The paper presents the theoretical development and several practical applications concerning new nonconventional approaches to the risk analysis specifically concerning the oil drilling activity. Starting from well consolidated knowhow concerning the matter itself, here two fundamental matters are considered and put into the analysis and the discussion of real cases: time (elapsing) and exploration strategies (changing, sometimes even rather quickly). According to well known technical operating standards, the paper faces nowadays requirements and suggests the corresponding best solution techniques. Real cases are provided and (with the maximum care) reliably developed as far as the risk analysis stage is concerned. The Author also suggests new disclosures able to face and accompany the technical improvements without any delay or "service interruption" anytime it is worth while immediately acting and operating. Both offshore and land rigs are concerned, in a unitary way of thinking, designing and considering the whole matter. Extreme approaches to particular environmental conditions (say polar and ultra deep water drilling, very low water heads even seasonally strongly varying) are considered as well, confirming and emphasizing the previously described concept of unitary analysis approach. For the purpose, the Author leads a permanent study and education energy & petroleum school branch in Italy

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