This paper had its origin in consideration of the work reported on by D. M. Boodman [Boodman, D. M. 1953. The reliability of airborne radar equipment. Jour. Op. Res. Soc. America 1 (February) 39–45.]. The purpose is to examine some of the implications arising from the assumption that a piece of complex equipment fails when, and only when, one of its component parts fails. The equipment is assumed made up of many individual parts, each of which is liable to prime failure independent of all other parts. Two different initial conditions are assumed at the beginning of observation or operation: (a) all components are new; (b) the equipment has been operating for a long time, components that have failed having been replaced by new ones at the time of failure. We consider the probability of failure of the equipment as a function of time and of the survival curve of individual components, and the possible improvement of reliability of equipment by replacement of components at a given age. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.