Zuverlässigkeitsmodelle auf der Grundlage stochastischer Modelle von Verschleiß prozessen

Abstract

Reliability of products of mechanical engineering is often decided by wear processes.

Suitable stcohastic precesses (cumulative stochastic precesses, Wiener-process with drift and related multiplicative processes) are applied to modelling of such wear processes. Then the lifetime is the random time to first crossing a given limiting wear level or wear reserve. Some lifetime distributions which are founded in such a wag for constant and random wear reserves are discussed (Birnbaum-Saunders-distribution, Inverse-Gaussian-distribution, special mixtures of distributions).

For some of these models a favourable statistical approach to lifetime distribution arises from samples of the wear process. Process. Possibilities to calculate characteristics or ordinary renewal processes are dealt with. In essential cases such characteristics can be expressed explicity.

By an example the application of the results is demonstrated beginning with samples from the wear process followed by choosing a wear model, estimating the parameters, testing goodness of fit, calculating characteristics of reliability up to optimal designing of block replacement in preventive maintenance and calculating the technical-founded demand for replacement parts.

Keywords:

• Verschleißmodelle
• stochastische Prozesse
• Statistik von Versehleißmodellen
• Zuverlässigkeit
• Niveauüberschreitungen
• Betriebsdauerverteilungen
• Erneuerungstheorie
• vorbeugende Instandhaltung
• Ersatzbedarfsbestimmung