This Slideshare presentation is a partial preview of the full business document. To view and download the full document, please go here: http://flevy.com/browse/business-document/capability-analysis-cpk-ppk-course-1013 DESCRIPTION Statistics and statistical techniques are a vital key to any world class organization However, statistics can be intimidating to many employees and managers. Although statistical training is widely available, if the knowledge is not used, it disappears quickly. By downloading this presentation course, you will have access to review terms and techniques at your own leisure. Not only that, but we put capability analysis into terms and concepts that are easy to understand and make sense to those who aren't big fans of statistics. How long would it take you to develop your own course? Hours? Weeks? Unless you can develop a similar course in less than an hour, this course will pay for itself at least ten times over! The course is yours to keep. Feel free to edit, change or modify however you want, or don't change a thing and teach directly from our material. No recurring costs, no "per student" charge, and no special software to download. Your employees can refer back to it anytime they like. Send it in a global email to everyone in your company, if you'd like! Don't spend thousands of dollars hiring a consultant to come in and speak in general terms. Use your knowledge of your company's major problems to elaborate on the material we have put together. Unless you can show how these concepts relate to actual issues that your employees deal with, you will have a hard time making much of an improvement in the way problems are resolved. This course has been utilized many times in various industries, and is exactly what you would create on your own, if only you had the time. We have done all the hard work for you, so just follow these simple - Download the Powerpoint course from our website (did we mention our courses are only $99) - Edit the master slide with your company logo - Skim the speaker notes, maybe add a few of your own company specific examples - Start training your company! The course is divided into four major sections: - Variation - What is variation, how to calculate average and standard deviation - Cp, Cpk, Pp and Ppk - What are they? What do they mean? How do I calculate process capability? How can I convert them into probability of failure rates? - Normal Distribution - properties of the normal distribution, including area under the curve estimations using the standard normal tables We've told you what it does, so what is this course missing? (we can't put everything in ) The following is NOT covered in the presentation, just so you are not disappointed. - Control Charts and Stability - Creating Histograms - Distributions and their properties other besides the normal (gaussian) curve - Skewness and Kurtosis - Central Limit Theorem

1. Capability Analysis
An Introduction to
Statistical Process Control

2. http://www.biz-pi.com Capability Analysis4
What is variation?
Variation
the differences that exist
between individual units of a
product or process
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3. http://www.biz-pi.com Capability Analysis7
Real Life Examples
Calories eaten per day
2285
2107
1998
2767
2488
2610
2575
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4. http://www.biz-pi.com Capability Analysis10
Median
Median is the center of the data set
• First sort data (smallest to largest)
1, 6, 12, 10, 8, 22, 7 1, 6, 7, 8, 10, 12, 22
• Find the point where half the data points are on each side
1, 6, 7, 8, 10, 12, 22
• For even number data sets, find point between two values and
average the two values (8.5 is middle of 7 and 10)
1, 6, 7, 10, 12, 22
Median = 8
Median = 8.5
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5. http://www.biz-pi.com Capability Analysis13
Measuring Variation
To quantify the amount of variation in a
data set, there are two statistics you
can use:
Range
Standard DeviationThis document is a partial preview. Full document download can be found on Flevy:
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6. http://www.biz-pi.com Capability Analysis16
Standard Deviation
• Calculate Standard Deviation of the sample
1, 6, 12, 10, 8, 22, 7
• Calculate average = 66/7 = 9.43
• Add up the differences between each value and the
mean, and square that difference
Value Mean Value - Mean Sq Diff
1 9.43 -8.43 71.065
6 9.43 -3.43 11.765
12 9.43 2.57 6.605
10 9.43 0.57 0.325
8 9.43 -1.43 2.05
22 9.43 12.57 158.0
7 9.43 -2.43 5.905
1 2 3 4
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7. http://www.biz-pi.com Capability Analysis19
Test Your Knowledge
Quiz
Calculate the mean,
median, range and standard
deviation of the following
data set
12 21 13
14 18 20
22 17 24
19 16 22
15 15 14
15 13 15
11 15 18
20 14 16
16 16 19
17 12 14
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8. http://www.biz-pi.com Capability Analysis22
Normal Distribution
1800 2000 2200 2400 2600 2800 3000
This “bell shaped” pattern is called a NORMAL or GAUSSIAN
distribution.
It is one of the most common distributions you will observe,
especially when you plot random variation in a process, product,
machine, etc.
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9. http://www.biz-pi.com Capability Analysis25
What is Cp?
Cp is a measure of how well the variation in
the data can fit within the tolerance limits
If the variation (6σ) is less
than the tolerance limits, you
have acceptable variation
If the variation (6σ) is greater
than the tolerance limits, you
have unacceptable variation
LL LLUL UL
6σ 6σ
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10. http://www.biz-pi.com Capability Analysis28
Example of calculating Cp
Calculate the standard deviation (s)
from the sample
s = 270.29
Determine spec limits (Doctor recommends
between 1800 and 3800 calories per day)
Cp =
USL - LSL
6s
=
4000 - 1800
6*(270.29)
=
2200
1621.74
1.36Cp = GOOD!
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11. http://www.biz-pi.com Capability Analysis31
Cp Examples
LL UL
LL UL
Cp = 1.5
Cp = 1.5
GOOD
GOOD
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12. http://www.biz-pi.com Capability Analysis34
Example of calculating Cpk
Take the previous “calories eaten”
example of 40 data points
⌧ = 2390
s = 270.29
Cp (upper) =
4000 - 2390
3*(270.29)
Cp (lower) =
2390 - 1800
3*(270.29)
Cp (upper) = 1610/810 = 1.99 Cp (lower) = 590/810 = 0.73
Cpk = 0.73 BAD!
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13. http://www.biz-pi.com Capability Analysis37
Cpk Examples
LL UL
LL UL
Cp = 0.75
Cpk = 2.0
Cpk = 0.75
Cp = 2.0
GOOD
BAD
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14. http://www.biz-pi.com Capability Analysis40
Percentages of Normal Distribution
68.3%
95.45%
99.73%
+1 +2 +3-3 -2 -1 0
6 sigma
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15. http://www.biz-pi.com Capability Analysis43
Examples
+1 +2 +3-3 -2 -1 0
USL
Cp = 0.67
2.27%2.27%
LSL
5.54%
Predicted failure
rate
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16. http://www.biz-pi.com Capability Analysis46
Example
Z-value = = = = 1.5
X - ⌧
s
300 - 270
20
30
20
From standard normal table …
Z = 1.5This document is a partial preview. Full document download can be found on Flevy:
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17. http://www.biz-pi.com Capability Analysis49
Calories Percent Fallout
Avg = 2390
Std Dev = 270.3
Value = 1800 (lower spec)
Z = = 2.18
2390 - 1800
270.3This document is a partial preview. Full document download can be found on Flevy:
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18. http://www.biz-pi.com Capability Analysis
What is Pp and Ppk?
• There are new terms related to
capability that are becoming more
popular
• Pp and Ppk are very similar to Cp and
Cpk, but with different estimates of
standard deviation
• Some confusion exists, since
requirements may ask for Cp and Cpk,
but formula is actually Pp and Ppk
52
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19. http://www.biz-pi.com Capability Analysis55
Review
You learned:
• What is average and variation, and
how to calculate it
• What is capability and how to calculate
Cp and Cpk
• How to use Cp and Cpk to understand
a process
• How to convert Cp and Cpk to percent
of failure
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