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Six Sigma
Six Sigma Projects: Key Concepts
11 Six Sigma Projects: Key Concepts
Just as at the initiative level there are a number of key concepts which need to be understood, the same is true for the
project level.
11.1
Basic Statistical Concepts
Large elements of the Six Sigma approach are statistical in nature. This text book does not purport to be a statistical textbook and so will not deal in detail with statistical tools and techniques; for a comprehensive treatment refer to “Essentials
of Statistics” also available on Bookboon.com.
11.1.1
Probabalistic Thinking
In many organizations there is a tendency to think deterministically. This basically means an expectation that there will be
no variation in outcomes, and that a given input (or inputs) will always generate the same output (or outputs). This flies in
the face of our general life experience; we know that, for example, that a particular Olympic runner will not always beat
other runners over the same distance and in the same conditions. This does not, however, stop organizations for assuming
that, for example, inspection systems will always reject products of poor quality and accept products of good quality.
Thinking probabilistically allows for more effective decision making by allowing us to quantify the probability of success
or failure, risk and reliability. Deterministic thinking tends to lead to overly simplistic characterisation of situations and
inappropriate responses when the simplistic model fails to predict reality effectively.
11.1.2
Probability Distributions
When there are a range of possible outcomes for a given process (for example the dimensions of a manufactured product
or time taken to complete a task) we can predict the probability of each outcome and thereby develop a probability
distribution which models the long-term outcomes of that process. This adds a layer of sophistication to the ability to make
decisions with respect to whether processes can meet design intent, or whether to give a contract to a particular supplier.
There are a number of general distribution shapes which describe situations within certain parameters. Key distributions
in the context of Six Sigma are Normal, Binomial, and Poisson.
Probability calculations and distributions are handled in detail in “Essentials of Statistics” also available on Bookboon.com.
11.1.3
Descriptive Statistics
When dealing with distributions and attempting to make appropriate decisions we need to summarise what we are dealing
with. This requires us to understand three key things:
• Central Tendency: Where is the distribution centred? This can be important in, for example, seeing if the
distribution of a process is centred on the target for that process.
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Six Sigma
Six Sigma Projects: Key Concepts
• Spread: How variable is the distribution? In general we want as much consistency as possible for a
distribution.
• Shape: For the same central tendency and spread differing shapes of distribution would lead to different
decisions.
The appropriate measures for central tendency and spread will vary with the particular measure, and the question being
asked.
11.1.4. Hypothesis Testing
A key question in process improvement is ‘has something changed?’. We may ask this question in relation to deterioration
of an existing process, or to establish whether an attempt to improve a process has been successful. There are a variety of
tests associated with different situations and different underlying distributions, and even some which are independent of
distribution. The essential question is whether the results under consideration can be explained by the natural variation
within the process before the ‘deterioration’ or ‘improvement’.
A specific form of hypothesis testing relates to correlation, where we are attempting to understand whether the variation
in one measure is related to the variation in another – usually as a precursor to establishing causation. For example we
might be concerned with whether a change in feed rate in a metal cutting process effects a change in the surface finish
of the material.
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Six Sigma
Six Sigma Projects: Key Concepts
11.2
Variation, the Normal Distribution, DPMO and Sigma Levels
11.2.1
Variation and the Normal Distribution
Variation reduction is the key mechanism for Six Sigma to deliver business benefit. By focusing on product, service or
process variation (depending on circumstances) projects create consistency of performance and improved conformance
to customer requirements.
Six Sigma focuses on the concept of defects per million opportunities (DPMO). It uses the standard normal distribution
as its measurement system. From the standard normal distribution, the mean is µ and the standard deviation is denoted
by σ. From figure 11.1, 68.2% of the population lies within ±1.0σ of the mean, 95.45% of the population lies within ±2.0σ
of the mean and 99.73% of the population lies within ±3.0σ of the mean
Figure 11.1. Standard normal distribution
When addressing variation it is important to remember the effects of special and common cause variation. The normal
distribution and DPMO cannot apply if special causes are dominant within the process.
11.2.2
Defects per Million Opportunities
Six Sigma uses the DPMO level of a process to generate a Sigma level for the process. The idea of a Sigma level is that it
compares the variation in process performance to the acceptable levels set by the customer, the higher the Sigma level
the better; a Six Sigma performance indicates 3.4 DPMO.
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Six Sigma
Six Sigma Projects: Key Concepts
Figure 11.2. A one-sided normal distribution
So for example, from figure 11.2, when σ = 3 there are 1350 DPMO ((1-0.998)*1000000).
According to the standard normal distribution a process a six sigma performance would actually produce a DPMO of
0.002, but Sigma levels are calculated using an inbuilt 1.5 σ shift for the process average. This is effectively an allowance
for the natural propensity of processes to drift and, although debate still rages as to the validity of the exact assumption
this is the commonly used approach.
The basic idea is to create a process quality metric which allows comparison of any type of process; Goh (2010) described
this as one of the six triumphs of Six Sigma. The DPMO are calculated first and then translated into a Sigma value via a
conversion table (see table 11.1 below).
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