Points which might be emphasized include: - Statistical process control measures the performance of a process, it does not help to identify a particular specimen produced as being “good” or “bad,” in or out of tolerance. - Statistical process control requires the collection and analysis of data - therefore it is not helpful when total production consists of a small number of units - While statistical process control can not help identify a “good” or “bad” unit, it can enable one to decide whether or not to accept an entire production lot. If a sample of a production lot contains more than a specified number of defective items, statistical process control can give us a basis for rejecting the entire lot. The issue of rejecting a lot which was actually good can be raised here, but is probably better left to later.
Students should understand both the concepts of natural and assignable variation, and the nature of the efforts required to deal with them.
This slide helps introduce different process outputs. It can also be used to illustrate natural and assignable variation.
Once the categories are outlined, students may be asked to provide examples of items for which variable or attribute inspection might be appropriate. They might also be asked to provide examples of products for which both characteristics might be important at different stages of the production process.
Transcript
1. © 2008 Prentice Hall, Inc. S6 – 1
Process Control
Process Capability
Measurement & Index
BY:- ABHISHEK RAJPUTBY:- ABHISHEK RAJPUT
SAKSHI SRIVASTAVSAKSHI SRIVASTAV
SWATI TANDONSWATI TANDON
2. © 2008 Prentice Hall, Inc. S6 – 2
 Process ControlProcess Control
 Process CapabilityProcess Capability
 Process Capability RatioProcess Capability Ratio (C(Cpp))
 Process Capability IndexProcess Capability Index (C(Cpkpk ))
3. © 2008 Prentice Hall, Inc. S6 – 3
 Variability is inherent
in every process
 Natural or common
causes
 Special or assignable causes
 Provides a statistical signal when assignable causes
are present
 Detect and eliminate assignable causes of variation
4. © 2008 Prentice Hall, Inc. S6 – 4
 Also called common causesAlso called common causes
 Affect virtually all production processesAffect virtually all production processes
 Expected amount of variationExpected amount of variation
 Output measures follow a probabilityOutput measures follow a probability
distributiondistribution
 For any distribution there is a measureFor any distribution there is a measure
of central tendency and dispersionof central tendency and dispersion
 If the distribution of outputs falls withinIf the distribution of outputs falls within
acceptable limits, the process is said toacceptable limits, the process is said to
be “in control”be “in control”
5. © 2008 Prentice Hall, Inc. S6 – 5
 Also called special causes of variationAlso called special causes of variation
 Generally this is some change in the processGenerally this is some change in the process
 Variations that can be traced to a specificVariations that can be traced to a specific
reasonreason
 The objective is to discover whenThe objective is to discover when
assignable causes are presentassignable causes are present
 Eliminate the bad causesEliminate the bad causes
 Incorporate the good causesIncorporate the good causes
6. © 2008 Prentice Hall, Inc. S6 – 6
To measure the process, we take samplesTo measure the process, we take samples
and analyze the sample statistics followingand analyze the sample statistics following
these stepsthese steps
(a)(a) Samples of theSamples of the
product, say fiveproduct, say five
boxes of cerealboxes of cereal
taken off the fillingtaken off the filling
machine line, varymachine line, vary
from each other infrom each other in
weightweight
FrequencyFrequency
WeightWeight
##
#### ##
####
####
##
## ## #### ## ####
## ## #### ## #### ## ####
Each of theseEach of these
represents onerepresents one
sample of fivesample of five
boxes of cerealboxes of cereal
Figure S6.1Figure S6.1
7. © 2008 Prentice Hall, Inc. S6 – 7
To measure the process, we take samplesTo measure the process, we take samples
and analyze the sample statistics followingand analyze the sample statistics following
these stepsthese steps
(b)(b) After enoughAfter enough
samples aresamples are
taken from ataken from a
stable process,stable process,
they form athey form a
pattern called apattern called a
distributiondistribution
The solid lineThe solid line
represents therepresents the
distributiondistribution
FrequencyFrequency
WeightWeightFigure S6.1Figure S6.1
8. © 2008 Prentice Hall, Inc. S6 – 8
To measure the process, we take samplesTo measure the process, we take samples
and analyze the sample statistics followingand analyze the sample statistics following
these stepsthese steps
(c)(c) There are many types of distributions, includingThere are many types of distributions, including
the normal (bell-shaped) distribution, butthe normal (bell-shaped) distribution, but
distributions do differ in terms of centraldistributions do differ in terms of central
tendency (mean), standard deviation ortendency (mean), standard deviation or
variance, and shapevariance, and shape
WeightWeight
Central tendencyCentral tendency
WeightWeight
VariationVariation
WeightWeight
ShapeShape
FrequencyFrequency
Figure S6.1Figure S6.1
9. © 2008 Prentice Hall, Inc. S6 – 9
To measure the process, we take samplesTo measure the process, we take samples
and analyze the sample statistics followingand analyze the sample statistics following
these stepsthese steps
(d)(d) If only naturalIf only natural
causes ofcauses of
variation arevariation are
present, thepresent, the
output of aoutput of a
process forms aprocess forms a
distribution thatdistribution that
is stable overis stable over
time and istime and is
predictablepredictable
WeightWeight
Time
Time
FrequencyFrequency
PredictionPrediction
Figure S6.1Figure S6.1
10. © 2008 Prentice Hall, Inc. S6 – 10
To measure the process, we take samplesTo measure the process, we take samples
and analyze the sample statistics followingand analyze the sample statistics following
these stepsthese steps
(e)(e) If assignableIf assignable
causes arecauses are
present, thepresent, the
process output isprocess output is
not stable overnot stable over
time and is nottime and is not
predicablepredicable
WeightWeight
Time
Time
FrequencyFrequency
PredictionPrediction
????
??
??
??
??
??
??????
??
??
??
??
??
??
??????
Figure S6.1Figure S6.1
11. © 2008 Prentice Hall, Inc. S6 – 11
Constructed from historical data, theConstructed from historical data, the
purpose of control charts is to helppurpose of control charts is to help
distinguish between natural variationsdistinguish between natural variations
and variations due to assignableand variations due to assignable
causescauses
12. © 2008 Prentice Hall, Inc. S6 – 12
FrequencyFrequency
(weight, length, speed, etc.)(weight, length, speed, etc.)
SizeSize
Lower control limitLower control limit Upper control limitUpper control limit
(a) In statistical(a) In statistical
control and capablecontrol and capable
of producing withinof producing within
control limitscontrol limits
(b) In statistical(b) In statistical
control but notcontrol but not
capable of producingcapable of producing
within control limitswithin control limits
(c) Out of control(c) Out of control
13. © 2008 Prentice Hall, Inc. S6 – 13
 Characteristics thatCharacteristics that
can take any realcan take any real
valuevalue
 May be in whole orMay be in whole or
in fractionalin fractional
numbersnumbers
 Continuous randomContinuous random
variablesvariables
VariablesVariables AttributesAttributes
 Defect-relatedDefect-related
characteristicscharacteristics
 Classify productsClassify products
as either good oras either good or
bad or countbad or count
defectsdefects
 Categorical orCategorical or
discrete randomdiscrete random
variablesvariables
14. © 2008 Prentice Hall, Inc. S6 – 14
1.1. Take samples from the population andTake samples from the population and
compute the appropriate sample statisticcompute the appropriate sample statistic
2.2. Use the sample statistic to calculate controlUse the sample statistic to calculate control
limits and draw the control chartlimits and draw the control chart
3.3. Plot sample results on the control chart andPlot sample results on the control chart and
determine the state of the process (in or out ofdetermine the state of the process (in or out of
control)control)
4.4. Investigate possible assignable causes andInvestigate possible assignable causes and
take any indicated actionstake any indicated actions
5.5. Continue sampling from the process and resetContinue sampling from the process and reset
the control limits when necessarythe control limits when necessary
15. © 2008 Prentice Hall, Inc. S6 – 15
16. © 2008 Prentice Hall, Inc. S6 – 16
 The natural variation of a processThe natural variation of a process
should be small enough to produceshould be small enough to produce
products that meet the standardsproducts that meet the standards
requiredrequired
 A process in statistical control does notA process in statistical control does not
necessarily meet the designnecessarily meet the design
specificationsspecifications
 Process capability is a measure of theProcess capability is a measure of the
relationship between the naturalrelationship between the natural
variation of the process and the designvariation of the process and the design
specificationsspecifications
17. © 2008 Prentice Hall, Inc. S6 – 17
CCpp ==
Upper Specification - Lower SpecificationUpper Specification - Lower Specification
66σσ
 A capable process must have aA capable process must have a CCpp of atof at
leastleast 1.01.0
 Does not look at how well the processDoes not look at how well the process
is centered in the specification rangeis centered in the specification range
 Often a target value ofOften a target value of CCpp = 1.33= 1.33 is usedis used
to allow for off-center processesto allow for off-center processes
 Six Sigma quality requires aSix Sigma quality requires a CCpp = 2.0= 2.0
18. © 2008 Prentice Hall, Inc. S6 – 18
CCpp ==
Upper Specification - Lower SpecificationUpper Specification - Lower Specification
66σσ
Insurance claims processInsurance claims process
Process mean xProcess mean x = 210.0= 210.0 minutesminutes
Process standard deviationProcess standard deviation σσ = .516= .516 minutesminutes
Design specificationDesign specification = 210 ± 3= 210 ± 3 minutesminutes
19. © 2008 Prentice Hall, Inc. S6 – 19
CCpp ==
Upper Specification - Lower SpecificationUpper Specification - Lower Specification
66σσ
Insurance claims processInsurance claims process
Process mean xProcess mean x = 210.0= 210.0 minutesminutes
Process standard deviationProcess standard deviation σσ = .516= .516 minutesminutes
Design specificationDesign specification = 210 ± 3= 210 ± 3 minutesminutes
= = 1.938= = 1.938
213 - 207213 - 207
6(.516)6(.516)
20. © 2008 Prentice Hall, Inc. S6 – 20
CCpp ==
Upper Specification - Lower SpecificationUpper Specification - Lower Specification
66σσ
Insurance claims processInsurance claims process
Process mean xProcess mean x = 210.0= 210.0 minutesminutes
Process standard deviationProcess standard deviation σσ = .516= .516 minutesminutes
Design specificationDesign specification = 210 ± 3= 210 ± 3 minutesminutes
= = 1.938= = 1.938
213 - 207213 - 207
6(.516)6(.516)
Process is
capable
21. © 2008 Prentice Hall, Inc. S6 – 21
 A capable process must have aA capable process must have a CCpkpk of atof at
leastleast 1.01.0
 A capable process is not necessarily in theA capable process is not necessarily in the
center of the specification, but it falls withincenter of the specification, but it falls within
the specification limit at both extremesthe specification limit at both extremes
CCpkpk = minimum of ,= minimum of ,
UpperUpper
Specification - xSpecification - x
LimitLimit
3σ3σ
LowerLower
x -x - SpecificationSpecification
LimitLimit
3σ3σ
22. © 2008 Prentice Hall, Inc. S6 – 22
New Cutting MachineNew Cutting Machine
New process mean xNew process mean x = .250 inches= .250 inches
Process standard deviationProcess standard deviation σσ = .0005 inches= .0005 inches
Upper Specification LimitUpper Specification Limit = .251 inches= .251 inches
Lower Specification LimitLower Specification Limit = .249 inches= .249 inches
23. © 2008 Prentice Hall, Inc. S6 – 23
New Cutting MachineNew Cutting Machine
New process mean xNew process mean x = .250 inches= .250 inches
Process standard deviationProcess standard deviation σσ = .0005 inches= .0005 inches
Upper Specification LimitUpper Specification Limit = .251 inches= .251 inches
Lower Specification LimitLower Specification Limit = .249 inches= .249 inches
CCpkpk = minimum of ,= minimum of ,
(.251) - .250(.251) - .250
(3).0005(3).0005
24. © 2008 Prentice Hall, Inc. S6 – 24
New Cutting MachineNew Cutting Machine
New process mean xNew process mean x = .250 inches= .250 inches
Process standard deviationProcess standard deviation σσ = .0005 inches= .0005 inches
Upper Specification LimitUpper Specification Limit = .251 inches= .251 inches
Lower Specification LimitLower Specification Limit = .249 inches= .249 inches
CCpkpk = = 0.67= = 0.67
.001.001
.0015.0015
New machine is
NOT capable
CCpkpk = minimum of ,= minimum of ,
(.251) - .250(.251) - .250
(3).0005(3).0005
.250 - (.249).250 - (.249)
(3).0005(3).0005
Both calculations result inBoth calculations result in
25. © 2008 Prentice Hall, Inc. S6 – 25
THANK YOUTHANK YOU
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