six sigma green belt part 3 - institute of industrial and …1).pdf · 3-1 six sigma green belt...

3-1

Six Sigma Green Belt

Part 3

Statistics

© 2011 IIE and Aft Systems, Inc. 3-2

Statistics

1. Central Location

1. Mean

2. Median

3. Mode

2. Variability

1. Range

2. Standard Deviation

3. Shape


Measures of Central Location

The average is the expected value or the balance point

– Mode is the most frequently occurring value

– Median is the middle value

– Arithmetic mean is the total of the individual values divided by the number of individual values

average population theis

average sample theis

x


Which Mean do you Mean?

• Use the median or the mode if the shape of the distribution is not symmetrical

• Use the arithmetic mean if the shape of the distribution is symmetrical


Example

Determine the mode, median, and the mean of the following sample:

6,7,7,8,8,8,9,9,9,9,10,10,11,11,12,13


Example

Calculate the mean of the following samples:

1) 2 3 6 9 1

2) 3 6 4 1 11

3) 2 7 22 0 9

4) -4 8 0 14 0


Measures of Variability

• The range is the difference between the largest and the smallest values in the sample. The symbol for the range is R.

• The standard deviation is a mathematical measure of the variability of the data about the mean. Its symbol is either s or s.


Exercise

Calculate the range of the following samples:

1) 2 3 6 9 1

2) 3 6 4 1 11

3) 2 7 22 0 9

4) -4 8 0 14 0


Calculating Sample Standard

Deviation

Where n is the number of values in the sample


Standard Deviation Significance

Between plus and minus one standard deviation of the mean, we normally expect to find about 68% of the values

1s 1s



Within 2 standard deviations of the mean we would expect to find approximately 95.5% of the values 2s 2s



Within 3 standard deviations of the mean we would expect to find about 99.73% of the values. This is virtually all of the values and represents the expected limits of common cause variation necessary for a stable and predictable process.

3s 3s


Six Sigma Quality

Customer requirements are 6 standard deviations from the mean in either direction

Requirements are Six

Standard Deviations on

each side of the mean

6s 6s

Lower

Customer

Requirement

Upper

Customer

Requirement


Grand Average

• The grand average is the process average. It is usually the average of the sample averages. (As long as all of the samples are the same size.)

• It is also the average of all the individuals.

x


Exercise

Calculate the grand average for the following:

1) 2 3 6 9 1

2) 3 6 4 1 11

3) 2 7 22 0 9

4) -4 8 0 14 0


Average Range

The average range is the estimate for total process variability. The average range is the average of the sample ranges.

R


Exercise

Calculate the R bar for the following data:

1) 2 3 6 9 1

2) 3 6 4 1 11

3) 2 7 22 0 9

4) -4 8 0 14 0


Describing Data

• We describe data to assist with the analyze in six sigma. In order to completely describe data we need to know the following:

– Location

– Spread

– Shape

– Variation Over Time


Target

Most measures have targets. For example, an organization may promise delivery in 24 hours. That is the target. (In manufacturing that is called the nominal. In service it may be called the customer requirement.)


Shape

The histogram shows us the shape of the distribution. Many measurements follow the normal or bell shaped curve.


Shape

• Sometimes the shape is not normal

• We must compare our shape with the expected shape to see if the process is behaving like it always has


Shape

• We can use the histogram to compare the observed shape with the expected shape

• If the pattern is different from what we expect, then we may not be doing what we always have. We may not be predictable. We may not be stable.

six sigma green belt part 3 - institute of industrial and …1).pdf · 3-1 six sigma green belt...

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