Narrow Results

In practice, it is not likely that enough data about the failure behavior can be collected to use the probability for reliability analyzing. In some cases, the information we have about the functioning of components and systems is not based on statistics, but is of a linguistic nature. Very often the reliability of the system is presented in a form of the mean time to failure (MTTF) or comparative MTTFs. In order to use this reliability measure for further computations the new models have to be developed. A theory of imprecise probabilities might be a basis for reliability analyzing when we have such the incomplete information about reliability behavior of systems. The basic tool for computing new reliability measures is the natural extension which can be regarded as a linear optimization problem. The reliability of series, parallel, cold standby, m-out-of-n and simple repairable systems is provided by using the natural extension. The chapter may be viewed as an attempt to generalize the classical reliability theory based on the probabilistic models and to study the basic properties and advantages of the new reliability models.