assessing process capability: a user’s view fred spiring & smiley cheng the university of...
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Perspective Fall Technical Conference 2000 –Post (2000)-Practitioner’s view –Ramberg (2000)-Research view J. of Quality Technology (January 2002) –Process Capability Indices-A Review, , Kotz and Johnson-Research view –Comments- variety of perspectivesTRANSCRIPT
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Assessing Process Capability: Assessing Process Capability: A User’s ViewA User’s View
Fred Spiring & Smiley ChengThe University of Manitoba
& Pollard Banknote Ltd
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OverviewOverview
PerspectiveProcess BackgroundAssessing Process CapabilityEstablishing Specs & TolerancesMonitoring the ProcessImproving the ProcessResearch areas
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PerspectivePerspective
Fall Technical Conference 2000– Post (2000)-Practitioner’s view– Ramberg (2000)-Research view
J. of Quality Technology (January 2002)– Process Capability Indices-A Review, 1992-
2000, Kotz and Johnson-Research view– Comments- variety of perspectives
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Process BackgroundProcess Background Producing Lottery Tickets
– Multistage process, involving up to five printing presses
– Multiplant organization, similar process with different equipment
– Requirements and regulations result in interplant production
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Process BackgroundProcess Background
Customer concepts
Marketing translates into
Customer Specifications
Prepress translates Customer
Specifications into Production Specifications
Manufacturing runs to the Production
Specifications
Customer Specifications
Production Specifications
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Process BackgroundProcess Background
Preproduction – Customer concepts/art/requirements
are translated into formal Customer Specifications by Marketing Group
– In-house artists translate Customer Specifications into Production Specifications
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Process BackgroundProcess Background
PreproductionPreproduction– Production Specifications were based
on artists’ knowledge of colour rather than production equipment
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Assessing Process CapabilityAssessing Process Capability
Design Specifications
– Continue to reflect artistic capabilities, such as colour sequence, traps, …
– incorporate equipment capabilities in the design of the Lottery Ticket
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Assessing Process CapabilityAssessing Process Capability
Customer concepts
Marketing translates into
Customer Specifications
Prepress translates Customer
Specifications into Production Specifications
Manufacturing runs to the Production
Specifications
Customer Specifications
Production Specifications
Design Specifications
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Assessing Process CapabilityAssessing Process Capability
Trim Edge
red-to-base across
red-to-base along
Stock Edge
gray-to-base across
gray-to-base along
Crosshairs and L marks
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Assessing Process CapabilityAssessing Process Capability Assessed the normality of the sample
results in both the “across” and “along” directions
Examined “along” and “across” correlations
Assessed proximity of sample averages to targets
Examined the variability in the “across” and “along” directions
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Assessing Process CapabilityAssessing Process Capability
Michigan
3 std deviations
Base to across along
red 0.011” 0.015”
gray 0.010” 0.015”
cyan 0.010” 0.019”
magenta 0.010” 0.020”
(n = 66)
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Establishing Specifications Establishing Specifications
Yred
Xred
Web direction(along)
XKO
YKO
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Establishing SpecificationsEstablishing Specifications
Assuming that the “Red box” must be within the KO 99.5% of the time, then:
Xred = XKO - .022 inches (across)
Yred = YKO - .030 inches (along)
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YKO
Establishing Specifications Establishing Specifications
Yred = YKO – 0.030”
Xred = XKO – 0.022”
XKO
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Establishing SpecificationsEstablishing Specifications
Critical area that requires workSpecifications need to be legitimate
and well thought outUnreasonable specifications have
lead to criticism of PCIsShould be based on the process
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Monitoring the processMonitoring the process
Process is monitored daily to assess the efforts required to maintain registration
– Automated data collection allows assessment of image location to press movement
– Variables control charts are used to identify mechanical changes (x-bar and S charts)
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Monitoring the ProcessMonitoring the Process
0.02
0.04
0.06
0.08
0.100.12
0.14
0.16
0.18
0.20
0 2 4 6 8 10 12 14 16 18 20
s
UCL
LCL
s
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Monitoring the processMonitoring the process
Process is monitored daily to assess the efforts required to maintain registration– Variables control charts are used to identify
changes
Process Capability assessment performed on a quarterly basis– Process Capability chart is used to monitor
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Monitoring the ProcessMonitoring the Process
Cpm = T) - ( + 3
LSL] - T T, - min[USL 22 μσ
pmC( )
1T-Xn + 3
LSL] - T T, - min[USL 2
2
−nS
=
Parameter
Estimator
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Monitoring the ProcessMonitoring the Process
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⎟⎠⎞⎜⎝
⎛+−
<<⎟⎠⎞⎜⎝
⎛ −
+−Cpmn
npmCCpmn
n
2
)1)(1(ˆ
21
)1)(1(
2,
2,
αχ
λ
αχ
λ
λνλν
Pr = (1-)
Where the limits (L1, U1) are such that
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Monitoring the ProcessMonitoring the Process
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
98 99 00
Cpm ^
L
U
Mean
1
1
01 97
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Monitoring the ProcessMonitoring the Process
Another area where work is requiredProcess Capability is dynamic“One-shot” assessments of
capability can be misleadingEstimates of the PCIs are stochastic Graphic assessments are critical
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Improving the ProcessImproving the Process
Screening Design used to identify key combinations of controllable variables
“Crosshairs” and “L” were used to quantify and assess
Results were summarized in the across and along directions
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Improving the ProcessImproving the Process
40
50
60
70
80
90
-10 0 10 20 Across
Bivariate Normal Ellipse P=0.950 run=1 Bivariate Normal Ellipse P=0.950 run=2 Bivariate Normal Ellipse P=0.950 run=3 Bivariate Normal Ellipse P=0.950 run=4 Bivariate Normal Ellipse P=0.950 run=5 Bivariate Normal Ellipse P=0.950 run=6 Bivariate Normal Ellipse P=0.950 run=7 Bivariate Normal Ellipse P=0.950 run=8 Bivariate Normal Ellipse P=0.950 run=9 Bivariate Normal Ellipse P=0.950 run=10
Along
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The target point (as measured from the film) is located at 10.66 (across) and 70.8 (along)
The “best” run would be one whose 95% ellipse is centered on the target and has the smallest area
Based on the criteria : 1) centered on target and 2) smallest area, run is “best”
Improving the processImproving the process
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Improving the ProcessImproving the Process
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
98 99 00
Cpm ^
L
U
Mean
1
1
01 97
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Research AreasResearch Areas Statistical input
– Decisions and inferences continue to lack statistical assessment
– Computer package incorporation of stochastic intervals/boundaries
Graphics and graphical methods – Inferences and monitoring tools
Links to costs/losses and benefits
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Selected ReferencesSelected References Spiring, F. A. Process Capability: A Total
Quality Management Tool, Total Quality Management, 1995, Vol. 6 (1), pp 21-33.
Spiring, F. A., A Unifying Approach to Process Capability Indices, Journal of Quality Technology, 1997, 29(1), pp 49-58.
Spiring, F. A., “Assessing Process Capability with Indices” in Statistical Process Monitoring and Optimization edited by S. H. Park & G. Geoffrey Vining, Marcel Dekker, 2000.