Can We Predict Occupational Accident Frequency?

0957–5820/06/$30.00+0.00 # 2006 Institution of Chemical Engineers Trans IChemE, Part B, May 2006 Process Safety and Environmental Protection, 84(B3): 208– 221

www.icheme.org/psep doi: 10.1205/psep.05113

CAN WE PREDICT OCCUPATIONAL ACCIDENT FREQUENCY? D. ATTWOOD1, F. KHAN2
and B. VEITCH2 1 Lloyd’s Register EMEA, Aberdeen, UK Faculty of Engineering & Applied Science, Memorial University, St John’s, NL, Canada

2

A

model has been developed to predict the frequency and associated costs of occupational accidents in the offshore oil and gas industry. Model inputs include (1) direct factors such as quality of personal protective equipment, (2) corporate factors such as training programme effectiveness, and (3) external factors such as royalty regime. Model development was based on a review of related literature, expert opinion, and reliability analysis concepts. The model accounts for the differing relative importance of influencing factors, using quantitative data derived from a survey of safety experts. The influences of external elements on corporate actions and of corporate actions on the direct accident process are also included in a quantitative manner, again benefiting from the expert opinion survey. An introduction to the problem is provided, followed by a brief summary of the literature reviewed, a description of the model and example runs demonstrating the model’s versatility and capability. Taking a broader perspective, the work offers an example of quantifying something which, at first, seems unquantifiable. Tools such as this offer valuable aids to management and provide an improvement on qualitative opinion, hunches and similar. Keywords: occupational accidents; offshore; oil and gas; quantitative prediction; reliability approach.

INTRODUCTION

accidents, i.e., ‘accidents will happen’. An unfortunate reaction to this position would be a relaxation of efforts to reduce accident frequency. Fortunately, this view is not widespread within the oil and gas community or industry in general. Following a review (International Labour Organisation, 2003) of global industrial accidents, the ILO makes the following comments: ‘Fatalities are not fated; accidents don’t just happen; illness is not random; they are caused.’ Most oil and gas operators’ policies mirror these comments. Particularly in projects being executed in mature markets, safety culture, systems, and equipment are well developed and effective, resulting in a relatively low likelihood of accident. However, as reserves are depleted in traditional locations and companies turn to frontier regions (e.g., Africa and China), the implementation of an effective safety programme becomes more difficult. Attempts to address the problem have been ongoing for at least a quarter of a century. Despite all the excellent efforts, however, the problem remains. Current occupational accident research is mostly qualitative in nature, compared to the more quantitative efforts directed toward major hazards. A specific gap in the body of research is assigning sufficient quantification to the analysis of occupational accidents, in terms of data gathering, model development, and analysis (Attwood et al., 2005a).

Occupational accidents constitute an area of significant and continuing risk for the oil and gas industry. The statistical data show (Figure 1) that fatalities are more likely to be caused by occupational accidents (e.g., falls, caught between, struck by) than by more catastrophic events such as explosions or air transport incidents. By some measures, in 2004, oil and gas workers were six times more likely to die from a fall than from an explosion/burn (International Association of Oil & Gas Producers, 2005). The situation is consistent with that observed in the general workplace, where it has been reported (UK HSE, 1996) that over a third of all major injuries reported each year result from a slip or trip, this being the single most common cause of injuries at work. Whilst occupational safety is regulated under various national legislative schemes, analysis of these types of accidents is not nearly so rigorous as for major accident hazards. This is likely due to the relatively more ruinous potential consequences of major accidents. A potentially contributing factor to the problem is the presence of an attitude adopting a certain inevitability to
Correspondence to: Professor F. Khan, Faculty of Engineering and zApplied Science, Memorial University, St John’s, NL, Canada A1B 3X5. E-mail: [email protected]

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CAN WE PREDICT OCCUPATIONAL ACCIDENT FREQUENCY?

Figure 1. Fatality causes, 1999– 2003 (excludes unknown) (International Association of Oil & Gas Producers, 2005).

Whilst occupational accidents occur through a direct (unsatisfactory) interaction between worker and workplace, it is the basic premise of the presently proposed model that workers’ behaviours are influenced by corporate culture, and their workplace environment and procedures are controlled corporately. Furthermore, corporate decisions and actions are, in turn, influenced by external elements. LITERATURE REVIEW A comprehensive discussion of the literature is presented in Attwood et al. (2005a). A summary is presented here, highlighting only information considered essential to this discussion. Review of Accident Models Early accident models were developed in reaction to the specific needs they tried to address. Medicine and the nuclear industry have historically demanded overwhelming attention to accident causation, prevention, and mitigation (Gordon, 1949; Le Bot, 2004). This is probably due to the high emotional attachment associated with problems in these industries—medicine due to the distress caused by loved ones’ illnesses, and the nuclear industry due to the catastrophic consequences of nuclear accidents. It is no surprise therefore, that many of the earliest accident models, which provided valuable basic philosophical direction to subsequent efforts, originated in these industries. One group of models studied (e.g., UK HSE, 2001, 2002b; Balkey and Phillips, 1993) concentrates on direct causes, for example quality of personal protective equipment, number of shifts worked and time of injury, effect of prescriptive safety regulations, and similar. These models help to produce improvements in specific areas, but they do not adopt a comprehensive view of the occupational accident problem. Other models take a more holistic view of accidents (Geyer and Bellamy, 1991; McCauley-Bell and Badiru, 1996a, b; Trontin and Bejean, 2004; Embrey, 1992; Hopkins, 2000), including corporate factors in the analysis. However, these models, in general, study catastrophic accidents such as

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explosions and toxic releases. The present work’s specific application to occupational accidents and inclusion of external factors differentiates it from these efforts. Human performance and personal reaction to dangerous situations provide the basis for some models (UK HSE, 2002a, 2003; Gordon et al., 2001; Strutt et al., 1998; Mosleh and Chang, 2004). Accident occurrence is considered to be a question of how well individuals react with their environment to prevent, mitigate the results of, or recover from, a potential accident. These models offer insight into the human element of the problem, but the present work considers human performance as just one of a series of factors in a holistic analysis. Other literature describes models which adopt a statistical approach (Kjellen, 1995; Luo, 1998; Thompson et al., 1998; Tomas et al., 1999; Guastello, 1989; Brown et al., 2000; Cheyne et al., 1999; Pate-Cornell and Murphy, 1996), suggesting methods for quantifying relationships between influencing elements. The present work expands on these concepts, providing a holistic and predictive approach specifically tailored to offshore oil and gas occupational accidents. Existing accident models contribute expertise to the offshore occupational accident problem from a wide range of perspectives. However, while some deal specifically with occupational accidents, some take a holistic approach to more catastrophic types of offshore accidents, and others consider non-traditional elements (i.e., societal, human) of the accident process, none adopt the holistic, quantitative approach to offshore occupational accidents proposed by this research. Occupational Accident Data Sources Since this work includes a significant quantitative element, an evaluation of the related available statistical data was undertaken. The available sources may be grouped as follows: . internet sources (e.g., United Kingdom Health & Safety Executive (HSE) website, Norwegian Petroleum Directorate (NPD) website); . company annual reports (e.g., Shell, ConocoPhillips, Exxonmobil); . open literature (International Association of Oil & Gas Producers, 2004, UK HSE, 2000, 2001, 2002b. The internet sources, developed by regulatory bodies in established offshore regions such as the UK North Sea and Norway, provide, amongst other things, unprocessed accident statistics. These data have been used to compare accident rates between regions and also between groups (i.e., contractors versus operators) within regions. Company annual reports provide a source of comparison between major operators. The data are limited, including a few annual indicators only for each operator, for example lost time incident rate, total recordable incident rate, and sometimes occupational illness frequency. The open literature offers various analyses of offshore occupational accident data, for example investigating the relative frequencies of accidents when performing certain activities, and comparisons of accident rates in various regions. Company comparisons are available, but only on an anonymous basis.

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ATTWOOD et al. Factors Affecting Occupational Accidents

Table 1. Frequency of mention of factors affecting safety results.

Model development necessarily includes the identification of constituent factors and the determination of their interrelationships. Literature offering suggestions for choice of factors and possible inter-relationships has been reviewed. Some examples are presented here. BOMEL proposes a two-level series of factors considered to affect occupational accidents in the UK offshore oil and gas industry (see UK HSE, 2002b for details). Whilst the factors suggested by BOMEL are similar to those proposed by the present work, their interdependency and the quantification method presently proposed is entirely different. Similar to BOMEL, Kjellen and Hovden (1993) view the accident process as having two levels—the accident sequence, and the underlying determining factors. The two approaches differ in the specific choice of factors and the degree to which non-direct factors are considered (see Kjellen and Hovden, 1993; UK HSE, 2002b for specifics). Wilson and McCutcheon (2003) recognize the importance of corporate factors (e.g., inadequate programmes and failure to comply with standards) in the industrial accident investigation process. The incident causation model used for their analysis was developed by Bird and Germain (1992). Hopkins (2000) applies the ‘AcciMap’ approach developed by Rasmussen (1997) to the Longford (Australia) gas plant explosion. Hopkins recognized the role of the following external elements in the accident:

Factors affecting occupational accidents (frequency of mention in brackets)

. market forces—specifically pressure to reduce costs; . market ideology (the notion that ‘the market is the best way to satisfy human wants and needs, and that governments should play as small a role as possible in this process’); . inadequate regulatory systems; . government shortcomings—for example failure to provide alternative domestic gas supplies. Whilst the roles of the external elements were noted by the author, the government appointed Royal Commission of enquiry was criticized for failing to do so. Other sets of factors, proposed by various researchers, have been reviewed (Pate Cornell and Murphy, 1996; UK HSE, 2003; Balkey and Phillips, 1993; McCauley-Bell and Badiru, 1996a, b; Embrey, 1992; Hurst, 1998; Thompson et al., 1998; Tomas et al., 1999; Brown et al., 2000; Cheyne et al., 1999). Almost all of the proposed factors and groupings include a series of direct factors, and some also include a set of corporate factors affecting the workers’ environment. There is less emphasis on external elements such as price of oil and regulatory regime, and the application of an external extension to the occupational accident problem constitutes one of the primary contributions made by the present work. It was felt worthwhile to introduce a degree of rigour to the review of factors suggested by others. Therefore, the groupings proposed in the literature were reviewed and the number of occurrences of specific factors in the direct, corporate, and external categories counted. The result of this exercise is shown in Table 1, with the numbers in brackets indicating the total number of times the factors were proposed. Because researchers often use slightly different terms to describe the factors, the process required

External Political influence (2) Regulatory influence (1) Market influence (1) Societal influence (2)

Corporate

Direct

Economic pressure (3) Corporate culture (11) Procedure/permit syst. (8) Corporate supervision/ audit programme (3) Safety management (2) Labour relations (2) Accident management (3) Training (10) Human resources (4)

Personnel experience (3) Staff knowledge/ learning (5) Safety design/layout (10) Staff errors (2) Safety behaviour (6) Fatigue (2) Housekeeping (1) Physical fitness (1) Weather (2) Quality of PPE (3) Attentiveness (2) Motivation (2) Compliance (1) Visual environment (1) Personnel attitude (4)

a degree of interpretation. However, the factors proposed most frequently by others have been included in the present model, which provides confirmation and validation to the choices. The relative scarcity of factors outside the organization proposed by previous researchers confirms the novelty of the present approach, which includes external societal and economic forces. MODEL DESCRIPTION Model Structure Occupational accidents result from an unsatisfactory interaction between workers and their environment. Direct factors affecting the process include staff behaviour and capabilities, weather conditions, safety related design of the workplace, and quality of protective equipment. Many of these factors are influenced by decisions taken at the corporate level. For example, worker attitudes and resulting behaviours are influenced by corporate ‘safety culture’. Additionally, the organization determines the quality of safety training, procedures and equipment. Other researchers (e.g., Cheyne et al., 1999; Thompson et al., 1998; Tomas et al., 1999) have considered the effect of corporate actions on the occupational accident process. Hopkins (2000) included external elements in the study of a gas plant explosion. Similar to Hopkins’ approach, the present model includes an external level, but as applied to the analysis of occupational accidents, instead of major events. Region-based cultural and financial pressures are considered to influence corporate actions and decisions which, in turn, directly affect occupational accident frequency. The following sections describe the components of the different levels, or layers. These components were chosen based on (1) discussions with offshore oil industry colleagues, (2) personal experience in the industry, and (3) the previously described literature review. The basic schematic of the model is shown in Figure 2. The direct layer The five components considered to directly affect accident frequency are (1) worker behaviour, (2) worker

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CAN WE PREDICT OCCUPATIONAL ACCIDENT FREQUENCY?

.

.

. Figure 2. Basic schematic of model.

. capability, (3) weather, (4) safety design, and (5) personal protective equipment. . Behaviours are personal choices which are influenced by one’s attitude and motivation. Collective staff attitude can sometimes be altered but is best affected at the hiring stage. Motivation to operate in a safe manner must be clearly provided by management and supervisors. Positive reinforcement is the more frequent option and usually takes the form of safety awards, financial or otherwise. Penalties for poor safety behaviour are less common, but may become more so in reaction to increasing corporate penalties for inferior safety performance. Some question the effectiveness of the safety award/penalty system, citing the encouragement of inappropriate non-reporting of accidents. Nevertheless,

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the system probably, on balance, encourages behaviour beneficial to both workers and the organization. Capabilities can be divided into mental and physical. Mental capabilities are of two categories, knowledge based, and intelligence based (Hurst, 1998). The ‘knowledge’ component comprises the safety related information retained by the worker following training sessions. The ‘intelligence’ component allows the worker to cope with safety issues not specifically covered by training and procedures. The physical capabilities associated with avoiding occupational accidents are considered to be good coordination, a reasonable degree of fitness, and lack of fatigue. Weather conditions at the time the work is performed can affect the likelihood of accidents. For example, rain or snow can make surfaces slippery, and extreme temperatures can affect concentration. Efforts to optimize safety related design can reduce accident frequency. Examples of measures taken are the use of non-slip walkways and clearly visible warning signs. Standard personal protective equipment (PPE), including for example safety boots, helmets, glasses and gloves, can be seen on just about all offshore installations.

The architecture of the direct layer is shown in the righthand columns of Figure 3. The corporate support layer The second fundamental layer (see middle column of Figure 3) is the safety related support provided by the company, comprised of (1) corporate safety culture, (2) safety training, and (3) safety procedures. Almost all offshore operators today expend considerable effort in developing a strong, positive safety culture, proclaiming ‘commitment to safety’ as their foremost concern. Corporate documents issue promises such as ‘safety takes precedence over production’, ‘safety is job one’,

Figure 3. Specific elements of model.

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and similar. Safety culture is often developed by enforcing day-to-day safety rules which may seem to border on the trivial, for example always placing plastic covers on coffee cups, backing into car parking spaces, holding handrails in offices, and so on. The motivation behind such rules is the belief that if staff are continuously aware of such detail, they will not need to ‘shift’ into a ‘careful’ mode when faced with more dangerous situations. In ‘mature’ oil and gas industry areas, the safety training programmes and procedures offered by most companies are well developed and effective. In some frontier regions, however, further efforts are required to raise the programmes’ level of quality to an acceptable standard. The external layer The view that safety results can be significantly improved solely by enhancements at the direct level is not supported by this or previous research (Hopkins, 2000; Pate-Cornell and Murphy, 1996; Cheyne et al., 1999; Thompson et al., 1998; Tomas et al., 1999). Better safety boots, a more stringent tank entry procedure, and similar initiatives may prevent an accident or two, but fundamental change requires improvement at least at the corporate level, which is, in turn, often driven by external factors such as the relative regional value placed on human life and the financial pressures exerted on the organization. Oil companies need to operate in regions where hydrocarbon reserves are discovered. Societal expectations differ throughout the world (and occasionally even within countries), and the associated forces affect an organization’s safety results. For example, some regions place a higher value on a human life than others. In regions where the value is high, operators will receive, usually through the regulatory process, relatively higher pressure to enact a ‘strict’ safety programme. This pressure will take many forms—including requirements for high expenditure on safety equipment through demanding prescriptive regulations, stiff corporate penalties for injuries, and requirements for expensive pre-project public safety performance forums. The opposite effect will be seen in regions with a comparatively lower societal value placed on life. Financial pressures on oil companies originate from several sources, including price of oil, corporate shareholder pressure, and regionally based royalty regime (see Figure 3 for the location of these items in the model architecture). An inverse correlation has been discovered between price of oil and accident frequency. This may be due to an effect which is more easily seen from a negative perspective—when money is scarce, i.e., when the price of oil is low, there is an increased pressure to ‘cut corners’ everywhere, and this includes, unfortunately, the quality of the safety programmes enacted by operators. Shareholder pressure is the degree to which a company is encouraged by its owners to improve performance. Unduly high pressure to retain extra money within corporate coffers rather than spending it on (what some shareholders perceive to be) an unnecessary expense lacking an obvious payback will negatively affect safety results. The royalty regime is heavily region-specific. It is interesting to observe government and public behaviour following the euphoria of an area’s first hydrocarbon discovery.

Usually the initial reaction is to make life very attractive for the companies, and a lucrative (for the company) royalty scheme is discussed and proposed. Gradually, however, the region’s historical economic situation is brought to bear on the process. If long term economics have been satisfactory and environmental concerns are considered important (usually due to valuable tourism or fishing industries), pressure is placed on government to enforce a strict royalty regime, which erodes project profitability and produces a negative ‘knock-on’ effect on safety results. On the other hand, in areas where the population has suffered from poor long-term economics, it is more likely that the public will encourage government to ensure that oil and gas operators are ‘made to feel welcome’ in every way, including financially. This will have a positive effect on disposable cash and, indirectly, safety results. Method of Analysis Many methods are available to study probabilistic events such as offshore accidents, including fault tree analyses and event tree analyses. Based on a review of existing research, it was decided that the accident process could be best modelled by a modified reliability network. The notion to use this approach originated with the recognition of similarities between a physical engineering system and a corporate safety programme, as described below. . Similar to an engineering system, safety programme success depends on the reliability of individual components. . Individual components will perform at different levels of reliability. . System improvements are usually enacted by making improvements in individual components. . The overall system can be realistically subdivided into sub-systems. . Some engineering system element subsets are configured in ‘series’ setups having the properties that (1) the reliability of the subset is the product of component reliabilities and (2) the subset reliability is always less than that of the least reliable component (see Figure 4). This corresponds to the concept that for some subsets of the safety system, all elements must be operating relatively efficiently to produce a satisfactory result. . Other engineering system elements are configured in ‘parallel’ setups having the properties that (1) the

Figure 4. Series versus parallel subsets.

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CAN WE PREDICT OCCUPATIONAL ACCIDENT FREQUENCY? reliability of the subset is calculated by subtracting the product of component probabilities of failure from unity, and (2) the reliability of the subset is always greater than that of the most reliable component (see Figure 4). This corresponds to the concept that for some subsets of the safety system, poor performance in some elements can be ‘compensated for’ by superior performance by others within the subset. A mathematical example can be used to illustrate the final two points above, with reference to the equations in Figure 4. Consider two subsets of elements, each containing two elements, one connected in series, the other in parallel. Assume a situation where the system reliabilities are approximately equal, produced (for example) when the component reliabilities of the series subset are 0.6 and 0.7, giving a system reliability of (0.6  0.7 ¼ 0.42), and the component reliabilities of the parallel subset are 0.2 and 0.3, producing a system reliability of (1 – (1 2 0.2)  (1 2 0.3) ¼ 0.44). Suppose system failure is proposed to occur when overall reliability falls below approximately 0.35. In the series arrangement, this would occur if the first component reliability were to fall below 0.5, a drop of only 17% from the original value of 0.6. However, in the parallel arrangement, a fall below system reliability of 0.35 would require the first component

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reliability to drop from 0.2 to approximately 0.06, a fall of 70%. A failure of the parallel system requires a much greater percentage component reliability drop than is the case for the series system. This example shows how the effect of ‘compensation’ by elements in the safety system is modelled by the parallel arrangement of components in the reliability network. Arrangement of elements The arrangement of elements in the model is shown in Figure 5. A few points to note are as follows: . The direct layer elements (behaviour, capability, weather, safety design, PPE and their subcomponents) are connected in a reliability network. The reliability of the overall safety system is calculated from these direct elements in much the same way as would be done for a physical network (Billinton and Allan, 1983). The only departure from formal system reliability calculation methodology is the necessary inclusion of relative strength factors, which is discussed in the next subsection. . The external elements influence corporate factors, and these in turn influence the direct components, as shown in Figure 5. The mathematics of this process is described in the next subsection.

Figure 5. Internal arrangement of the elements in the model.

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. The main direct elements (behaviour, capability, weather, safety design and PPE), are connected in a series configuration, reflecting the belief that all must work well in an efficient safety programme. . Some element subsets, for example (1) knowledge and intelligence and (2) coordination, fitness and lack of fatigue, are connected in parallel arrangements. This reflects the belief that a degree of compensation is available in the process. Examples of this would be when good intelligence facilitated accident avoidance for a worker having a less than ideal knowledge of safety procedures, or when a high level of coordination and fitness allowed a fatigued worker to successfully avoid an accident. Note the analogy in this analysis to a redundant, parallel – connected, pump providing increased system reliability in a multi-unit pump house. Strength of individual elements The model accounts for the fact that not all elements affect overall safety performance equally. Consistent with the overall model structure, choices about levels of importance have been made on a layer by layer basis. First, the relative importance of the five overall elements directly affecting accidents (behaviour, capability, weather, safety design and PPE) has been quantified. Moving to the next level, within the group of capability elements, is physical capability more important than mental, and, by how much? And moving down still further in the structure, which of the physical capability elements (coordination, fitness and lack of fatigue) is the most important, and by how much? These choices are required for all the direct elements. The specific decisions regarding relative element importance were based on information gained from a survey of safety experts representing industry, regulatory agencies and the academic community. The experts were asked to assess, using a 1 –10 scale, each direct element’s ability to affect occupational accident frequency. The arrangement of survey questions was consistent with the model subgroups shown in Figure 3. The results were then normalized to ensure that the relative importance of each element

within each group was extracted in a consistent manner (Attwood et al., 2005b). The resulting ‘relative importance’ values (Figure 6) were then used within the mathematical model, utilizing a process of ‘strengthening’ or ‘weakening’ individual components in the reliability network, analogous to adding redundant units to a physical system. Note that, following the normalisation process, the strengths of components within the following subgroups sum to unity. . primary direct level ¼ behaviour, capability, weather, safety design, PPE . behavioural subgroup ¼ attitude, motivation . capability subgroup ¼ mental, physical . mental capability subgroup ¼ knowledge, intelligence . physical capability subgroup ¼ coordination, fitness, lack of fatigue

Influence at the external—corporate and corporate— direct interfaces The model philosophy proposes that external elements affect corporate decisions and actions, and these, in turn, influence factors directly affecting the accident process. An example would be the multiple positive effects of operating in a regime with an increased value placed on life, which would result in increased pressure on companies to improve corporate safety culture, which in turn would result in improvements in things such as personal protective equipment and staff motivation. Using an approach similar to that proposed by Sadiq et al. (2003), these effects have been accounted for in the calculation. Matrices of ‘influence coefficients’ have been generated for both the external—corporate (Table 2) and corporate—direct interfaces. As was the case for the strength values discussed previously, the specific values used to populate the matrices were extracted from the expert survey. The relevant survey questions in this case asked the respondents to quantitatively assess each external and corporate element’s level of influence on the corporate and direct level factors respectively.

Figure 6. Element strengths.

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CAN WE PREDICT OCCUPATIONAL ACCIDENT FREQUENCY? Table 2. External—corporate influencing coefficients.

Value placed on life Price of oil Shareholder pressure Royalty regime

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Table 3. Method of element influence on junior elements.

Safety training

Safety procedures

Corporate safety culture

0.43
0.18 0.27 0.12

0.43 0.19
0.26 0.12

0.44 0.18 0.25
0.13

Safety training reliability Value of life Price of oil Shareholder pressure Royalty regime

Component reliability

Influencing coefficient

(Component reliability)  (influencing coefficient)

0.60 0.50 0.40 0.60

0.43 0.18 0.27 0.12

0.26 0.09 0.11 0.07

Sum of the products ¼ reliability value

0.53

There was a high degree of consistency between individual questionnaire responses. The following points can be made for illustration. . Ninety-six percent of the respondents considered value of life to be the external element having the most influence on safety training. . Eighty-nine percent of the respondents considered royalty regime to be the external element having the least influence on corporate safety culture. . The sample standard deviations for the normalised coefficients asterisked (
) in Table 2 were all calculated as 0.07 or 0.08. It can be shown (Johnson, 2005) that for the present sample size and these standard deviations, the maximum error in the prediction of the mean, with 95% confidence, is about 0.02. . Figure 7 shows the relative frequency of occurrence of normalised influence coefficients for the effect of (1) value of life on training, and (2) royalty regime on safety culture. The coefficients shown in Table 2 are used to adjust the lower level element reliabilities whenever the higher level values change. For example, the ‘reliability’ of corporate safety culture is automatically increased with increases in the values associated with either ‘Value placed on life’, ‘Price of oil’, ‘Shareholder pressure’, or ‘Royalty regime’. The specific calculation is as follows (Sadiq et al., 2003). The more junior reliability (at this interface the corporate element) is the sum of the products of the reliabilities of those more senior elements (at this interface the external elements) considered to have an effect on the element, and the respective influencing coefficients. For example, training, as shown in Table 2, is considered to be affected by value of life (0.43), price of oil (0.18), shareholder pressure (0.27), and royalty regime (0.12). Assuming, for

the purposes of this example only, the initial reliabilities of the external factors to be 0.60, 0.50, 0.40 and 0.60, the reliability for safety training is calculated as shown in Table 3. This process does not preclude the adjustment of any element reliability based on ‘stand alone’ specific changes made in the respective area. For example, improvements in personal protective equipment may be made in isolation of changes in the more senior elements.

The reliability calculation Overall system reliability is a function of the direct layer components’ reliabilities. The latter can either be directly input, intentionally over-written, or determined from the corporate element reliabilities using the method described in the previous subsection. The corporate element reliabilities can in turn be determined from external element values. This is consistent with the work’s general philosophy of accidents being caused directly at the workplace, but being affected by corporate and external elements. This means that predictions can be made on the basis of a complete set of direct, corporate, or external element reliabilities. Once component reliabilities have been assigned, system reliability is calculated according to the following formula. The method is based on standard reliability theory (Billinton and Allan, 1983), adjusted to account for relative element strength, as discussed previously. Rsys ¼ (Rb )sb  (Rc )sc  (Rw )sw  (Rsd )ssd  (Rppe )sppe (1) where Rb ¼ reliability of behaviour Rc ¼ reliability of capability Rw ¼ reliability of weather Rsd ¼ reliability of safety design Rppe ¼ reliability of personal protective equipment sb ¼ strength of behaviour sc ¼ strength of capability sw ¼ strength of weather ssd ¼ strength of safety design sppe ¼ strength of personal protective equipment

Figure 7. Frequency of influence coefficients.

Equations to calculate these reliabilities are given in Appendix A.

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Expected number of accidents Once system reliability has been calculated, the expected accident rate (usually accidents per year) is calculated according to the well known reliability model (Billinton and Allan, 1983) shown below.
ðt  R(t) ¼ exp  l dt ¼ elt ,

t.0

(2)

0

where

l ¼ accident rate R(t) ¼ system reliability t ¼ time Taking natural logarithms of both sides and setting t ¼ 1, we get:

l ¼  ln (R(t))

(3)

The suitability of this approach depends upon the validity of an assumption of constant failure rate. The relationship between failure rate and time for physical components is characterized by (1) a high initial rate, usually caused by start-up problems (burn-in period), (2) a period of constant failure rate (useful life), and finally (3) a period of increasing failure rate (wear out) (Billinton and Allan, 1983). Because a plot of this relationship has a shape similar to a bathtub, it is sometimes referred to as ‘the bathtub philosophy’. Applying the philosophy to offshore occupational accident frequencies, the parallel could be drawn that until accident causation became relatively well understood (i.e., during the ‘burn-in’ period), the accident rate was relatively high. However, evidence (see Figure 8, overall industry Fatal Accident Rate, or FAR, defined as fatalities per 100 million hours worked) exists to confirm that the industry has reached a state of relatively constant accident rate, which validates the required constant failure rate assumption. The cost of accidents The model provides a method to evaluate cost savings associated with accident frequency reduction. Financial rewards can be immediately observed upon improvements made in individual components, which will encourage an optimisation of safety spending. The model assumes an average offshore accident will have costs as detailed in Table 4 (Attwood, 2005). It has been assumed that the worker will

Figure 8. Overall oil and gas fatal accident rate versus time (International Association of Oil & Gas Producers, 2004).

Table 4. Occupational accident cost. Element

Cost ($ Canadian)

First aid Procure and provide replacement worker Salary cost of replacement worker Management time in replacement Accident investigation costs Rehabilitation costs Reputational cost

500.00 2500.00 7000.00 3500.00 4500.00 2500.00 10 000.00

Total

30 500.00

remain unable to work for an average period of two weeks. The cost element is determined by multiplying the cost of an accident by the expected number of accidents.

PARAMETRIC ANALYSIS In order to demonstrate individual elements’ relative importance to overall system performance, a series of hypothetical model runs have been executed. Base case component reliabilities were determined by calibrating the model so that the output corresponded to the number of accidents on an average platform assuming global industry average total recordable incident rate. Individual component reliabilities were then incrementally increased from the calibrated starting positions and the output noted. Figure 9 shows predicted numbers of accidents as six factors’ individual component reliabilities are increased from the starting position to 30% improvement. The greatest system improvement is seen with improvements in ‘value placed by society on life’, which might be expected, since the results of the expert survey showed that it heavily affects all three corporate elements, which in turn affect the direct elements. The next most important elements are safety culture and safety design. Safety culture heavily influences the direct elements, and safety design ‘improvements’ prove more influential than weather, lack of fatigue, and price of oil, due to the following considerations. . safety design (0.21) carries a higher “strength” value than weather (0.15), as derived from the poll of safety experts; . whilst capability and safety design carry similar strength values (0.21), lack of fatigue is a sub-element of capability only, and is a member of the group of physical

Figure 9. Number of accidents versus improvement in component reliability.

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CAN WE PREDICT OCCUPATIONAL ACCIDENT FREQUENCY? Table 5. Cost savings versus individual component reliability improvement. Cost savings on 30% improvement ($)

Factor Value placed on life Safety culture Safety design Price of oil Weather Lack of fatigue

2876 2416 1657 1252 1185 251

elements, which carry relatively lower strength values (0.36) than mental factors (0.64); . price of oil was, on average, assigned a relatively low influencing coefficient (0.18) (compared to its external factor competitors value of life (0.43) and shareholder pressure (0.26)). At first glance these results might encourage operators to immediately attempt to increase the value placed by society on life. It is noted that this suggestion represents a reversal in the direction of influence proposed by this research, from external through corporate to direct factors, but as oil companies grow over more influential and operate in sometimes impoverished countries, such a thought is not inconceivable. Also, a 30% change in a cultural attitude such as value placed on life would be next to impossible to achieve. On the other hand, organisations have it within their power to produce a 30% enhancement in things such as safety design, corporate safety culture, and lack of worker fatigue. The large effect produced by changes in the value of life factor also highlights the difficulties organisations face when oil and gas reserves are discovered in regions where societal value of life is lower than that in more developed regions. This will continue to be a challenge for operators as reserves in more safety conscious areas are depleted. Table 5 shows cost savings (based on the method and estimated cost of a single accident documented previously) realized with a 30% improvement in six individual components. In the current financial environment where the price of a barrel of oil exceeds USD $50, possibly the only value which would get the attention of a major operator is that obtained with a 30% improvement in the ‘value placed on life’ element, and, as mentioned earlier, this would likely prove very costly to implement. Discussions with operator safety representatives indicate, however, that despite the relatively modest financial rewards, there is no lack of appetite for attempts to improve safety. Political and reputational benefits are sufficiently attractive to maintain a strong desire to produce the best possible safety results.

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Example 1: Ideal Situation versus Worst Case Scenario Consider a drilling contractor interested in comparing predicted safety results under the opposite extremes described below: Ideal case: . operating in a region where society places a high value on life; . the client demands, and is offered, the very best safety equipment, procedures, and training schemes; . the weather conditions are benign; . the available workforce has a generally cautious attitude toward safety concerns; . the price of oil is at a relatively high level. Worst case: . operating in a region where societal value of life is less than average; . the client is interested in developing a marginal field and is therefore satisfied with safety equipment, procedures and training schemes which (only) comply with regulatory requirements; . the weather conditions are extreme; . the workforce is generally categorised as more risktaking than average; . the price of oil is at a relatively low level. The model can be used to predict the number of accidents under these two extremes, as compared to average conditions. To do this the model is run three times: . a ‘base case’ with all factor reliabilities set at average value; . an ‘ideal’ case where all factor reliabilities are set at average value þ20%; . a ‘worst case’ scenario where all factor reliabilities are set at average value – 20%. The result is shown in Figure 10. The actual figures resulting from these extremes (4.8 for worst case versus 3.8 for ideal) indicate that for a typical 100 POB (persons on board) platform, one less accident per year is predicted for the ideal situation than for the worst case scenario. The cost saving associated with this would be about CAD $30K, which is not very significant in today’s world of oil company finance. However, since occupational accidents periodically result in fatalities, the avoidance of a single accident can be quite attractive from other (for example public relations) perspectives. On a percentage basis, a 21% improvement in safety results is achieved when the change from worst to best case conditions is made, which seems appropriate.

EXAMPLE CASES

Example 2: Rig Hired and Moved to Location

The model can be used for a variety of purposes. Three examples are presented here. The first compares safety results in an ‘ideal’ situation to those obtained in a ‘worst case’ scenario. Two subsequent examples show how the model can be used to predict changes in occupational accident probability as an asset moves through different stages in its operational life, i.e. from ‘off hire’ to operating in a given regime, or during the de-mobilization process.

The model can be used to predict changes in safety results as an asset moves through stages in its life cycle. For mobile drilling units (MDU), a typical cycle includes idle time, hiring, mobilization, operating, and de-mobilization. The corresponding stages for a fixed installation include construction, installation, commissioning, operating and decommissioning. The examples in this and the next section concern a MDU.

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Figure 10. Results of Example 1.

Figure 11. Accidents versus position in hiring/operational cycle.

Upon hire of an idle MDU, an operator will specify things such as operational and training requirements, safety targets, and so on, all of which will affect safety results. The drilling location will be specified, and this will, by definition, determine the reliability values assigned to weather, value placed by society on life, and royalty regime. Furthermore, crew make-up will be a determining factor in safety results. In most cases operators will be required by national legislation to employ local workers for most jobs. If this is not the case, however, some operators prefer to avoid the perceived risk associated with using a local workforce that may, for many reasons, be more likely to experience accidents than a group more familiar to the operator, the unit, and the offshore business. Alternatively, the operator may insist on replacing the MDU’s normal crew with another deemed more safety conscious. In any event, these decisions will have a significant affect on safety results. Figure 11 presents results of model runs conducted to predict changes in accident probability as a MDU moves from an idle condition to one where enhanced safety procedures and training programmes are implemented, a workforce with superior safety attitude is hired, better PPE is purchased, and the MDU is moved to a harsh weather area where value placed on life is lower than average. To study this scenario, the model is run seven times— once for each of the changes in situation indicated below. Note the changes are sequential, and factor reliabilities are not reset to average between runs.

(4) Take on staff with superior safety attitude—this factor adjusted to average þ20%. (5) Purchase enhanced PPE—this factor adjusted to average þ20%. (6) Move to region with lower than average value placed on life—this factor adjusted to average – 20%. (7) Move to area with poor operating (weather) conditions—this factor adjusted to average –20%.

(1) Base case—all factors set at average value. (2) Improve safety procedures—this factor adjusted to average þ20%. (3) Improve safety training process—this factor adjusted to average þ20%.

(1) Base case—all factors set at average value. (2) Replace unfamiliar crew with one more familiar with rig—this factor adjusted to average þ20%. (3) Return to benign weather conditions—this factor adjusted to average þ20%.

Note that the number of predicted accidents reduces with each positive change, but moving to an area with lower than average value placed on life and harsh weather conditions returns the value close to the original prediction. Example 3: Rig Taken Off-Hire Similar to Example 2, Figure 12 shows accident probability as a rig is taken off hire. In this case, it is proposed that a local and unfamiliar crew is replaced by one more familiar with the rig and its safety arrangements, the rig is moved from harsh to calmer weather conditions, and the company decides to abandon enhanced safety training and procedures. To study this scenario, the model is run five times—once for each of the changes indicated below. The ‘base case’ in this scenario is the ‘on hire’ condition—subsequent runs predict incremental changes in accident rate from this base case. Note the changes are sequential, and factor reliabilities are not reset to average between runs.

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The model predicts financial rewards and penalties associated with changes in various safety factors. Users can conveniently see the effects of changes in safety elements, offering them a practical means of deciding where to spend their available capital. As with any research, possibilities for enhancements exist. Improved knowledge with respect to strength of individual factors and influence of senior factors on junior members can be directly input. Changes in structural relationships are possible with very little effort, as are additions of newly considered elements. For example, it would be interesting to consider the inclusion of a function to model the reputation and political benefits associated with a reduction in accident frequency, or to include these types of pressures as external input factors. The authors believe that the proposed reliability based model, with its capability to predict occupational accidents and offers direction and focus to the safety improvement effort in the offshore oil and gas industry. The next stage in the research will be the application of the model to a real offshore oil and gas project. Figure 12. Rig taken off hire.

(4) Abandon enhanced safety training—this factor adjusted to average 220%. (5) Abandon enhanced safety procedures—this factor adjusted to average 220%. The number of predicted occupational accidents is reduced upon crew replacement and weather improvement, but again approaches the on-hire levels with the abandonment of the enhanced training and procedures. CONCLUSIONS An accurate prediction of occupational accidents is a difficult and complicated endeavour. If accidents could be reliably foreseen, they could all be prevented. Unfortunately, a satisfactorily low frequency of occupational accidents has not been achieved today. Many different approaches to accident reduction have been taken over the years. The model proposed here relies on the similarities between a physical engineering system and a safety programme utilized by a company in its efforts to reduce occupational accidents. The model’s approach recognizes several fundamental beliefs, as follows: . for some sub-sets of a safety system, individual factors must all be working efficiently to produce good results; for others, a degree of compensation is available; . both external and corporate elements affect the accident process; . the degrees to which the component factors affect the accident process differ. The model accounts for these beliefs in a quantitative way, incorporating the views of safety experts. It can be used to predict safety results following enhancements of individual elements at the direct, corporate, or external level. Also, the model can be used to evaluate relative probability of occupational accidents under various scenarios or during stages in an asset’s deployment cycle.

REFERENCES Attwood, D., Khan, F. and Veitch, B., 2005a, An analysis of occupational accidents in offshore oil and gas operations, J Loss Prevent Petroleum Indust (submitted). Attwood, D., Khan, F. and Veitch, B., 2005b, Offshore oil & gas occupational accidents—what is important? Safe. Sci. (in press). Attwood, D., 2005, Personal discussion with Lloyd’s Register Aberdeen Verification and Classification Manager, 28 January. Balkey, J.P. and Phillips, J.H., 1993, Using OSHA process safety management standard to reduce human error, PVP Vol. 251, Reliab. Risk Pressure Vessels Piping, ASME 1993, pp 43–54. Billinton, R. and Allan, R.N., 1983, Reliab. Evaluat. Eng. Syst.: Concepts Techniques (Plenum Press, New York, London). Bird, Jr, F.E. and Germain, G.L., 1992, Practical loss control leadership, Loss Control Manage (Det Norske Veritas, Inc). Brown, K.A., Willis, P.G. and Prussia, G.E., 2000, Predicting safe employee behaviour in the steel industry: development and test of a sociotechnical model, J Operations Management, 18: 445–465. Cheyne, A., Tomas, J.M., Cox, S. and Oliver, A., 1999, Modelling employee attitudes to safety: a comparison across sectors, Eur Pychol, 4(1): 1–10. Embrey, D.E., 1992, Incorporating management and organisational factor into probabilistic safety assessment, Reliab Eng System Safety, 38: 199–208. Geyer, T.A.W. and Bellamy, L.J., 1991, Pipework Failure, Failure Causes and the Management Factor (IMechE, London, UK). Gordon, J.E., 1949, The epidemiology of accidents, Amer J Public Health, 207: 3 –11. Gordon, R., Flin, R. and Mearns, K., 2001, Designing a human factors investigation tool to improve the quality of safety reporting, Proceedings of the 45th Annual Meeting of the Human Factors and Ergonomics Society. (Beijing, China). Guastello, S.J., 1989, Catastrophe modelling of the accident process: evaluation of an accident reduction programme using the occupational hazards survey, Accident Anal and Prevent, 21(1): 61–77. Hopkins, A., 2000, Lessons from Longford: The Esso Gas Plant Explosion (CCH Australia Limited, Sydney, Australia). Hurst, N.W., 1998, Risk Assessment—The Human Dimension (The Royal Society of Chemistry, Cambridge, UK). ISBN 0-85404-554-6. International Association of Oil & Gas Producers (OGP), 2004, OGP safety performance, 2003, Report number 353, June 2004. International Association of Oil & Gas Producers (OGP), 2005, OGP Safety Performance Indicators 2004, Report number 367, May 2005. International Labour Organisation, 2003, Safety in Numbers, Global Safety Culture at Work (The International Labour Organisation, Geneva). Johnson, R.A., 2005, Miller & Freund’s Probability and Statistics for Engineers, 7th edition (Pearson Prentice Hall, Upper Saddle River, New Jersey, USA).

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Kjellen, U., 1995, Integrating analyses of the risk of occupational accidents into the design process. Part II: Method for predicting the LTI rate, Safe Sci, 19: 3–18. Kjellen, U. and Hovden, J., 1993, Reducing risks by deviation control a retrospection into a research strategy, Saf Sci, 16: 417–428. Le Bot, P., 2004, Human reliability data, human error and accident models—illustration through the Three Mile Island accident analysis, Reliab Eng System Safe, 83: 153–167. Luo, Y.-X., 1998, Study of the application of gray theory to modern safety management, Proceedings of the 1998 International Symposium on Safety Science Technology, ISSST, 369– 373 (Beijing, China). McCauley-Bell, P. and Badiru, A.B., 1996a, Fuzzy modelling and analytic hierarchy processing to quantify risk levels associated with occupational injuries—Part I: The development of fuzzy-linguistic risk levels, IEEE Trans Fuzzy Syt, 4(2): 124–131. McCauley-Bell, P. and Badiru, A.B., 1996b, Fuzzy modelling and analytic hierarchy processing—means to quantify risk levels associated with occupational injuries—Part II: The development of a fuzzy rule-based model for the prediction of injury, IEEE Trans Fuzzy Syst, 4(2): 132– 138. Mosleh, A. and Chang, Y.H., 2004, Model-based human reliability analysis: prospects and requirements, Reliab Eng Syst Safe, 83: 241– 253. Pate-Cornell, M.E. and Murphy, D.M., 1996, Human and management factors in probabilistic risk analysis: the SAM approach and observations from recent applications, Reliab Eng Syst Safe, 53: 115–126. Rasmussen, J., 1997, Risk management in a dynamic society: a modelling problem, Safe Sci, 27(2/3): 183 –213. Sadiq, R., Kleiner, Y. and Rajani, B., 2003, Forensic of water quality failure in distribution systems—a conceptual framework, J Indian Water Works Association, 35(4): 1– 23. Strutt, J.E., Wei-Whua, L. and Allsopp, K., 1998, Progress towards the development of a model for predicting human reliability, Qual Reliab Eng Inte, 14: 3–14. Thompson, R.C., Hilton, T.F. and Witt, L.A., 1998, Where the safety rubber meets the shop floor: a confirmatory model of management influence on workplace safety, J Safe Res, 29(1): 15 –24. Tomas, J.M., Melia, J.L. and Oliver, A., 1999, A cross-validation of a structural equation model of accidents: organisational and psychological variables as predictors of work safety, Work & Stress, 13(1): 49–58. Trontin, T. and Bejean, S., 2004, Prevention of occupational injuries: moral hazard and complex agency relationships, Safe Sci, 42: 121 –141. UK HSE (Health & Safety Executive), 1996, Preventing slips, trips and falls at work. HSE Books, Sudbury, Suffolk, UK, ISBN 07176 1183 3. UK HSE (Health & Safety Executive), 2000, Offshore accident rates for April 1996 to March 1998, Offshore Technology Report # OTO 2000/12. UK HSE (Health & Safety Executive), 2001, Multivariate analysis of injuries data, Offshore Technology Report 2000/108, Prepared by the University of Liverpool. UK HSE (Health & Safety Executive), 2002a, Human factors integration: implementation in the onshore and offshore industries, Research Report 001, Prepared by BAE Systems Defence Consultancy. UK HSE (Health & Safety Executive), 2002b, Slips, trips and falls from height offshore, Offshore Technology Report 2002/001, Prepared by BOMEL Ltd. UK HSE (Health & Safety Executive), 2003, Factoring the human into safety: translating research into practice, Volumes 1–3, Research Report 062, Prepared by the University of Aberdeen. Wilson, L. and McCutcheon, D., 2003, Industrial Safety and Risk Management (The University of Alberta Press, Edmonton, Alberta, Canada). Wolfram, J. 1993, Safety and risk: models and reality, J Process Mech Eng, IMechE. The manuscript was received 13 May 2005 and accepted for publication after revision 19 September 2005.

APPENDIX A Rw (reliability value for weather conditions) is a direct input (independent variable not based on the values of other elements). Reliabilities of the other elements are

calculated as follows: Behaviour: Rb ¼ (1  (1  Ra )sa  (1  Rm )sm ) composed of: Attitude: Ra ¼ Rt  Ita þ Rpr  Ipra þ Rsc  Isca Motivation: Rm ¼ Rt  Itm þ Rpr  Iprm þ Rsc  Iscm where: Rt ¼ reliability of training (defined below) Rpr ¼ reliability of safety procedures (defined below) Rsc ¼ reliability of safety culture (defined below) Ita ¼ influence coefficient of safety training on attitude Ipra ¼ influence coefficient of safety procedures on attitude Isca ¼ influence coefficient of safety culture on attitude Itm ¼ influence coefficient of safety training on motivation Iprm ¼ influence coefficient of safety procedures on motivation Iscm ¼ influence coefficient of safety culture on motivation sa ¼ strength of attitude sm ¼ strength of motivation Safety training: Rt ¼ Rpo  Ipot þ Rsp  Ispt þ Rrr  Irrt þ Rvl  Ivlt Safety procedures: Rpr ¼ Rpo  Ipopr þ Rsp  Isppr þ Rrr  Irrpr þ Rvl  Ivlsp Safety culture: Rsc ¼ Rpo  Iposc þ Rsp  Ispsc þ Rrr  Irrsc þ Rvl  Ivlsc where: Rpo ¼ reliability of price of oil (direct input) Rsp ¼ reliability of shareholder pressure (direct input) Rrr ¼ reliability of royalty regime (direct input) Rvl ¼ reliability of value of life (direct input) Ipot ¼ influence coefficient of price of oil on safety training Ispt ¼ influence coefficient of shareholder pressure on safety training Irrt ¼ influence coefficient of royalty regime on safety training Ivlt ¼ influence coefficient of value of life on safety training Ipopr ¼ influence coefficient of price of oil on safety procedures Isppr ¼ influence coefficient of shareholder pressure on safety procedures Irrpr ¼ influence coefficient of royalty regime on safety procedures

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CAN WE PREDICT OCCUPATIONAL ACCIDENT FREQUENCY? Ivlpr ¼ influence coefficient procedures Iposc ¼ influence coefficient culture Ispsc ¼ influence coefficient safety culture Irrsc ¼ influence coefficient culture Ivlsc ¼ influence coefficient culture

of value of life on safety of price of oil on safety

slf ¼ strength of lack of fatigue sc ¼ strength of coordination Mental capability: Rme ¼ (1  (1  Rk )sk  (1  Ri )si ) composed of:

of shareholder pressure on of royalty regime on safety of value of life on safety

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Knowledge: Rk ¼ Rt  Itk þ Rpr  Iprk þ Rsc  Isck Intelligence: Ri ¼ direct input where:

Capability: sp

Rc ¼ (Rp )  (Rme ) Physical capability:

sme

composed of:

Rp ¼ (1  (1  Rf )sf  (1  Rlf )slf  (1  Rc )sc ) composed of: Fitness: Rf ¼ Rt  Itf þ Rpr  Iprf þ Rsc  Iscf Lack of fatigue: Rlf ¼ Rt  Itlf þ Rpr  Iprlf þ Rsc  Isclf Coordination: Rc ¼ direct input where: Itf ¼ influence coefficient of safety training on fitness Iprf ¼ influence coefficient of safety procedures on fitness Iscf ¼ influence coefficient of safety culture on fitness Itlf ¼ influence coefficient of safety training on lack of fatigue Iprlf ¼ influence coefficient of safety procedures on lack of fatigue Isclf ¼ influence coefficient of safety culture on lack of fatigue sp ¼ strength of physical capability sme ¼ strength of mental capability sf ¼ strength of fitness

Itk ¼ influence coefficient of safety training on knowledge Iprk ¼ influence coefficient of safety procedures on knowledge Isck ¼ influence coefficient of safety culture on knowledge sk ¼ strength of knowledge si ¼ strength of intelligence Safety Design: Rsd ¼ Rt  Itsd þ Rpr  Iprsd þ Rsc  Iscsd where: Itsd ¼ influence coefficient of safety training on safety design Iprsd ¼ influence coefficient of safety procedures on safety design Iscsd ¼ influence coefficient of safety culture on safety design PPE: Rppe ¼ Rt  Itppe þ Rpr  Iprppe þ Rsc  Iscppe where: Itppe ¼ influence coefficient of safety training on PPE Iprppe ¼ influence coefficient of safety procedures on PPE Iscppe ¼ influence coefficient of safety culture on PPE

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