Basic Statistics and Introduction to Reliability

Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


Billions of dollars are currently spent producing high-technology products and services in a variety of production systems operating in different manufacturing and service sectors (e. g., aviation, automotive industry, software development, banks and financial companies, health care). Most of these products are very complex and sophisticated owing to the number of functions and components (many systems are made of millions of parts). A good example is the largest passenger airliner in the world, the Airbus A380, also known as the “Superjumbo,” with an operating range of approximately 15,200 km, sufficient to fly directly from New York City to Hong Kong. The generic part of this very complex product can be characterized by life cycle and failure behavior, but also by repair behavior in case of failure detection, and in the presence/ absence of a maintenance strategy, e. g., based on replacement and/or inspection or preventive action. Moreover, the failure and repair behavior of the generic part of the system can be directly or indirectly associated with thousands of different safety implications and/or quality expectations and performance measurements, which simultaneously deal with passengers, buildings, environment, and communities of people. In particular, reliability can be defined as the probability that a component (or system) will perform a required function for a given period of time when used under specific operating conditions. Another important basic definition is that of availability, which is the probability that a component (system) is performing its required function at a given point in time when used under specific operating conditions. Finally, maintainability is the probability that a failed component (system) will be restored (or repaired) to a specified condition within a period of time when maintenance is carried out in accordance with prescribed procedures. These definitions mean that the improvement,measurement, and control of software reliability and availability to support the operability of production systems are very important issues. In fact, most system outages and machine crashes are generated by malfunction of the software management system. The aim of this chapter is to introduce the reader to the definition, measurement, management, and control of the main reliability parameters that form the bases for modeling and evaluating activities in complex production systems.


Lognormal Distribution Hazard Rate Hazard Function Repair Rate Cumulative Function 
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© Springer-Verlag London Limited 2010

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