1

Our Process

Elevation Arm

Tower

Front Back

2

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

3

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

4

Data | Data Analysis

Descriptive Statistics Histogram

5

Box and Whiskers XLS

Insert | Line Chart

6

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

8

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

9

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

3

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)

6

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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