A mathematical model for the export development process of firms using reliability applications

Abstract

The lifetimes of machine components in industrial reliability are considered failure times. For example, ball bearings are tested under cycles of different stresses and failure time is the number of cycles to failure. Failure time have the complicating feature of containing 'censored' observations. A right censored failure time for a ball bearing might arise if the ball bearing is still in operation at the end of the time period set aside for observation. A left-censored observation is one in which the unit is known only to have failed prior to some time. Meanwhile social scientists and economists are facing similar problems in analyzing data on the export development process of firms. In this case, 'failure time' is the length of time between the birth of the firm and the year of its first export (pre-export stage). If the firm has not exported yet (has not 'failed') at the end of the observation period, it will be referred as a right-censored observation. If the firm has already exported at the beginning of the observation period and the date of its first export is unknown, it will be referred as a left-censored observation. The object of the present paper is to fit a mathematical model to the export development process of Spanish manufacturing firms using reliability applications