Influence of the three different types of standby components on the performance of a <italic>k</italic>–out–of–<italic>n</italic>:F system in the dynamic stress–strength model.

Abstract We consider the effect of adding three different types of standby components to a <italic>k</italic>–out–of–<italic>n</italic>:F system based on the dynamic stress–strength model. For this purpose, the system reliability in the three different types of standby components, i.e., cold, warm and hot standby components, are calculated. Also, it is assumed that the stress and the strength components follow the Weibull distribution and the Weibull process, respectively. The maximum likelihood estimators of the redundancy system reliability are obtained. In addition, a simulation study is performed based on the Monte Carlo method. Finally, the results are illustrated via a practical example that is the time of successive failures of the air conditioning system of every member of a fleet of jet airplanes. [ABSTRACT FROM AUTHOR]