Operability analysis of marine projects based on Markov theory

Abstract The operability of marine operations, that is, the estimation of their weather downtime and duration, is traditionally determined either by means of risk analysis or Monte Carlo simulation techniques. The work presented herein establishes analytically the probability distribution and statistical parameters of the duration of individual activities of a marine project based on the theory of Markov chains. According to the proposed Markov model the distribution of the duration of an activity is associated with certain statistical properties of the return time, that is the period between two successive passages from the non-operable state. Information about individual activities is then combined according to the PNET methodology, as proposed by Ang, A. H. S., Abdelnour, J. & Chaker, A. A., Analysis of activity networks under uncertainty. J. Engng Mech. Div., ASCE , 101 (EM4) (1975) 373–387 which considers the sequence of the execution of the activities, as defined by the operations scenario of the project, in order to establish analytically the probability distribution of the duration of the project. The statistical analysis distinguishes between activities which do not require a weather window for their execution and those which do. Policies which affect the execution of an activity are incorporated into the analysis by taking into consideration secondary tasks which are performed before or after its temporary suspension. Furthermore, performance efficiency factors are also introduced in order to reflect the influence of the prevailing sea state/vessel responses on the ability of the crew to carry out the activity. The Markov model is applied for a range of uninterrupted durations to activities which do or do not require a weather window and the results are compared with those from a Monte Carlo simulation. Good agreement is obtained for the mean durations but significant deviation is evident for the second order moments. This behaviour is attributed to the length of the record and also to the distribution of the return times. Agreement between the results of the two models is generally better for activities of low uninterrupted duration which do not require a weather window. Finally, the combined Markov/PNET methodology is illustrated with an example for a hypothetical project and results are compared with those from a Monte Carlo simulation. Similar conclusions to those mentioned above are drawn.