On the Relationship between the Conditional and Unconditional Distribution of a Random Variable

This paper studies the relationship between the unconditional and conditional distribution of the same random variable, say Y, when the distribution of the conditioning random variable X is of a known form. The problem is tackled in the general case where the distribution of Y and Y given X are mixed. Attention is focused to two particular cases. In the first X is assumed to follow a Poisson distribution; in the second X is allowed to have a mixed Poisson form. Potential applications are also discusse

Warranty Cost Analysis for Nonrepairable Services Products

Many service products are installed in a complex system that is operated only when the entire system is completed. The time from their installation to commissioning, called a dormant state in this article, may take several years for systems such as complete buildings or aircraft. Warranties for the products may cover the time starting from their installation to a certain time. Warranty cost on replacements for such products is different from normal products without any dormant state. This article analyses the replacement cost for nonrepairable services products from a manufacturer perspective. We consider four warranty policies, which include two types of warranty terms (i.e., nonrenewing or renewing) and two types of replacements (i.e., with preventive replacement or replacement only upon failures). Relationships between the failure patterns at the dormant state and at the operating state are also discussed. Numerical examples and sensitivity analysis are presented to demonstrate the applicability of the methodology described in this article

A flexible extended warranty and related optimal strategies

The choice of extended warranties (EWs) currently available to consumers is extremely limited. Their EW purchase decisions have to be made at or very close to the time that they purchase the products and, at this point, they are uncertain about item reliability, future operating costs, and usage time before replacement. In this paper, we discuss an EW that offers more flexibility and we investigate optimal pricing strategies for the EW provider and optimal maintenance and replacement strategies for the consumer

Modelling of maintenance data

The modelling of maintenance data starts with the black-box approach (where the model selection is based solely on the maintenance data) and then through the grey-box approach for proper analysis (where one can gain insights to build better models). These models allow for more effective maintenance of the object. This paper deals with the grey-box approach to modelling. It discusses the process of modelling and illustrates this through a real case study