Download Our Process

Our Process
Tower
Elevation
Front
Arm
Back
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Operational Definition
•
Need two things:
– a method of measurement or test
– a set of criteria for judgment
• For example, what are operational
definitions for the following:
– on-time delivery
– good service
– 50% wool blanket
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source: Moen, Nolan and Provost, Improving Quality Through Planned Experimentation
Data Collection
•
•
•
Collect 5 data points for each team member
Plot run chart (use chart wizard)
Construct a histogram (Tools | Data Analysis |
Histogram)
• Construct a box and whiskers plot (use
box&whiskers.xls)
• Calculate x-bar and s ( … | Descriptive Statistics)
• Discuss results and be prepared to brief results to
other groups
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Tools | Data Analysis
Descriptive Statistics
Histogram
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Chart Wizard | Line Chart
Box and Whiskers XLS
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What the Exercise Statistics Reveal
• The sample mean (x-bar) describes
typical distances in one number.
• Other measures of central tendency
include: median and mode.
• The sample standard deviation (s)
provides a measure of the ‘average’
deviation around the mean.
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Using x-bar and s
•
The empirical rule assumes the
underlying distribution is normal:
– 68% within ± 1 s
– 95% within ± 2 s
– 99 % within ±3 s
•
For any distribution:
– At least 75% within ± 2 s
– At least 89% within ± 3 s
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Histograms
• Shows the distribution of process
outcomes.
• Look for center, shape and spread
• Compare to:
– your expectations and knowledge
– target and specification requirements
– across shifts, operators, machines, etc
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Process capability
Cp 
 USL x x  LSL 
USL  LSL

or C pk  min 
,
6 * sigma
 3 * sigma 3 * sigma 
EXCEL: =Normdist(x, mean, std dev, 1) to calculate percent non-conforming material.
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The Statistical Meaning of Six Sigma
Process capability measure
Upper
Specification
Limit (USL)
Lower
Specification
Limit (LSL)
Process A
(with st. dev sA)
X-3sA
X-2sA
X-1sA
X
X+1sA X+2s
X+3sA
3s
Process B
(with st. dev sB)
X-6sB
X
Cp 
USL  LSL
6sˆ
xs
Cp
P{defect}
ppm
1s
0.33
0.317
317,000
2s
0.67
0.0455
45,500
3s
1.00
0.0027
2,700
4s
1.33
0.0001
63
5s
1.67
0.0000006
0,6
6s
2.00
2x10-9
0,00
X+6sB
• Estimate standard deviation: ŝ =R /d2
• Look at standard deviation relative to specification limits
• Don’t confuse control limits with specification limits: a process can be out of
control, yet be incapable
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