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The purpose of this study is to propose and model an inspection and preventive maintenance policy for randomly failing systems that alternate operating and idle periods according to their mission profile.

A maintenance policy is defined and modeled mathematically. The paper focuses on finding the age T for inspection which maximizes the stationary availability of the system.

Except for the case of only self‐announcing failures, there always exists a finite optimal strategy T*. Two sufficient conditions for the uniqueness of such an optimum are also derived.

Many productive systems alternate operating and inactive periods, their failures may be self‐announcing or not self‐announcing (detected only through inspection). This paper presents a maintenance strategy for such systems in order to maximize their stationary availability. The proposed strategy suggests submitting the system to inspection when its age reaches T units of time.

This paper states a general expression of the system stationary availability which is considered as the performance criterion. Conditions of existence and uniqueness of an optimal strategy are developed.

The purpose of this paper is to investigate herding behavior around the crude oil market and the stock market and the possible cross-herding behavior between the two markets. The analysis examines also the herding behavior during financial turmoil and includes the investor sentiment and market volatility.

The authors use a modified version of the cross-sectional standard deviation and the cross-sectional absolute deviation to include investor sentiment, financial crisis and market volatility.

The authors find that the volatility of the stock market reduces the herding behavior around the oil market and boosts that around the stock market. However, the investors’ sentiment reduces the herding around the stock market and boosts that around the crude oil market. Consequently, the authors can conclude that the herding behavior around the two markets moves inversely and the herding in each market is enhanced by the lack of information in the other market.

This paper is limited to the herding of stocks around the crude oil market and ignores the possible herding of commodities around the oil market.

The originality of the paper rests on the study of the possible cross-herding behavior between the oil market and the stock market especially during financial turmoil.