# The Concept of “Statistical” Reliability

• Massimo Lazzaroni
• Loredana Cristaldi
• Lorenzo Peretto
• Paola Rinaldi
• Marcantonio Catelani
Chapter

## Abstract

The reliability of an item or a system can be think, as a first approach, as the probability that the device or the system will adequately perform the specified function for a well-defined time interval in specified environmental conditions. Starting from this first definition it is well clear the importance of the probability and statistics science in both reliability definition and evaluation. This chapter is devoted to introduce some important probability and statistics concepts necessary for reliability evaluation. In particular, the statistical point of view is developed and discussed as a first approach to dependability feature of a system or device. A brief overview on probability and statistics concepts is given in the first pages of this chapter. In particular, in 2.2.1 the axioms of probability are given and the law of the large number is discussed in 2.2.2. Random variables are introduced in 2.3 and probability distributions are detailed in 2.4. Finally, the reliability function is derived. Furthermore, it is defined the concept of the failure rate model in section 2.7. In 2.8 the more used distribution laws are discussed.

## Keywords

Failure Rate Probability Density Function Weibull Distribution Sample Space Reliability Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
IEC 60050-191 ed1.0, International Electrotechnical Vocabulary. Chapter 191: Dependability and quality of service, Forecast publication date for Ed. 2.0 is 2012-06-02. IEC International Electrotechincal Commission, Geneve (December 31, 1990)Google Scholar
2. 2.
Montgomery, D.C., Runger, G.C.: Applied Statistics and probability for engineers, 2nd edn. John Wiley & Sons, Chichester, ISBN 0-471-17027-5Google Scholar
3. 3.
IEC XE ”IEC” 60812:2006 – Analysis techniques for system reliability – Procedure for Failure XE ”Failure” mode and effects analysis (FMEA XE ”FMEA”) Google Scholar
4. 4.
Leemis, L.M.: Relaibility, Prbabilistic Models and Statistical methods, 2nd edn., ISBN 978-0-692-00027-4Google Scholar
5. 5.
Birolini, A.: Reliability Engineering – Theory and Practice, Springer, Heidelberg, ISBN: 978-3-642-14951-1 Google Scholar

## Authors and Affiliations

• Massimo Lazzaroni
• Loredana Cristaldi
• Lorenzo Peretto
• Paola Rinaldi
• Marcantonio Catelani

There are no affiliations available