1 Introduction

Marine and offshore industries play a vital role in ensuring a sustainable future. Covering over 70% of the world’s surface, the oceans comprise a huge potential for both marine and offshore industries. Successful performance in all aspects of the offshore industry, including the extraction of offshore oil and gas reserves, offshore winds, and wave energy is of vital importance to the economy of all countries that actively indulge in this unique yet inherently hazardous industry. In particular, accidents in which passenger ships are involved may pose a high risk regarding human casualties. Therefore, a number of studies have been conducted to improveme ship safety. One outcome of these studies is the concept of Risk-Based Design (RBD) for passenger ships, for which the major criterion is the ability of a ship to survive in damage conditions. While these studies have addressed ship design, less attention has been paid to risk-based design in ship operations (Montewka et al., 2014). Failure of heavy and light lifting is one of the most common accidents that occur in the offshore industry. As has been dramatically demonstrated in a variety of cases, offshore lifting activities entail the hazard of a major accident with potentially severe consequences to the life and health of workers, pollution of the environment, direct and indirect economic losses, and deterioration of the security of energy supply.

Because of the importance of offshore industry, many investigations have been carried out by researchers and many results have been generated with regard to accident analysis, risk assessment, and safety procedure approaches. From these studies, it can be construed that the effective management of risk is vital to the safe development and operation of complex projects. As a rule of thumb, risk assessment—part of the risk management cycle—should be cost-effective and sufficiently detailed to enable the ranking of risks in order for the subsequent consideration of risk reduction. In particular, the introduction of risk-based safety management systems has led to the use of qualitative studies, both of which relate to specific offshore operations. More recently, in all aspects of the‘management of change’concept, a quantitative risk assessment may include the quantification of the probability and consequences of accidental events with respect to one or several of the following risk dimensions: personnel, environment, and assets. The use of quantitative risk assessments is often viewed negatively. Ferdous et al. (2009) stated that, in practice, it is difficult and expensive to obtain precise estimates of event probabilities because in most cases these estimates are the result of an expert’s limited knowledge, incomplete information, poor quality data, or imperfect interpretation of a failure mechanism. These unavoidable issues impart uncertainties to risk assessment methods and make the entire risk analysis process less credible for decision making.

It is commonly assumed that uncertainty can be classified into two categories. Aleatory uncertainty, also called stochastic or variable uncertainty, refers to uncertainty that cannot be reduced by more exhaustive measurements or a better model and is an inherent uncertainty due to probabilistic variability. Epistemic or subjective uncertainty refers to reducible uncertainty. However, we must state that more information might reduce the uncertainty. In the literature, (Oberkampf et al., 2000; Sentz and Ferson, 2002; Helton and Oberkampf, 2004), epistemic uncertainty is addressed using two methods: non-probabilistic methods such as evidence (Dempster-Shafer) theory, possibility theory, fuzzy set theory, and interval analysis; and probabilistic methods such as the Bayesian approach or the classical probability approach, that use the transformation of bounds to probability density functions (Urbina and Mahadevan, 2011).

Unfortunately, to date, risk assessment involving multiple hazards is commonly performed in independent analyses that neglect possible cascade effects (Marzocchi et al., 2012) and standard approaches for dealing with multi-risk situations that are not viable (Kappes et al., 2012; Nadim and Liu, 2013). As a result, the assessments are carried out without the expected accuracy. In fact, the impact of each hazard and risk on the others, i.e., the occurrence of each of the identified risks on the probability of occurrence of the others, is ignored in the evaluation. The implementatin of a Bayesian Network (BN) is more suitable within the overall analysis framework and has many advantages over traditional probabilistic methods. BNs merge domain knowledge and multiple source data within a consistent system and have a flexible network structure that is beneficial for identifying a locally optimal solution (Li et al., 2010). A BN is a graphical inference technique used to express the causal relationships among variables. BNs are used either to predict the probability of unknown variables or to update the probability of known variables, given the certain state of other variables (evidence) through the process of probability propagation or reasoning (Khakzad et al., 2011).

In addition, the safety of offshore installations often requires human action. On a regulatory basis, there is generally no clear definition or specific requirement for the inclusion of human error considerations in management systems or risk assessments (Khan et al., 2006). Overlooking the role of human error as one of the most important hazards can be considered to be the other cause of underestimated or overestimated risk assessment. Where safety-related human actions and administrative controls are required and justified, the feasibility and reliability of these actions can be demonstrated qualitatively using task analysis. This qualitative modelling can be used to substantiate any human-based safety claims and to quantitatively model the probability of associated human error. Task analysis provides the necessary support to demonstrate the appropriateness of the human reliability assessment process.

Human error is directly or indirectly related to a number of factors known as Performance Shaping Factors (PSFs), which are commonly categorized as external, internal, psychological, or physiological factors (Abbassi et al., 2015). By considering all mentioned aspects of PSFs, quantifying the potential for human error with respect to these actions is made possible by an analytical approach known as the Success Likelihood Index Methodology (SLIM) (Kirwan, 1994). This approach is crucial for quantifying risks with pin-point accuracy. Conversely, the role of humans in enhancing the reliability of a system should also be taken into account. Although dozens of quantitative risk assessment techniques are employed today, most lack any calculation of the likelihood of human error.

The objective in this paper is to make an epistemic estimation based on limited knowledge of the probability and frequency of the failure of each system by applying Bayesian theory to determine a reassonable result. This paper is organized in the following sections. In section 1, we briefly desribe the sub-activities of the proposed case study in regard to lifting operations. In section 2, we introduce an Event Tree (ET) scenario for making a Quantitative Risk Assessment (QRA). In section 3, we adopt the SLIM to determine Human Error Probability (HEP) and highlight the significant outcomes. In section 4, we present the BN concept for depicting the causal and consequence relationships between random variables. On this basis, we also discuss Bayesian inference for making epistemic estimations of the probability of a top event. We summarize the outcomes of this research and make future research recommendations in the final section.

2 Epistemic-based investigation approach

As illustrated in Fig. 1, we developed an epistemic-based investigation approach to assess the risk of studied operations, including qualitative and quantitative risk assessments, each of which consists of several steps. Qualitative and quantitative risk assessments are presented, respectively, by applying an ET and a BN. We divide the epistemic estimation of hazard-promoting events into two categories: human error probabilities as estimated by applying the SLIM process, and the probability of other hazard-promoting events, calculated using the Homogeneous Poisson Process (HPP). After obtaining the HEPs for a specific scenario, we calculate the final risk value by integrating the HEPs and the consequence analysis results, using BN inference.

3 Case study

To implement the proposed methodology for making an epistemic estimate of risks in connection with offshore operations and considering human error, we carried out a thorough task analysis of a light-weight lifting operation in the South Pars oil and gas field in the Persian Gulf of Iran. To summarize the related activities, a quick description for each sub-activity is given below.

3.1 Mobilization

Prior to mobilizing equipment for transport to the vessel, all equipment is first tested, including the positioning equipment (such as multibeam, Ultra-Short Baseline (USBL), and related survey system), Remotely Operated Vehicle (ROV), crane, and personnel. During mobilization, the equipment must be installed, checked at the component level, and calibrated accurately.

It is essential that equipment be installed on the vessel with the following order of priority:

(a) Safely located and securely fitted.

(b) Easily accessible and operated.

Moreover, any changes on deck and other parts of the ship must be double-checked in order to comply with current ship regulations.

3.2 Support structure installation

The following procedure must be followed during support installation:

(a) Vessel is located at correct coordinates. After confirmation of the vessel position by the survey team, lifting operation is initiated. The heading of each crossing and the coordinates must be checked and approved by the client representative prior to starting the installation process.

(b) The USBL system is used for underwater positioning and the underwater gyro system is used for the support/mattress orientation.

(c) Beacon(s) and underwater gyro must be connected to the proper frame, which is attached to the spreader bar.

(d) Lifting equipment, including the sling, belt, and spreader bar must be ready for lifting support. After verification of the support coordinates, lifting is carried out by the onboard crane.

(e) The support must be lowered by the crane to up to 1 m above the seabed. In this situation, the position must be checked and confirmed by the survey team and the ROV. For this purpose, the USBL system is used and the ROV supervisor controls the entire operation. These devices indicate the relative position of the support and the existing pipe line.

(f) The ROV supervisor must check the operation by monitor and extract fix points to validate the position of the support installation on the seabed. Should the support not match its proper position, the orientation of the support must be changed using taggers that had been previously connected. Using winches on deck, with instructions given by the survey and ROV supervisor onboard, this auxiliary tagger is used to control the offset and direction of the support and to steer it into the correct position. Then, the support is lowered onto the seabed. Again, a beacon must be used to check the coordinates. After the final check and confirmation by the survey team, the support is released from the spreader bar.

(g) The tolerance of the orientation and the position is±1 m and±4°, respectively, considering the relative distance of 1 m between two tandem supports. However, the subcontractor will make every attempt to perform the operation perfectly.

(h) After installation is completed, the support is released and the ROV detached from the spreader bar, whereupon all rigging and the survey frame is returned to the surface.

4 ET for most probable scenario

ETs are an inductive or forward logic—a technique that examines all possible responses to the initiating event progressing from left to right across the page. It is also a commonly applied technique for identifying, analyzing, assessing, and evaluating the consequences that can result following the occurrence of a potentially hazardous event (Rausand, 2011). Typically, the branch points on the tree structure represent the success, failure or partial failure of different systems and subsystems that can respond to the initiating event.

According to epistemic knowledge gained from accident reports, related research, and expert opinions, the most probable accident scenarios are illustrated in the ET diagram shown in Fig. 1, in which human error may lead to the failure to check the connection between the belt and trunnion. This situation may result in the weight of the support structure not being in accordance with the Safe Working Load (SWL) of the derrick. The inadequate connection of slings may cause breakages in the process of lowering the support. Regardless of the nature of the break, the slamming of the load is a plausible outcome, especially near the surface. Consequently, disconnection of the load and derrick may occur. The diagram in Fig. 2 illustrates these potential accident scenarios.

5 Probability of top events 5.1 HEP: Using SLIM

HEPs are usually determined either by an analyst’s judgement or by the use of one or more Human Reliability Assessment (HRA) quantification techniques, such as the human error assessment and reduction technique (Williams, 1986), the SLIM (Kirwan, 1994), or the Technique For Human Error Rate Prediction (THERP) (Swain and Guttmann, 1983). While some of these techniques have displayed reasonable accuracy (Comer et al., 1984; Kirwan, 1988; Kirwan et al., 1995), some concerns regarding their precision remain unsolved. In the offshore world, this uncertainty is compounded because the techniques were developed largely for nuclear power applications and much of the data used to develop or validate the techniques originated in the nuclear power context. As such, while these techniques and some human error data exist, the relevance of their translation into the context of offshore systems is uncertain. Offshore risk assessment must establish at least some of its own data with respect to human error probabilities to support its risk assessment practices (Basra and Kirwan, 1998).

If the significant human contributions to the likelihood of the occurrence of major accidents is omitted, then the probability of the event occurrence may be seriously underestimated. Conversely, the human role in enhancing the reliability of a system must also be taken into account. Although dozens of quantitative risk assessment techniques are employed today, most lack any calculation of the likelihood of human error.

5.1.1 Task analysis

The first step in HEP analysis is to identify the required task analysis (TA) acitivites. TA is a fundamental methodology in the assessment and reduction of human error, as well as the relative risk. The starting point of a TA investigation is the systematic description of the ways in which the task was being carried out when the incident occurred (Embrey, 2000).

When the scenario is developed, the human-related activities and the probability of error for each activity is identified. A summarized representation of the various activities and tasks involved in this study’s lift operation procedure is presented in Table 1.

5.1.2 Success Likelihood Index (SLI)

The SLIM integrates various PSFs that are relevant to a task into a single number called the SLI. The SLI is calculated using Eq. (1) below. To determine the related SLI for task j^th, numerous sub-activities for each task SLI are calculated separately, so related HEPs are calculated using Eq. (2), in which“n”is the number of the sub-activity and“m”is the number of PSFs.

$ {\rm{SLI}} = \sum\limits_{i = 1}^m {{R_i}{W_i}} $

(1)

$ {\rm{SL}}{{\rm{I}}_j} = \sum\limits_{j = 1}^n {\sum\limits_{i = 1}^m {{R_{ij}}{W_i}} } $

(2)

For a given SLI, the HEP for a given task is estimated using Eq. (3):

$ {\rm{lg}}\left( {{\rm{HEP}}} \right) = a \times {\rm{SLI + }}b $

(3)

$ {\rm{HEP}} = {10^{a \times {\rm{SLI}} + b}} $

(4)

where

a and b are constants determined from two or more tasks for which the HEPs are known. In this study a and b are considered to be-1.95 and 10^-4, respectively.

Identifying the PSFs is a substantial step in the SLIM. The first step, HRA, focuses on human behavior and identifying a set of human factors believed to be related to performance. These PSFs are then employed to estimate the probability of human error in a given situation(Musharraf et al., 2013).

5.1.3 Identification and assessment of PSFs

PSFs provide a basis for considering the potential influences on human performance and systematically considering them in the quantification of HEPs (Groth, 2009). Determining the weight of the PSFs to develop the SLIs is one of the most pivotal steps. In this assessment, the PSFs with the highest rank are considered to be related PSFs, as listed in Table 2. The number in the second column denotes the normalized importance (weight W_i) of a particular PSF for the task under consideration, as determined by expert analysis.

Rating the PSFs is another important procedural step in the SLIM. Participant experts, such as technical engineers, give a rating R from 0 to 1 for each of the PSFs, where a rating of 1 is given for a human performance judged to be optimal. These ratings are based on the six PSFs listed in Table 2 as most important in the lifting of light structures.

5.1.4 HEP

By applying Eq.(2), we obtain the SLI for each activity. Then, Eqs. (3) and (4) are used to calculate the HEP of each task. The HEP values of the activities in our study example are presented in Table 3.

It is obvious that the first top event in the event tree is related to human error, so the cumulative probability of the first top event-human error must be calculated, using the probabilities of the sub-activities from Eq. (4). The probability of total human error, HEP_T, for lifting a light structure in the offshore industry can be calculated using Eq. (5):

$ {\rm{HE}}{{\rm{P}}_T} = 1 - \prod\limits_{j = 1}^n {\left( {{\rm{HE}}{{\rm{P}}_j}} \right)} $

(5)

5.2 Probability of other hazard-promoting events

Here, we assume that the distribution of the frequency of accidents follows a Poisson distribution. In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events. The occurrences of a hazardous event are often modeled by a homogeneous Poisson process (HPP) that includes the frequency of failure rate λ, which is the expected number of occurrences per year (or some other time unit).

Failure rate estimates are based on minimal field data for the probability and frequency of each failure and expert judgment. We calculated the HPPs of the hazardous events in the ET shown in Fig. 2 using Eq. (6), and the results are shown in Table 4. However, the probability of the first top event, human error, was derived using SLIM approach.

$ Pr(N(t) = n) = \frac{{{{(\lambda t)}^n}}}{n}{{\rm{e}}^{ - \lambda t}}\;\;\;\;\;\;{\rm{for}}\;\;\;n = 0,1,2, \cdots $

(6)

6 Bayesian Network 6.1 Bayesian Network (BN) in Brief

The BN is a graph with a set of probabilities. Combining the probability and graph theories, BNs consist of nodes, joints between nodes, and Conditional Probability Tables (CPTs)(Chen and Leu, 2014). A BN is based on the well-defined Bayes theorem represented by the Directed Acyclic Graph (DAG), with nodes representing random variables and arcs denoting direct causal relationships between connected nodes (Abimbola et al., 2015). This graphic probability model, introduced by Judea Pearl in the 1980s, has been the source of a number of practical tools that are useful for representing uncertain knowledge and provides a reasoning process to deal with incomplete information (Bouhamed et al., 2015). A BN with a set of random variables is an ordered pair (B_S, B_P), such that:

● B_S =G(V, E) is a DAG, called the network structure of B, where E ∈ V× V is the set of directed edges, representing the probabilistic conditional dependency relationship between random variable nodes that satisfy the Markov condition. That is, there are no direct dependencies in B_S that are not already explicitly shown via edges, E. Also:

● B_P ={γu : _u × _πu → [0... 1] | u ∈ V} is a set of assessment functions, where the state space _u is the finite set of values of u; πu is the set of parent nodes of u, indicated by B_S. If X is a set of variables, _X is the Cartesian product of all state spaces of the variables in X, and γu uniquely defines the joint probability distribution P(u | πu) of u conditional on its parent set, πu.

BNs provide an elegant mathematical structure for modeling complicated relationships among random variables and for inferring the probability of a cause when its effect is observed. This construct allows scientists to supplement their existing knowledge or expertise with new data.

BNs are based on the Bayes theorem, wherein the posterior probability of a hypothesis is inferred according to some evidence. Mathematically, the Bayes' rule states,

$ \begin{array}{l} {\rm{posterior}} = \frac{{{\rm{likelihood}} \times {\rm{prior}}}}{{{\rm{evidence}}}} \cdots \to \\ P(\theta \left| x \right.) = \frac{{p(x\left| \theta \right.)p(\theta )}}{{p(x)}} \end{array} $

(7)

where P (θ|x) denotes the probability that random variable“θ”has a specific value given the evidence“x”. Prior probability for the parameters is what is known before performing the experiment. Posterior probability relates to the parameters given the existing data. The factor in the denominator is a normalizing constant that ensures that the posterior value adds up to 1. These can be computed by summing up the numerator over all possible values of θ; meaning that:

$ p(x) = \int {p(x\left| \theta \right.)} p(\theta )d\theta $

(8)

BNs can represent the joint probability distribution that is relevant to all variables, in a compact way:

$ P({X_1},{X_2}, \cdots ,{X_n}) = \prod\limits_{i = 1}^n {P({X_i}\left| {{P_a}} \right.({X_i}))} $

(9)

The number of all possible BN structures has been shown to increase sharply as a super-exponential number of variables. Indeed, (Robinson, 1977) derived the following recursive formula for the number of DAGs with n variables:

which gives: r(1)=1, r(2)=3, r(3)=25, r(5)=29 281, r(10)=4, 2×10¹⁸ (Bouhamed, 2015).

6.2 Converting ET to BN

Any ET with three or a higher number of events can be represented by a BN. In the process of conversion, two arc types are applied to complete the network:

● Consequence arcs connect each event node to the consequence node. This relationship is deterministic. The probability table for the consequence node encodes the logical relationship between the events and the consequences.

● Causal arcs connect each event node to all events later in time.

In this paper, we take both types of arcs into account in constructing the BN. The solid lines in Figs. 2 and 3 are related to the causal arcs and the dotted lines are related to the consequence arcs. The properties of each node are provided in Table 4. The BN presented in Fig. 2 presents the hazard-promoting factors of our research and, as a result, this network contains all possible scenarios based on these events. The BN of the ET in this study is presented in Fig. 3.

7 Bayesian inference

Attention must be given to the fact that the investigation in this study does not concentrate on the most serious accident but on the most probable scenario, and the estimation of risk in this process depends on multiple factors, all of which are subject to uncertainty. Building on available epistemic knowledge and the best traditional approaches, we apply new techniques in this paper to enhance the degree of accuracy in risk assessment and, thus, to decrease the risk of potential loss.

According to the quality and nature of the relationship between events in the BN, the process of inference will differ. We calculated the probability of failure in both types of BN (Fig. 3). The failure probability is based on minimal field data regarding the probability, frequency of each failure, and expert judgment. The Bayesian inference of the network with the causal arcs is indicated in Table 5. According to these calculations, we can infer that the probability of human error increases due to the omission of the inspection. There is only one variable (N₂) for which the posterior probability declines in light of its evidence (N₃). It is obvious that the probability of failure in lifting will be 1 if disconnection occurs, which is calculated and listed in Table 5.

Table 6 lists the epistemic estimations of the BN with consequence arcs (Fig. 4), meaning that the posterior probability of the union of all variables given the occurrence of failure in lifting (specific scenario) is 1.442E-01. By applying BN and considering the probability of failure in the lifting process as evidence for the probability of the union of all events, the probability of failure is estimated with the assumption of dependency between the hazard promoting factors. The interaction and influence between events are taken into account and. Finally, the posterior probability is calculated.

8 Conclusions

In this work, we built on existing epistemic knowledge, incorporated the best traditional approaches, and applied new techniques to enhance the degree of accuracy of risk assessment and, thus, to decrease the risk of potential loss.

In the first half of the paper, we specified the most probable accident scenario and constructed an event tree based on minimal field data, related research, and expert opinions. We then estimated the probability of each hazard promoting factor in the structure of the event tree. Human error probability was determined using the SLI method, and was computed to be 86.23%. In the second half of the paper, we presented a Bayesian network of the consequences outlined in the event tree to estimate the probability of failure based on causal and consequence arcs. As such, in this study, we demonstrated the use of Bayesian networks in the estimation of accident occurrence probability.

The main findings of this paper are summarized in the following:

1) A better estimation of human reliability would help in the design of effective safety systems and in the accuracy of risk assessments. Failure to include the estimating of human error probability can only lead to inaccurate final failure estimations for top events in the event tree, because human error is one of the main causes of failure in everyday functioning.

2) We recommend the integration of a forward logic and inductive risk assessment approach (event tree) for an offshore operation with a well-defined probability method (Bayesian network), based on epistemic knowledge, to estimate the probability and frequency of each failure, which can be used jointly with existing algorithms and heuristics.

3) The investigation of accident scenarios in an ET and, subsequently, the conversion of accident scenarios in the BN, with respect to both the causal and consequence relationships between factors, will result in a better interpretation of the interaction between risk factors and a better calculation of risk assessment.

Since the available data and information in connection with operational activities in the South Pars oil and gas field of the Persian Gulf are not sufficient, it is not possible to make a robust quantitative reliability assessment. However, we highly recommend the interdisciplinary study of reliability tests and statistical methods to develop more realistic reliability estimations and to clarify as yet unidentified operational risks, especially those related to lifting and transportation.