ISO/TR 20693:2019

TECHNICAL ISO/TR
REPORT 20693
First edition
2019-04
Statistical methods for
implementation of Six Sigma —
Selected illustrations of distribution
identification studies
Méthodes statistiques pour la mise en œuvre du Six Sigma - Exemples
choisis d'études d'identification de la distribution
Reference number
©
ISO 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 2
5 Basic principles . 3
5.1 General . 3
5.2 Exploratory data analysis (EDA). 4
5.3 Discrete data case . 4
5.3.1 Graphical methods . 4
5.3.2 Numerical methods . 4
5.4 Continuous data case . 5
5.4.1 Graphical methods . 5
5.4.2 Numerical methods . 5
5.4.3 Distribution family unknown and no prior information available . 5
6 General description of distribution identification . 6
6.1 Overview of the structure of distribution identification . 6
6.2 State overall objectives . 6
6.3 Formulate a model theory . 6
6.4 Collect, prepare and explore data . 7
6.5 Select underlying probability distributions . 8
6.6 Perform goodness of fit test . 8
6.7 Draw conclusions . 8
7 Examples . 9
Annex A (informative) Test uniformity in the Super Lotto .10
Annex B (informative) Distribution of the number of technical issues found after product
release to the field.13
Annex C (informative) Software development effort estimation .18
Annex D (informative) Determining the warranty period of a product .26
Bibliography .33
Foreword
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This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 7, Applications of statistical and related techniques for the implementation of Six Sigma.
Any feedback or questions on this document should be directed to the user’s national standards body. A
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iv © ISO 2019 – All rights reserved

Introduction
Many statistical techniques assume that the data to be analysed come from a given distribution (or
population). Such assumptions are crucial to the effectiveness of subsequent statistical inference
methods. In the Six Sigma community, when using such statistical methods, one needs to consider
whether this assumption is reasonable. More generally, sometimes it is interesting and necessary to
find the distribution which generated the data set (or sample) at hand. Identification of the distribution
may provide some ways to answer this question. It consists of finding a distribution (or a family of
distributions) which provides a good representation of a sample.
The distribution identification within Six Sigma projects should ideally be performed before the end
of the Measure phase and can continue throughout the other phases of the DMAIC. From a Six Sigma
perspective, the distribution identification can have multiple purposes based on the considered phase.
It is used, for example, to characterise a baseline of the process performance, during the Measure
or Analyse phase, to characterise the new process during the Improve phase, and to continuously
monitor the process performance during the Control phase to ensure that the change is sustained.
From a statistical perspective, distribution identification may be helpful to find appropriate statistical
techniques for the related data, since many parametric statistical inference methods need certain
distributional assumptions.
In general, distribution identification methods may be used as a tool to:
a) verify that a distribution used historically is still valid for the current data;
b) choose the appropriate distribution.
The choice of appropriate distribution should be guided by the knowledge of physical phenomena or the
business process. It is recommended to start from a tentative theory to avoid just curve fitting.
In practice, there is always certain context or business background which can be used in determining
the distribution. For example, under some circumstance, one can expect the measurement error is
normally distributed. In reliability fields, the life distributions for certain products are exponential,
lognormal, Weibull, or extreme distributions and so on. However, when such knowledge is not available,
the possible underlying distribution for the data should also be identified if one wants to use parametric
statistical methods. In this case, exploratory data analysis methods should be used to gain a better
understanding. Through graphical visualisation methods, one could form a hypothesis on the possible
distributions, stratification of the data or other aspects. Once the hypothesis is formed, hypothesis
testing, including goodness of fit testing, can be applied to check one’s guess. Finally, a suitable
distribution may be found for the data.
1)
1) 1)
In some commercial software packages including MINITAB , SAS-JMP and Q-DAS , although there
are buttons for distribution identification, one should take knowledge of context and process related
to data into consideration instead of simply relying on the software packages. Otherwise, misleading
results can be given.
1)  MINITAB is the trade name of a product supplied by Minitab Inc. JMP is the trade name of a product supplied
by SAS Institute Inc. Q-DAS is the trade name of a product supplied by Q-DAS GmbH. This information is given for the
convenience of users of this document and does not constitute an endorsement by ISO of these products.
TECHNICAL REPORT ISO/TR 20693:2019(E)
Statistical methods for implementation of Six Sigma —
Selected illustrations of distribution identification studies
1 Scope
This document provides guidelines for the identification of distributions related to the implementation
of Six Sigma. Examples are given to illustrate the related graphical and numerical procedures.
It only considers one dimensional distribution with one mode. The underlying distribution is either
continuous or discrete.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 3534-1:2006, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used
in probability
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at https: //www .electropedia .org/
3.1
population
totality of items under consideration
[SOURCE: ISO 3534-1:2006, 1.1, modified - Notes 1, 2, and 3 deleted.]
3.2
sample
subset of a population (3.1) made up of one or more sampling units
[SOURCE: ISO 3534-1:2006, 1.3, modified - Notes 1and 2 deleted.]
3.3
observed value
obtained value of a property associated with one member of a sample (3.2)
[SOURCE: ISO 3534-1:2006, 1.4, modified - Notes 1 and 2 deleted.]
3.4
family of distributions
distribution family
set of probabili
...