07.020 - Mathematics
ICS 07.020 Details
Mathematics
Mathematik
Mathematiques
Matematika
General Information
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This document specifies mathematical symbols, explains their meanings, and gives verbal equivalents
and applications.
This document is intended mainly for use in the natural sciences and technology, but also applies to
other areas where mathematics is used.
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This International Standard provides mathematical expressions for selected reliability, availability, maintainability and maintenance support measures defined in IEC 60050192:2015. In addition, it introduces some terms not covered in IEC 60050-192:2015. They are related to aspects of the system of item classes (see hereafter).
According to IEC 60050-192:2015, dependability [192-01-22] is the ability of an item to perform as and when required and an item [192-01-01] can be an individual part, component, device, functional unit, equipment, subsystem, or system.
To account for mathematical constraints, this standard splits the items between the individual items considered as a whole (e.g. individual components) and the systems made of several individual items. It provides general considerations for the mathematical expressions for systems as well as individual items but the individual items which are easier to model are analysed in more detail with regards to their repair aspects.
The following item classes are considered separately:
• Systems;
• Individual items:
– non-repairable [192-01-12];
– repairable [192-01-11]:
i) with zero (or negligible) time to restoration;
ii) with non-zero time to restoration.
In order to explain the dependability concepts which can be difficult to understand, keep the standard self-contained and the mathematical formulae as simple as possible, the following basic mathematical models are used in this standard to quantify dependability measures:
• Systems:
– state-transition models;
– Markovian models.
• Individual items:
– random variable (time to failure) for non-repairable items;
– simple (ordinary) renewal process for repairable items with zero time to restoration;
– simple (ordinary) alternating renewal process for repairable items with non-zero time to restoration.
The application of each dependability measure is illustrated by means of simple examples.
This standard is mainly applicable to hardware dependability, but many terms and their definitions may be applied to items containing software.
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IEC 60050-103:2009 gives the terminology relative to functions of one or more variables. Together with IEC 60050-102, it covers the mathematical terminology used in the fields of electricity, electronics and telecommunications. It maintains a clear distinction between mathematical concepts and physical concepts, even if some terms are used in both cases. Mathematical symbols are generally in accordance with IEC 60027-1 and ISO 80000-2. This standard cancels and replaces Sections 101-13, 101-14 and 101-15 of International Standard IEC 60050-101:1998.
It has the status of a horizontal standard in accordance with IEC Guide 108.
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This part of IEC 60050 gives the general mathematical terminology used in the fields of electricity, electronics and telecommunications, together with basic concepts in linear algebra. It maintains a clear distinction between mathematical concepts and physical concepts, even if some terms are used in both cases. Another part will deal with functions.
It has the status of a horizontal standard in accordance with IEC Guide 108.
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Provides mathematical expressions for reliability, availability, maintainability and maintenance support measures. - Non-repaired items and - repaired items with zero and non-zero time to restoration are considered separately in this standard.
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ISO 80000-2 gives general information about mathematical signs and symbols, their meanings, verbal equivalents and applications. The recommendations in ISO 80000-2 are intended mainly for use in the natural sciences and technology, but also apply to other areas where mathematics is used.
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ISO 80000-2:2009 gives general information about mathematical signs and symbols, their meanings, verbal equivalents and applications. The recommendations in ISO 80000-2:2009 are intended mainly for use in the natural sciences and technology, but also apply to other areas where mathematics is used.
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