Supuestos para calcular las sigmas del proceso
P. Reyes / Julio 2005
Process Sigma Calculator Assumptions
Definitions
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Unit
Opportunity
Defect
DPU
DPMO
Defects (%)
Yield (%)
Understanding The Basic And Advanced Modes
The Basic Mode of the Sigma Calculator automatically adds a 1.5 Sigma shift to the process Sigma
value that is calculated. Why is this done? It's done because it is the "standard" way that Sigma is
reported (note: this may be different in your company, but it is done in this manner by Motorola, GE
and many other companies). By doing so, the calculator result assumes that you are providing longterm data and it is providing short-term Sigma. The 1.5 Sigma shift is based on the assumption that
over time, and with a sufficiently large number of samples, a realistic Sigma value is 1.5 Sigma less
than that calculated to show the success of your project (i.e. that shown in this calculator and in
reports to your company).
If you want to calculate the process Sigma using data other than long-term, you should switch to the
Advanced Mode where you can change the process Sigma shift value from 1.5 to whatever you feel
is appropriate.
Here are a couple of examples to help illustrate the calculations. A long-term 93% yield (e.g. 100
opportunities, 7 defects) equates to a process Sigma long-term value of 1.48 (with no Sigma shift)
or a process Sigma short-term value of 2.98 (with a 1.5 Sigma shift). A long-term 99.7% yield (e.g.
1,000 opportunities, 3 defects) equates to a process Sigma long-term value of 2.75 (with no Sigma
shift) or a process Sigma short-term value of 4.25 (with the 1.5 sigma shift).
Final Thought: When we talk about a Six Sigma process, we are referring to the process short-term
(now). When we talk about DPMO of the process, we are referring to long-term (the future). We
refer to 3.4 defects per million opportunities as our goal. This means that we will have a 6 sigma
process now in order to have in the future (with the correction of 1.5) a 4.5 sigma process -- which
produces 3.4 defects per million opportunities.
Notice: Sigma with a capital "S" is used above to denote the process Sigma, which is different than
the typical statistical reference to sigma with a small "s" which denotes the standard deviation.
Understanding The Formula
Defects Per Million Opportunities (DPMO) = ((Total Defects) / (Total Opportunities)) * 1,000,000
Defects (%) = ((Total Defects) / (Total Opportunities)) * 100
Yield (%) = 100 - (Defects Percentage)
process Sigma = NORMSINV(1-((Total Defects) / (Total Opportunities))) + 1.5
Alternatively,
process Sigma = 0.8406 + SQRT(29.37 - 2.221 * (ln(DPMO))).
Reference: Breyfogle, F., 1999. Implementing Six Sigma: Smarter Solutions Using Statistical
Methods. 2nd ed. John Wiley & Sons.
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Supuestos para calcular las sigmas del proceso
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Understanding Negative Sigma
Sigma value is simply a modified Z score (Table of the Standard Normal (z) Distribution). Sigma
(with a capital "S") is not the same thing as the standard deviation of a process, referred to as
sigma (with a lower case "s" or as the greek letter ). Consequently, it is quite possible to get a
negative sigma value. A negative sigma value means that most of your product or service (process)
is completely outside your customer's specification range. A full discussion can be found on
negative Sigma.
Unit
A unit is any item that is produced or processed which is liable for measurement or evaluation
against predetermined criteria or standards.
Posted By:
Modified By: amy loverde
Last Modified: Nov. 21, 2002
Opportunity
Any area within a product, process, service, or other system where a defect could be produced or
where you fail to achieve the ideal product in the eyes of the customer. In a product, the areas
where defects could be produced are the parts or connection of parts within the product. In a
process, the areas are the value added process steps. If the process step is not value added, such
as an inspection step, then it is not considered an opportunity.
Opportunities are the things which must go right to satisfy the customer. It is not the number of
things we can imagine that can go wrong
Defect
Any type of undesired result is a defect.
A failure to meet one of the acceptance criteria of your customers. A defective unit may have one or
more defects.
'A defect is a failure to conform to requirements' (Crosby, 'Quality Is Free'), whether or not those
requirements have been articulated or specified.
The non-conformance to intended usage requirement.
Defects Per Unit - DPU
DPU or Defects Per Unit is the average number of defects observed when sampling a population.
DPU = Total # of Defects / Total population
Consider 100 electronic assemblies going through a functional test. If 10 of these fail the first time
around, we have a first pass yield of 90%. Let's say the 10 fails get reworked and re-tested and 5
pass the second time around; the 5 remaining fails pass on the third attempt. Feel free to work out
how this would look as a rolling yield. (100 'passes'/115 tests).
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Supuestos para calcular las sigmas del proceso
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DPU takes a fundamentally different approach to the traditional measurement of yield. It is simply a
ratio of the number of defects over the number of units tested (don't worry about how many tests or
how many opportunities for defects).
In the above example, the DPU is 15/100 or 0.15. There are 100 units which were found to have a
cumulative total of 15 defects when tested.
One interesting feature of DPU is that if you have sequential test nodes, i.e. if the above 100 units
had to go through 'Final Test' and threw up a DPU figure of 0.1 there, you simply add the DPU
figures from both nodes to get the overall DPU of 0.25 (this is telling you that there were 25 defects
in your 100 units). There are a few assumptions which must be realised for this statement to be
wholly accurate, but there isn't really time to go there in a 'definition' space.
Defects Per Million Opportunities - DPMO
Defects per million opportunities (DPMO) is the average number of defects per unit observed during
an average production run divided by the number of opportunities to make a defect on the product
under study during that run normalized to one million.
Defects Per Million Opportunities. Synonymous with PPM.
To convert DPU to DPMO, the calculation step is actually DPU/(opportunities/unit) * 1,000,000.
Yield
Yield is the percentage of a process that is free of defects.
OR
Yield is defined as a percentage of met commitments (total of defect free events) over the total
number of opportunities.
First Time Yield - FTY
Rolled Throughput Yield – RTY
1.5 Sigma Process Shift Explanation
By Zack Swinney
iSixSigma recently released a process sigma calculator which allows the operator to input process
opportunities and defects and easily calculate the process sigma to determine how close (or far) a
process is from 6 sigma. One of the caveats written in fine print refers to the calculator using a
default process shift of 1.5 sigma. From an earlier poll, greater than 50% of polled quality
professionals indicated that they are not aware of why a process may shift 1.5 sigma. My goal is to
explain it here.
I'm not going to bore you with the hard core statistics. There's a whole statistical section dealing
with this issue, and every green, black and master black belt learns the calculation process in class.
If you didn't go to class (or you forgot!), the table of the standard normal distribution is used in
calculating the process sigma. Most of these tables, however, end at a z value of about 3 (see the
iSixSigma table for an example). In 1992, Motorola published a book (see chapter 6) entitled Six
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Supuestos para calcular las sigmas del proceso
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Sigma Producibility Analysis and Process Characterizationbuy it now!, written by Mikel J. Harry and J.
Ronald Lawson. In it is one of the only tables showing the standard normal distribution table out to a
z value of 6.
Using this table you'll find that 6 sigma actually translates to about 2 defects per billion
opportunities, and 3.4 defects per million opportunities, which we normally define as 6 sigma, really
corresponds to a sigma value of 4.5. Where does this 1.5 sigma difference come from? Motorola
has determined, through years of process and data collection, that processes vary and drift over
time - what they call the Long-Term Dynamic Mean Variation. This variation typically falls between
1.4 and 1.6.
After a process has been improved using the Six Sigma DMAIC methodology, we calculate the
process standard deviation and sigma value. These are considered to be short-term values
because the data only contains common cause variation -- DMAIC projects and the associated
collection of process data occur over a period of months, rather than years. Long-term data, on the
other hand, contains common cause variation and special (or assignable) cause variation. Because
short-term data does not contain this special cause variation, it will typically be of a higher process
capability than the long-term data. This difference is the 1.5 sigma shift. Given adequate process
data, you can determine the factor most appropriate for your process.
In Six Sigma, The Breakthrough Management Strategy Revolutionizing The World's Top
Corporations, Harry and Schroeder write:
"By offsetting normal distribution by a 1.5 standard deviation on either side, the adjustment takes
into account what happens to every process over many cycles of manufacturing… Simply put,
accommodating shift and drift is our 'fudge factor,' or a way to allow for unexpected errors or
movement over time. Using 1.5 sigma as a standard deviation gives us a strong advantage in
improving quality not only in industrial process and designs, but in commercial processes as well. It
allows us to design products and services that are relatively impervious, or 'robust,' to natural,
unavoidable sources of variation in processes, components, and materials."
Statistical Take Away: The reporting convention of Six Sigma requires the process capability to be
reported in short-term sigma -- without the presence of special cause variation. Long-term sigma is
determined by subtracting 1.5 sigma from our short-term sigma calculation to account for the
process shift that is known to occur over time.
This topic was revisited and more information has been provided.
Customer CTQs - Defining Defect, Unit and
Opportunity
By Kerri Simon
In order for any process capability to accurately be calculated, one must properly define and
quantify the process defect, unit and opportunity. Every process should have definitions for defect,
unit and opportunity. This article will define the defects, units and opportunities, as well as provide
examples.
Jump To The Following Sections:
 Start With The Customer
 Define Your Product/Service Defects
 Define Your Product/Service Units
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Supuestos para calcular las sigmas del proceso
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 Define Your Product/Service Opportunities
 CTQ Examples Including Defect, Unit and Opportunity
Start With The Customer
Before you can define your process defects, units and opportunities, you need to understand the
needs of your customers. Voice of the Customer (Customer Needs, eSurveys, Focus Groups,
Surveys) is the process of gathering customer comments/quotes and translating them into issues
and specifications. From these comments, issues and specifications come the customer CTQ
(Critical To Quality) - a product or service characteristic that must be met to satisfy a customer
specification or requirement.
Define Your Product/Service Defects
A defect is defined as any part of a product or service that:
 does not meet customer specifications or requirements, or
 causes customer dissatisfaction, or
 does not fulfill the functional or physical requirements.
It should be noted that the term customer refers to both internal and external customers.
Define Your Product/Service Units
A unit is something that can be quantified by a customer. It is a measurable and observable output
of your business process. It may manifest itself as a physical unit or, if a service, it may have
specific start and stop points.
Define Your Product/Service Opportunities
Simply stated, opportunities are the total number of chances per unit to have a defect. Each
opportunity must be independent of other opportunities and, like a unit, must be measurable and
observable. The final requirement of an opportunity is that it directly relates to the customer CTQ
(see Start With The Customer above). The total count of opportunities indicates the complexity of a
product or service.
Next Page > CTQ Examples Including Defect, Unit and Opportunity
Customer CTQs - Defining Defect, Unit and
Opportunity
By Kerri Simon
In order for any process capability to accurately be calculated, one must properly define and
quantify the process defect, unit and opportunity. Every process should have definitions for defect,
unit and opportunity. This article will define the defects, units and opportunities, as well as provide
examples.
Jump To The Following Sections:
 Start With The Customer
 Define Your Product/Service Defects
 Define Your Product/Service Units
 Define Your Product/Service Opportunities
 CTQ Examples Including Defect, Unit and Opportunity
CTQ Examples Including Defect, Unit and Opportunity
Area: Call Center
Customer Quote: 'I consistently wait too long to speak to a representative.'
CTQ Name: Representative Responsiveness
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Supuestos para calcular las sigmas del proceso
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CTQ Measure: Time on hold (seconds)
CTQ Specification: Less than 60 seconds from call connection to the automated response system
Defect: Calls with hold time equal and greater than 60 seconds
Unit: Call
Opportunity: 1 per call
Calculate Your Sigma (Plug in the values below to calculate Sigma)
Defects: 263 calls
Units: 21,501 calls
Opportunities: 1 per call
Sigma: 3.75
Area: Book Publisher
Customer Quote: 'I can't stand typos in books I purchase.'
CTQ Name: Typographic Quality
CTQ Measure: Number of typographical mistakes
CTQ Specification: Zero typographical mistakes
Defect: Any typographical mistakes
Unit: A word
Opportunity: Words per book
Calculate Your Sigma (Plug in the values below to calculate Sigma)
Defects: 2 typographical mistakes
Units: 100,000 (500 words/page x 200 pages/book)
Opportunities: 1 per word
Sigma: 5.61
Area: Printed Circuit Board Manufacturing
Customer Quote: 'Boards must work when I plug them in.'
CTQ Name: Board Functionality
CTQ Measure: Non-functioning or improperly functioning boards
CTQ Specification: All boards function properly (a board wil not function properly if any individual
component is bad)
Defect: Any non-functioning or improperly functioning board
Unit: A board
Opportunity: Total number of parts plus solder points
Calculate Your Sigma (Plug in the values below to calculate Sigma)
Defects: 18 boards
Units: 1,000 boards
Opportunities: 58 (1 board + 13 resistors + 4 capacitors + 2 diodes + 38 solder points)
Sigma: 4.92
Do you have a completed example that you would like to share with fellow iSixSigma readers?
Copy the following information and paste into an email, fill out your example specifics and mail it to
content@iSixSigma.com with the subject line 'Re: Defining Defects, Units and Opportunities' as the
title:
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