Multivariate Nonparametric Classes in Reliability.

摘要

This paper examines multivariate nonparametric classes and methods in reliability. Hollander and Proschan (1984) described the various univariate nonparametric classes in reliability. The classes of adverse aging described include the IFR, IFRA, NBU, NBUE, and DMRL classes. The dual classes of beneficial aging are also covered. Several new univariate classes have been introduced since that time. One that this document briefly mentions is the HNBUE class, since we are aware of several multivariate generalizations of this class. The univariate classes in reliability are important in applications concerning systems where the components can be assumed to be independent. In this case the components are often assumed to experience wearout or beneficial aging of a similar type. For example, it is often reasonable to assume that components have an increasing failure rate (IFR). In making this IFR assumption it is implicit that each component separately experiences wear and no interactions among components can occur. However in many realistic situations, adverse wear on one component will promulgate adverse wear on other components. From another point of view a common environment will cause components to behave similarly. In either situation, it is clear that an assumption of independence on the components would be valid. Consequently multivariate concepts of adverse or beneficial aging are required.