A Dynamic Reliability Analysis for the Conditional Number of Working Components within a Structure

In the present work, we study the number of working units of a consecutive-type structure at a specific time point under the condition that the system’s failure has not been observed yet. The main results of this paper offer some closed formulae for determining the distribution of the number of working components under the aforementioned condition. Several alternatives are considered for identifying the structure of the underlying system. The numerical investigation which is carried out takes into account different distributional assumptions for the lifetime of the components of the reliability system. Some concluding remarks and comments are provided for the performance of the resulting consecutive-type design.