly line?performance
• 2.????---finance
  organization???,
• marketing,material and
  procurement,
• customer support,field
  service,engineering
• development and
  design,software
• development and
  programming?

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• ???????SPC??,??????
• 1. ???????????
• 2. ????????????
• ?????
• 1. Flow charts---???identify?process?value
  -added
• 
  ?non-value-added?activities.
• 2. Operation process charts
• ?????????????process?

• ???????10??????non-value-added?activities.
• e.g. ?????????

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?????????????????? planning
organization???????
????plans?documents,??? ???

• ????plans???,???????,????,
• ???factory floor?????
• e.g. rework, scrap, overtime, lost
  production time, missed
• delivery schedule.

• ?high-level flow chart,??flow chart???,??
• ?????non-value-added activities?

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• ???step-down?approach?
• e.g. ???block(?planner, check)??????
• ?????.

• ?planning organization????????planning
• errors??????????

• ???????????
• managers, planners, and checkers?

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• ????planning process????,???identify???
• ???planner???????supervision??,????
• ???????poor input information???,???
• causes???????????,????????SPC?
• ????,??planning errors????one planning error
  
• per 1000 operations?

• ??????????3?plans,???????errors?

• Check sheet(????plan)
• ?Summary check sheet(??????)

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• Pareto analysis65?planning error???operations
  
• section?

• Pareto analysisomitted operations?process
  specification
• ?operation
  section error????

• ????planning errors???????
• 1. Planner???????????????
• 2. Planner?????????process
  specification?

• ??????program??planner??????,??
• ?planner??????planning
  errors?????
• feedback?

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• ???run chart of planning errors???
• planning errors / per
  operation?????????
• ???,?????????Planner?
• 1. Increased training2.
  Supervision activities?
• ????????????planning error????
• ??

• ???????????team??????????plan,
• ???????????plan,??????factory?
• planning?????????

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• ??SPC???????planner???,??????
• ????????,?run chart of planning errors??
• ???cater line????,???????control chart?

• Control chart????????????identify assignable
• cause?

• ????assignable causes,?????????????
• ??????chance cause!

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• ??assignable cause??,???????,????root
• causes?

• ?chance cause?????????????,?????
• ?????????????????????????,
• ?????Management????

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A typical control chart
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Next
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How the control chart works
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Process improvement using the control chart
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Action limit
Warning limit
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Check sheet for logbook
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Pareto analysis of controller failures
??Reagent replenish????concentration
variation???,????????(???process back on line)
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Pareto analysis of concentration variation
??colorimeter drift???, ??????
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???????,????????
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??lack of statistical control.
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?????10???non-value-added???

1. Rearranging the sequence of work-steps.
2. Rearranging the physical location of the
   operators n the system.
3. Changing work methods.
4. Changing the type of equipment used in the
   process.
5. Redesigning forms and documents for more
   efficient use.
6. Improving operator training.
7. Improving supervision.
8. Identifying more clearly the function of the
   process to all employees.
9. Trying to eliminate unnecessary steps.
10. Trying to consolidate process steps.

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Check sheet for the planning example
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The summary check sheet
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Pareto analysis of planning errors
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Pareto analysis of operations section errors
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A run chart of planning errors
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