The Graphical Method for the Estimation of Lifetime Distributions from Summary Data

摘要

A graphical method has been developed to obtain a rough estimate of the lifetime distribution of an item in a system where no detailed history of the system is available. Only summary information on installation, scrap, and replacement is known. The estimate of the lifetime distribution produced can be used to predict the number of replacements required by the system. The system to be analyzed is assumed to be composed of identical units. Each unit has one or more items whose failure and replacement are of interest. For simplicity, in this discussion, each unit will be assumed to have only one item of interest. Installation and scrapping of units, and failure with replacement of items, are observed in discrete periods of time. A unit is assumed to last at least one time period after being installed before it is scrapped or removed from the system; an item lasts at least one period before it fails and is replaced. An item failing in the same period that it unit is to be scrapped will not be replaced. Since a detailed history of units and items in the system is not available, assumptions are made that the oldest unit will be the first to be scrapped, and that the item that has remained longest in the system will be the first to be replaced.