Some Results on a New Class of Shock Models

Abstract

Traditional shock models view system failure time as a first passage problem. Yeh Lam proposed a new class of models called δ-shock models in which failure was dependent on the frequency of shocks. The present work generalizes Yeh Lam's results for renewal shock arrivals and random threshold. Several special cases and an optimal replacement problem are also discussed.

Generalized Shock Model Based On The Frequency of Shocks: A Simple Approach

“…(8) At this juncture we wish to observe that the results of Lam [5] and Rangan and Tansu [9] are reduced by setting k = 1 in our model in accordance with their model assumptions. We now present an example by considering the lifetime δ to be a constant to illustrate our model.…”

“…The system fails when the accumulated damage crosses a threshold. However Lam [5] and Rangan and Tansu [9] have considered δ− shock models which concentrate on the frequency of shock occurrences, as contrasted to the accumulated damage of the earlier models. In these class of models, system fails when two successive shocks are not separated by a sufficiently long interval δ (which could be random).…”