Profust Reliability Behavior of Engineering Systems

Abstract

As well-known, the problem of street-lighting replacement is one of the most early problems approached in the context of reliability. In 1941 N.R.Campbell formulated the problem of street-lighting lamps replacement as follows: N street-lighting posts have to be provided continually with (functioning) lamps [8]. This implies that the lighting system is modeled as a series system with N components (lamps) and a new lamp has to be taken to replace the failed lamp upon failure. Unfortunately, this doesn’t coincide with reality. The situation often comes to us that some of the street-lighting lamps fail but are not replaced immediately. This implies that some failed lamps may be tolerable in the lighting system as long as the total light output of the system keeps to an acceptable level. So Campbell’s modeling of the lighting system as a series system is no longer appropriate. The system states should be determined in the context of the total light output rather than the number of functioning lamps directly, though some relation may exist between them. Then what is the system state, functioning or failed, if there are two failed lamps and N - 2 functioning lamps in the system? And what is the system state if there are N - 2 failed lamps and 2 functioning lamps in the system? The answers are fuzzy. Fuzzy methodology should be employed to define the system states when the lighting system is required to provide an acceptable level of the total light output, since fuzziness is attached to the term ‘acceptable’ [3]. We can treat the lighting system as a profust system.