1 our process elevationarm tower frontback. 2 operational definition need two things: –a method of...
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Our Process
Elevation Arm
Tower
Front 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
source: Moen, Nolan and Provost, Improving Quality Through Planned Experimentation
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Data Collection• Collect 5 data points for each team member• Plot run chart (use chart wizard)• Construct a histogram (Data | Data Analysis |
Histogram)• Construct a box and whiskers plot (use
box&whiskers.xls)• Calculate x-bar and s (Data | Data Analysis |
Descriptive Statistics)• Discuss results and be prepared to brief results
to other groups
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Data | Data Analysis
Descriptive Statistics Histogram
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Box and Whiskers XLS
Insert | Line Chart
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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
sigma
LSLx
sigma
xUSLCor
sigma
LSLUSLC pkp *3
,*3
min*6
EXCEL: =Normdist(x, mean, std dev, 1) to calculate percent non-conforming material.
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Process capability measure
• Estimate standard deviation:• 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
s = R / d 2
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Upper Specification Limit (USL)
LowerSpecificationLimit (LSL)
X-3sA X-2sA X-1sAX X+1sA
X+2s X+3sA
X-6sBX X+6sB
Process A(with st. dev sA)
Process B(with st. dev sB)
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LSLUSLC p
x Cp P{defect} ppm
1 0.33 0.317 317,000
2 0.67 0.0455 45,500
3 1.00 0.0027 2,700
4 1.33 0.0001 63
5 1.67 0.0000006 0,6
6 2.00 2x10-9 0,00
The Statistical Meaning of Six Sigma
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