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Process Capab i li ty
Process Capabi l i ty is the Ab i l ity o f aProcess to Consis tent ly Meet Specif iedCustom er-Driven Requ irements
Speci f icat ion Lim its are Set by Management
in Response to Customers Expectationsand needs
The Upper Specif icat ion Lim it (USL) is theLargest Value that Can Be Obtained and Sti ll
Conform to Customers Expectation The Lower Speci f icat ion Lim it (LSL) is theSmallest Value that is Stil l Con form ing
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Process Capab i li ty
Range of natural var iabi l ity in pro cess
Measured w ith con tro l chart for
indiv iduals.
Process cannot meet speci f icat ions i f
natu ral variabi l i ty exceeds tolerances
3-sigma qual ity
Specif icat ions equal 3 variat ionf rom the mean
6-sigma qual ity
Specif icat ions equal 6 variationf rom the mean
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Capabi l i ty Versus Con tro l
Control
Capability
Capable
Not Capable
In Control Out of Control
IDEAL
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Process Capab i li ty
(b) Design specificationsand natural variation thesame; process isjustcapable of meetingspecifications most thetime.
DesignSpecifications
Process
(a) Natural variationexceeds designspecifications; processis not capable of
meeting specificationsall the time.
DesignSpecifications
Process
LSL USL
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Process Capab i li ty
(c) Design specificationsgreater than naturalvariation; process iscapable of always
conforming tospecifications.
DesignSpecifications
Process
(d) Specifications greaterthan natural variation,but process off center;capable but some outputwill not meet upperspecification.
DesignSpecifications
Process
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Capab i l ity Ind ices
Aggregate Measures of a Process Abilityto Meet Speci f icat ion Lim its
The larger (>1) the values, the more capable a
proc ess is of meeting requirements Measure o f Process Potent ia l Performance
Cp>1 impl ies that a process has the po tential ofhaving m ore than 99.73% of outcomes with inspeci f icat ions
2specification spread
process spread6 /p
USL LSLC
R d
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Process Capab i li ty
MeasuresProcess Capabi l i ty Ratio
Cp =
=
tolerance range
process range
upper specification limit -lower specification limit
6
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Compu ting Cp
Net weight specification = 9.0 oz 0.5 ozProcess mean = 8.80 oz
Process standard deviation = 0.12 oz
Cp =
= = 1.39
upper specification limit -lower specification limit
6
9.5 - 8.5
6(0.12)
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Capab i l ity Ind ices
Measures of Actual Process Performance
For one-sided speci f icat ion l imi ts
CPL (CPU)>1 impl ies that the process mean is mo re
than 3 standard deviat ions away from th e low er
(upp er) specif icat ion l imit
(continued)
23 /X LSLCPL
R d
23 /USL X
CPUR d
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Capab i l ity Ind ices
For two -sided speci fication l imi ts
Cpk= 1 ind icates th at the process average is3 standard deviat ions away from the closest
speci f ication l imi t
LargerCpkind icates larger capabi l i ty of
meet ing the requirements
(continued)
min ,pkC CPL CPU
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Process Capab i li ty
MeasuresProcess Capabi l i ty Index
Cpk= minimum
x- lower specification limit
3=
upper specification limit - x
3=
,
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Comput ing Cpk
Net weight specification = 9.0 oz 0.5 ozProcess mean = 8.80 oz
Process standard deviation = 0.12 oz
Cpk= minimum
= minimum , = 0.83
x- lower specification limit
3=
upper specification limit - x
3
=
,
8.80 - 8.50
3(0.12)
9.50 - 8.80
3(0.12)
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Est imat ing Process
Capabil i ty Mus t Have an In-Con tro l Process First
Est imate the Percentage of Produc t or
Servic e Within Specif icat ion
Assum e the Populat ion ofX Values is
Approx imately Normal ly Dis t r ibuted wi th
Mean Est imated by and Standard
Deviation Est imated byX
2/R d
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Key Idea
Process capability calculations make littlesense if the process is not in statisticalcontrol because the data are confoundedby special causes that do not representthe inherent capability of the process.
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Process Capability
Process capability refers to the performance of
the process when it is operating in control.
Two graphical tools are helpful in assessingprocess capability:
Tolerance chart (or tier chart)
Histogram
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Process Capability
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Process Capability
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Process Capability
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Process Capability
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Remedial act ion fo r Cp < 1(fo r b i lateral specif icat ion s case)
1. a) X = (U+L)/2
b) We must maintain control charts
with high value of n so that controlchart is more sensitive and we get a
quick indication that process has gone
out of control
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Remedial act ion for Cp < 1(fo r b i lateral specif icat ions case)
2. Sometimes spec. limits are fixed arbitrarily and no
time/ effort is spent on their justification.
THEREFORE REVIEW AND REVISE THE
SPECIFICATION LIMITSIf spec. limits can be relaxed then problem can be
solved to a certain extent
Note: While fixing the spec. limits the designer
must give due considerations to Functional needs
Process Capability
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Remedial act ion for Cp < 1(fo r b i lateral specif icat ions case)
3. Reduce (process dispersion)a) can be done to some extent by
Employing better and skilled persons
Better training & supervision
Material of better quality
b) If we many different machines withvarying process capability, then jobs
requiring narrow tolerances should beassigned to those machines capable ofholding narrow tolerances
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Remedial act ion for Cp < 1(fo r b i lateral specif icat ions case)
c ) Make a fundamental change in the productionprocess in o rder to reduce the whichimplies we can go for a process of higher
precision but this change will be a matter of
cost in terms of additional investment inhigher precision equipment.
NPV
IRR
Payback periodEvaluating investments
on financial criteria
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Remedial ac t ion for Cp < 1(fo r b i lateral specif icat ion s case)
4. The wors t so lu t ion w i ll be to con tinuethe process as such and segregate the
defect ives thru 100% inspect ion
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Sing le speci f icat ion case
23 /X LSL
CPLR d
23 /USL X
CPUR d
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Single speci f icat ion case (L )
Al l the i tems p rodu ced w i l l be non defect ive i f
X - 3 LThree possible cases are
1. X - 3 > L Cp l > 12. X - 3 ~ L Cp l ~ 13. X - 3 < L Cp l < 1
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Sing le spec i f icat ion case (L )
Add i t ional remedial act ions forCp l < 1
Increase the process average
Review and revise the specif icat ion
l imits
Reduce dispers ion of the process
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LIMITATIONS OF X BAR R & CHARTS
1. Can be used on ly fo r var iab le q lt y. Ch.
Some ql ty. ch . can no t be measu red or
quant i f ied
---- appearance, cracks , damages, scratches
etc.
Such qlty . Ch. Can only be viewed as
attr ibute.
Each inspected i tem can on ly beclassi f ied as defect ive or non defect ive
In such cases charts fo r var iables can
no t be used
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LIMITATIONS OF X BAR R & CHARTS
2. Measurements fo r above char ts are
expens ive and take more t ime.
Somet imes to reduce time and cost
someq lty. ch . are measu red as
attr ibutes.GO / NO GO GAUGES
3. A Separate con tro l char t is needed fo r
each qual i ty char. This is a ser ious
l imitat ion/disadvantage.therefore we use above charts for
cr i t ic al variab les caus ing
subs tant ia l Rework or Reject ion .
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LIMITATIONS OF X BAR R & CHARTS
4. Use of X BAR R has to be justified.
Used when
a. U L b. Mass production item
c. Cs & Crare substantial
5. Economic Justificationa. Savings --- in reduction of defectives
b. Cost Cost of data collection and charting
Cost of interpretation of chart (specialist required)
Actual troubleshooting based on evidence from control
chart because this may involve loss in production or
shutdown