Imprecise inference for warranty contract analysis

a b s t r a c t This paper presents an investigation into generalised Bayesian analysis of warranty contracts, using sets of prior distributions within the theory of imprecise probability. Explicit expressions are derived for optimal lower and upper bounds for the expected profit for the manufacturer of a product, corresponding to an imprecise negative binomial model for which two sets of prior distributions are studied. The results can be used to set a maximum value of compensation such that the manufacturer's expected profit remains positive, under vague prior knowledge

Imprecise inference for warranty contract analysis

Abstract This paper presents an investigation into generalized Bayesian analysis of warranty contracts, using sets of prior distributions within the theory of imprecise probability. Explicit expressions are derived for optimal lower and upper bounds for the expected pro…t for the manufacturer of a product, corresponding to an imprecise negative binomial model for which two sets of prior distributions are studied. The results can be used to set a maximum value of compensation such that the manufacturer's expected pro…t remains positive, under vague prior knowledge

Knowledge and Information Systems c ○ Springer-Verlag 1999 Imprecise Reliability of General Structures

Abstract. The paper discusses the important aspects of the reliability of systems with an imprecise general model of the structure function. It is assumed that the information about reliability behavior of components is restricted by the mean levels of component performance. In this case the classical reliability theory cannot provide a way for analyzing the reliability of systems. The theory of imprecise probabilities may be a basis in developing a general reliability theory which allows us to solve such problems. The basic tool for computing new reliability measures is the natural extension which can be regarded as a linear optimization problem. However, the linear programming computations will become impracticable when the number of components in the system is large. Therefore, the main aim of the paper is to obtain explicit expressions for computing the system reliability measures. We analyze the reliability of general structures and typical systems. The numerical examples illustrate the usefulness of the presented approach to reliability analyzing