A new generalized δ-shock model and its application to 1-out-of-(m+1):G cold standby system

Abstract

According to the classical δ-shock model, the system failure occurs upon the occurrence of a new shock that arrives in a time length less than δ, a given positive value. In this paper, a new generalized version of the δ-shock model is introduced. Under the proposed model, the system fails if there are m shocks that arrive in a time length less than δ after a previous shock, m≥1. The mean time to failure of the system is approximated for both discretely and continuously distributed intershock time distributions. The usefulness of the model is also shown to study 1-out-of-(m+1):G cold standby system. Illustrative numerical results are presented for geometric, exponential, discrete and continuous phase-type intershock time distributions.