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The purpose of this paper is to study the evolution of a system stationary availability and determine the optimal preventive maintenance period, which maximises it in a context where preventive and corrective maintenance actions are imperfect and have non‐negligible durations.

The quasi‐renewal process approach and a (p, q) rule are respectively used to model corrective and preventive maintenance. Considering the durations of the preventive and corrective maintenance actions as well as their respective efficiency extents, a mathematical model and a numerical algorithm are developed in order to compute the system stationary availability.

It has been proven that for any given situation regarding the system, the repair and preventive maintenance efficiency extents, and the downtime durations for preventive and corrective maintenance, there is necessarily a finite optimal period T* of preventive maintenance which maximises the system stationary availability. A sufficient condition for the uniqueness of the optimal solution has also been derived. Numerical examples illustrated how preventive and corrective maintenance efficiency extents affect simultaneously the system optimal availability.

The study considers a general industrial framework where preventive and corrective maintenance actions are imperfect. In fact, neither the best‐qualified technicians nor the most suitable tools or spare parts are found to carry out maintenance actions. In such a context for a large variety of technical systems, when implementing preventive maintenance policies one should take into account the efficiency extents of maintenance actions as well as their durations in order to evaluate and optimise the system availability. The paper provides maintenance managers with a decision model allowing not only the computation and optimisation of system availability, but also the investigation of how preventive and corrective maintenance efficiency extents affect simultaneously the system optimal availability. The proposed model also allows one to find to what extent corrective actions ineffectiveness should be tolerated without having an important availability loss.

The paper proposes a modified formulation of the quasi‐renewal process taking into account the non‐negligible duration of corrective maintenance actions and periodic preventive maintenance. A new numerical algorithm is also developed in this context to compute the quasi‐renewal function that it is impossible to find in closed form. This allowed the computation and optimisation of system stationary availability.

This paper aims to investigate the hedge, safe-haven and diversifier properties of Islamic indexes, Bitcoin and gold for ten of the most affected countries by the coronavirus, which are the USA, Brazil, the UK, Italy, Spain, Germany, France, Russia, China and Malaysia.

This research uses the Ratner and Chiu (2013) methodology based on the dynamic conditional correlation models to improve Baur and McDermott (2010). The authors adopt a careful investigation of the features of a diversifier, hedge and safe haven using the dynamic conditional correlation–GARCH and quantile regression models.

Empirical results indicate that Islamic indexes are not considered as hedge assets for the conventional market for all studied countries during the COVID-19 pandemic crisis period. However, gold works as a strong hedge in all countries, except for Brazil and Malaysia. Bitcoin is a strong hedge in the USA and a strong hedge and safe haven in China.

International investors in China and the US stock markets should replace Islamic ‎indexes with Bitcoin in their conventional portfolio of securities during the pandemic.

To the best of the authors’ knowledge, this is the first paper that re-evaluates the hedge, safe-haven and diversifier properties of Islamic indexes, Bitcoin and gold for ten of the most affected countries by the coronavirus.

This paper aims to investigate whether Islamic indexes, Bitcoin and gold still act as hedges or/and “safe-haven” assets during the COVID-19 pandemic crisis. This paper examines the role of the Morgan Stanley Capital International all-country world index, Islamic index, gold and Bitcoin as a hedge or safe-haven asset for the world conventional stock market over the period from April 30, 2015 to March 27, 2020.

In this paper, the authors re-evaluate the hedge and safe haven properties of Islamic indexes, gold and Bitcoin following Baur and Lucey’s (2010) and Baur and McDermott’s (2010) methodology.

Empirical results show that the Islamic index is not a hedge or a safe haven asset for the world conventional stock market during the recent coronavirus crisis period. Different from the whole period, the authors find that gold is a strong hedge but only a weak safe or is not a safe haven during the coronavirus sub-period. Bitcoin reports distinctive properties, as it acts as a weak hedge and not a safe-haven asset.

This paper is the first study that investigates whether the global Islamic index still acts as hedges or “safe-haven” assets during the new COVID-19 crisis period. The results can help investors make informed decisions when adding cryptocurrencies and Islamic indexes to their portfolios during the coronavirus crisis.