assessing process capability: a user’s view fred spiring & smiley cheng the university of...

Assessing Process Capability: Assessing Process Capability: A User’s ViewA User’s View

Fred Spiring & Smiley ChengThe University of Manitoba

& Pollard Banknote Ltd

OverviewOverview

PerspectiveProcess BackgroundAssessing Process CapabilityEstablishing Specs & TolerancesMonitoring the ProcessImproving the ProcessResearch areas

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

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

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

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

Process BackgroundProcess Background

PreproductionPreproduction– Production Specifications were based

on artists’ knowledge of colour rather than production equipment

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

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

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

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

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)

Establishing Specifications Establishing Specifications

Yred

Xred

Web direction(along)

XKO

YKO

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)

YKO

Establishing Specifications Establishing Specifications

  Yred = YKO – 0.030”

Xred = XKO – 0.022”

XKO

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

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)

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

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

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

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

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

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

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

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

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

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

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

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.