Computing with Words and Life Data

One of the most important problems of reliability analysis is to estimate the mean lifetime of the item under study. In technical applications this parameter is also called the mean time to failure (MTTF) and is often included in the specification of a product. For example, producers are interested whether this time is sufficiently large, as a large MTTF allows them to extend a warranty time. Classical estimators require precise data obtained from strictly controlled reliability tests (for example, those performed by a producer at his or her laboratory). In such a case a failure should be precisely defined, and all tested items should be continuously monitored. However, in a real situation these requirements might not be fulfilled. In an extreme case, the reliability data come from users whose reports are expressed in a vague way. The vagueness of the data has many different sources: it might be caused by subjective and imprecise perception of failures by a user, by imprecise records of reliability data, by imprecise records of the rate of usage, etc. Therefore we need different tools appropriate for modelling vague data, and suitable statistical methodology to handle these data as well.