CC BY
8
General Hazard Specific Hazard
Impacts and collision Vessel collision
Striking while at berth Flooding
Loading/overloading Navigation error Vessel not under command
Fine manoeuvring error Berthing/unberthing error Cargo tank fire/explosion Fire in accommodation Other fires
Loss of containment Release of flammables Release of toxic material
4. The building blocks
The evaluation setting assumed through out the paper reflects a rather representative situation faced by hazard evaluators. This is mainly characterized by the following:
- There is a number of hazards and the objective is to evaluate the relative impact for each hazard and finally to provide an ordering from the "highest" (highest score) to the "lowest" (lowest score) of the set of the hazards. The highest hazard is that one which causes the worst consequences.
- For the evaluation process a set of criteria is used, which follows a tree-like structure. The depth of the criteria tree, which somehow reflects the depth of the analysis, is usually not constant but varies with the thematic area under consideration. The totality of evaluation criteria is divided in two clusters: the group of general and thematic criteria. As the name indicates, the criteria of the thematic class vary with the hazard domain, with the general criteria can be naturally applied to general situations according to type of effects (e.g. safety, property damage, mission interruption, environmental effects e.t.c.).
- A panel of experts is used to evaluate hazards by means of the evaluation criteria hierarchy. Generally, both thematic area and evaluation hierarchy are given in advance and experts are asked either to give their opinion using linguistic terms on the relative importance of the criteria to the overall objective or to the degree at which every hazard appeals to the requirements set by each criterion.
5. Methodology using fuzzy logic 5.1. Fuzzy numbers and arithmetic
When dealing with numeric evaluation data, finding the weighted average of individual scores and aggregating across the hierarchy is more or less a trivial task. However, when dealing with fuzzy "quantities" it is not clear at all what is the outcome of certain expressions, such as "very good" or "very important". One needs an arithmetic that could suitably generalist basic number operations such as addition or multiplication. The theory of fuzzy sets offers a more systematic framework for handling expert linguistic assessments. This scientific area attempts to capture the "vagueness" that is an inherent characteristic of qualitative appraisals [2], [7], [11], [23].
A fuzzy number is considered as a fuzzy set over the set of all real numbers. Generally, there is much freedom in choosing between different shapes for the membership function (refers to the degree of membership for a fuzzy number, varying from no to full membership and takes rates from 0 to 1) of a fuzzy number. However, simple ones, such as a triangular or trapezoidal, are frequently more convenient to handle.
A trapezoidal (triangular) fuzzy number is a fuzzy number whose membership function forms a trapezium (triangle). Throughout this paper, trapezoidal fuzzy numbers are denoted by (a1, a2, a3, a4), where
Ship related Navigation
Manoeuvring Fire/explosion
ai, a2, a3, a4 correspond to the trapezium's angle points (ai < a2 < a3 < a4). Note that a triangular fuzzy number is a special case of trapezoidal with a2=a3.
Arithmetic similar to that of real numbers can be also developed by fuzzy numbers by extending the basic algebraic operations of addition, subtraction, multiplication and division. The application of the above operations to fuzzy numbers yields always a new fuzzy number [6]. In the case of trapezoidal fuzzy numbers computations are greatly simplified.
Let A = (a1, a2, a3, a4) and B = (b1, b2, b3, b4) be any two strictly positive trapezoidal fuzzy numbers (it is custom in fuzzy sets literature to use above letters to discriminate fuzzy from crisp quantities). Then, it can be proven that corresponding algebraic operators {©,©, ® ,0} for fuzzy sets are as follows [3]:
A © B = (ai+bi, a2+b2, a3+b3, a4+b4)
A © B = (a1-b1, a2-b2, a3-b3, a4-b4)
A ® B = (a1xb1, a2xb2, a3xb3, a4xb4)
A 0 B = (a1/b4, a2/b3, a3/b2, a4/b1) where the "circle" is used to notify that the operator applies to fuzzy and not ordinary numbers.
5.2. Defuzzification procedure
Going back to the problem of ranking e-services, we see that fuzzy numbers and their arithmetic provide us with a convenient tool for reasoning with qualitative linguistic assessments.
In particular, one could easily represent each linguistic term, such as "poor", "fair", etc., by a fuzzy number on a predefined numeric scale (e.g. 0-1, 0-10). In such a way, one gives rise to a set offuzzy weights and fuzzy rates, upon which an assessment scheme can be based. Moreover, the algebra of fuzzy numbers, presented above and in particular the extended operations of addition © and multiplication ®, provide us with a tool for calculation-weighted averages of linguistic data.
As seen, the overall performance of e-services is given in terms of a fuzzy set, which is somehow expected as any algebraic operation on two arbitrary fuzzy numbers yields always a new one. This "vague" picture of the overall performances generally hinders the task of ranking alternatives, since the ordering of fuzzy numbers is not as obvious as that of real numbers. To overcome difficulties of that kind, several approaches have been proposed in the fuzzy literature, the most common being the defuzzification.
Defuzzification is the procedure of selecting the most representative among all members of a fuzzy set. By means of defuzzification we attempt to eliminate the "fuzziness" from a fuzzy set, providing thus a "crisp" result. Probably, the simplest defuzzification technique that one can think of is to choose among all members of a fuzzy set the one with the highest degree of membership. However, a more sophisticated method, which takes into account all the information included in the membership function, is the centre of area or centroid. This is simply the centre of area formed under the membership function. The following equation gives the general formula for calculating the centroid x of an arbitrarily shaped membership function u( x)
J xj( x)dx
x =X-. (1)
J ju( x)dx
X
In the formula above, X denotes the referential of the fuzzy set, which in the case of fuzzy numbers is identified with the real line ^ . For the trapezoidal fuzzy number (a1 a2, a3, a4) the above formula reduces to [4]:
x = (a1+a2+a3+a4)/4 (2)
6. Evaluation framework
We use two variations of the evaluation process, denoted by V.1 and V.2 whose main difference lays in the way the various rating and importance assessments are aggregated to provide a ranking of the alternative hazards.
The separation of the rating from the importance assessment is a means of making the evaluation of hazards as fair and objective as possible. In order to avoid disagreement or discrepancies among evaluation committee's members we selected to follow Delphi method. Generally speaking, the Delphi method is an iterative procedure, which aims at the convergence of various subjective opinions into a more widely acceptable view. In general, a set of assumptions form the basis of our evaluation plan:
- All people being involved in the assessment procedure agree to categorization of hazards, evaluation criteria and assessment terms.
- There are a number of hazards, which are to be ordered from the highly to the least recommended.
6.1. Assessment of criteria importance
In our hazards evaluation project a panel of experts has to evaluate the criteria importance by answering a questionnaire. Despite the numerous books and articles that have been written on the subject, questionnaire design lacks until today a coherent theory [15]. For more details about the topic the interested reader could be referred to bibliography [8], [9], [10], [17].
Evaluator's task is to debate on the linguistic weights of the general and thematic criteria, which have been predetermined. Each expert is asked to assign weights:
- To every pair of general-thematic trees and
- At each node of the hierarchical structure, moving from the lowest to the highest-level criteria. The importance of every single criterion is evaluated by a closed-format question (or description of the
criterion in general), whose answer set includes the five linguistic values: "very low (VL)", "low (L)", "medium (M)", "high (H)", "very high (VH)". From a methodological point of view, those values correspond to a suitably chosen trapezoidal (and triangular) fuzzy numbers on the numeric scale 0-1 (see Table 2).
After the assessment has been completed for the totality of thematic areas, a Delphi study is carried out for each thematic area separately, in order that an acceptable level of consensus is achieved.
Table 2. The linguistic rates of criteria importance
6.2. Rating of hazards
Evaluators are asked to give their opinion on the impact of each hazard with respect to the criteria set by the particular evaluation problem. Rates are only given at the lowest level of the general and thematic hierarchy. Rating questionnaires could be very similar (or even the same) in design to those described in the previous section. In order to refer in a subjective attribute of hazard impact we use linguistic terms of consequence assignment (see Table 3). The impact for every single criterion is assessed by means of closed-format questions with the answer set: "catastrophic (CA)", "critical (CR)", "significant (SI)", "minor (MI)", "negligible (NE)".
Table 3. Linguistic terms of hazard impacts
Very Low (VL) Low (L) Medium (M) High (H) Very High (VH)
(0.0, 0.0, 0.1, 0.3) (0.1, 0.3, 0.3, 0.5) (0.3, 0.5, 0.5, 0.7) (0.5, 0.7, 0.7, 0.9) (0.7, 0.9, 1.0, 1.0)
Linguistic term
Hazard impact
Negligible Injury not requiring first aid, no cosmetic vessel damage, no
environmental impact, no missed voyages Minor Injury requiring first aid, cosmetic vessel damage, no
environmental impact, no missed voyages Significant Injury requiring more than first aid, vessel damage, some
environmental damage, a few missed voyages or financial loss Critical Severe injury, major vessel damage, major environmental
damage, missed voyages Catastrophic_Loss of life, loss of vessel, extreme environmental impact
Each of the above linguistic terms corresponds to a fuzzy number on the numeric rating scale 0-10. Details of the correspondence are given in Table 4.
After the assessment has been completed for the totality of evaluators, a Delphi study is carried out for each hazard separately. The information described above together with the proper criteria weights is used in the next phase of the evaluation problem: the hierarchy aggregation.
Table 4. The linguistic rates of hazards impact
Negligible (NE) (0, 0, 1, 3)
Minor (MI) (1, 3, 3, 5)
Significant (SI) (3, 5, 5, 7)
Critical (CR) (5, 7, 7, 9)
Catastrophic (CA) (7, 9, 10, 10)
6.3. Hierarchy aggregation
All have discussed by far refer to the first stage of methodology, the acquisition data. In that part, procedures were less standardized and automated, due to the strong involvement of human expertise. From this stage onwards, tasks tend to be of more algorithmic nature, which definitely calls for the use of specially designed computer programs for performing the required computations.
The steps following the data acquisition could be summarized in two phases:
- Phase I: The evaluation of the aggregate performance of each hazard.
- Phase II: The ranking of hazards with respect to their overall rate.
Those are, according to H. J. Zimmerman, the two typical stages of a multicriteria decision-making problem in which fuzzy sets are used in the assessment process [18]. It is worth mentioning that in most classical (non-fuzzy) multicriteria methods, the results of phase I are numeric scores. Hence, phase II becomes a trivial task, as for the ranking of hazards all that is needed is the pair wise comparison of scores.
However, in fuzzy multicriteria analysis, the situation is more perplexed. Usually, the overall impact of hazards is described by a fuzzy number or a fuzzy set in general, which calls for an additional technique for "removing" the fuzziness and providing a crisp result.
Generally, many approaches have been proposed in the literature that addresses the issues of the overall rating and ranking of alternatives when fuzzy sets are involved in the decision-making process. For an overview of different approaches the reader could refer to several extensive surveys [15]. In the proposed methodology is used a technique that is based on the idea of weighted averaging, properly adjusted to fuzzy numbers [4], [5], [7], [20]. Is proposed the implementation of two variations of the weighted-average scheme (referred V.1 and V.2), whose difference mainly lies at the stage where defuzzification is applied. Those variations are described below in detail.
Variation V.1
In the first variation, is applied a fuzzy weighted averaging scheme for evaluating the aggregate impact of hazards. For each hazard we compute a weighted average of fuzzy linguistic rates, where each rate is multiplied by a suitable fuzzy linguistic weight. In variation V.1 the aggregate impact of hazards is given
in terms of a fuzzy score. Therefore, defuzzification is applied to obtain a single numeric value from each fuzzy score. Those values are then used for ranking hazards.
To give a more concrete presentation of the method, let us assume that for the arbitrary thematic area (say XYZ), the evaluation criteria hierarchy is given, consisting of both the general and the XYZ criteria tree. Let the overall evaluation hierarchy comprise K branches in total, which is also the number of both end-criteria and rates per hazard. Then, the following algorithm is followed:
1. Form the evaluation matrix:
Bi B2 - Bk
H i ~2 - ~k
H 2 ~21 r •• 22 r '2 K
Hm r m1 r • • ' m 2 r mK
Where by BK, k=l,2,...,Kwe denote the branches of the criteria tree and by Ht, i=1,2,...,m the hazards to be evaluated. Every element ~k of the matrix corresponds to the rate achieved by hazard Hi for the particular sub-criterion that lies at the end of branch Bk . The entries of the evaluation matrix are chosen
from the set of linguistic rates ("very poor (VP)", "poor (P)", "fair (F)", "good (G)", "very good (VG)"), which correspond, to the trapezoidal fuzzy numbers presented in Table 2.
2. For obtaining the weight ~k that corresponds to rate ~k, trace down the evaluation criteria tree by
following the k branch. For every node of the branch that is visited, adjust ~k by multiplying with the fuzzy weight assigned to this node.
3. The aggregated fuzzy rates ~, i=l,2,...,m are obtained by multiplying the evaluation matrix with the vector of fuzzy weights:
s =
f\
s r
V m J V ml
r r
'21 '22
m2
' 2K
®
mK J
V(k J
2
where ® denotes the product operation for fuzzy matrices, which works exactly the same as in ordinary matrix algebra. Note that every ~, i=\,2,...,m is a trapezoidal fuzzy number.
4. In order to obtain an ordering on the set of hazards, apply the defuzzification formula for trapezoidal membership functions (eq. 2). The defuzzification values are used for ranking hazards from the highest to the lowest impacting.
Variation V.2
In the second variation, the various fuzzy linguistic assessments (rates and weights) are a priori defuzzified by using the "centre of gravity" technique. The aggregate impact of each hazard is found by computing weighted averages of defuzzified rates. The numeric scores obtained are used for ranking purposes. More precisely, let us again assume that the overall evaluation criteria tree consists of K branches, B1, B2,...,BK. Suppose that there are also m hazards, Hi, i=1,2,.. ,,m to be evaluated. Then, the procedure followed is:
1. Given the fuzzy rates of each e-service, apply the "centre of gravity" defuzzification technique to obtain a set of numeric rates rik , i=1,2,...,m and k=1,2,...,K (denotes the numeric score achieved by hazard
Hi for the sub-criterion that lies at the end of branch Bk). Use these rates to form the following evaluation matrix:
Bi B2 * BK
H1 H 2 r11 r21 r12 r 22 ■ r1K r 2K
Hm r m1 r m2 r mK
2. Given the fuzzy weights, applying to the particular evaluation hierarchy, use the "centre of gravity" to obtain numeric weights for each node of the evaluation tree. Tracing down each branch k=1,2,...,K and multiplying the numeric weights assigned to each node, find the value of <ak that multiplies each of rik,
i=1,2,...,m.
3. A crisp aggregate score si for each hazard Ht, is obtained by computing the weighted average of rik, k=1,2,...,K. In matrix form:
is \ (
ril ri2
'1K
A
s r r
m J V ml ' m2
œ2
rmK J \œK J
4. Hazards Hi, i=1,2,...,m are ranked by means of their aggregate score.
s
r21 r22
r
2
s
7. Conclusion
In this paper we present an innovative methodological approach to the evaluation, ranking and selection of hazards. The proposed methodology introduces a hierarchical analysis of the decision-making problem, in which general and domain specific criteria compose the evaluation structure. The adopted "fuzzy" approach provides us with a suitable tool for modelling and processing linguistic assessments and subjective views in a simple and rather intuitive way.
Apart from methodological issues, this paper also discusses many practical aspects of the evaluation framework and gives multiple guidelines on how such an evaluation procedure could be implemented. Nevertheless, is obvious that the proposed framework is of more general use. Most important it gives enough flexibility in modelling an evaluation problem, since it affectively remains insensitive to changes in many individual components of the methodology.
References
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B.R. Duffey, W.J. Saull - RISK PREDICTION FOR MODERN TECHNOLOGICAL SYSTEMS
R&RATA # 2 (Vol.1) 2008, June
RISK PREDICTION FOR MODERN TECHNOLOGICAL
SYSTEMS
Duffey Romney B.
Atomic Energy of Canada Limited, Chalk River, ON, Canada
Saull John W.
International Federation of Airworthiness, East Grinstead, UK
Keywords
technological systems, risk, outcome, failure, error, events, probability Abstract
We have already examined the worldwide trends for outcomes (measured as accidents, errors and events) using data available for large complex technological systems with human involvement. That analysis was a dissection of the basic available, published data on real and measured risks, for trends and inter-comparisons of outcome rates. We found and showed how all the data agreed with the learning theory when the accumulated experience is accounted for. Here, learning includes both positive and negative feedback, directly or indirectly, as a result of prior outcomes or experience gained, in both the organizational and individual contexts. Our purpose here and now is to try to introduce some predictability and insight into the risk or occurrence of these apparently random events. In seeking such a general risk prediction we adopt a fundamental theoretical approach that is and must be testable against the world's existing data. Comparisons with outcome error data from the world's commercial airlines, the two shuttle failures, and from nuclear plant operator transient control behaviour, show a reasonable level of accord. The results demonstrate that the risk is dynamic, and that it may be predicted using the MERE learning hypothesis and the minimum failure rate, and can be utilized for predictive risk analysis purposes.
1. The risk prediction purpose
Modern technological systems fail, sometimes with catastrophic consequences, sometimes just everyday injuries and deaths. The risk is given by the probability of failure, error or more generally any outcome. Recently the crash of the NASA Space Shuttle Columbia, the great blackout of the North East USA and Canada, the explosion at the Texas City refinery all occurred. Other smaller but also key accidents have also occurred: the midair collision over Europe of two aircraft carrying the latest collision avoidance system; the glider landing of a jet aircraft out of fuel in the Azores; a concrete highway overpass collapsing in Laval, Quebec; the huge oil tank fire in England; more ships sinking, more trains derailing, even more cars colliding, and evermore medical errors. We have already examined the worldwide trends for outcomes (measured as accidents, errors and events) using data available for large complex technological systems with human involvement. That analysis was a dissection of the basic available, published data on real and measured risks, for trends and inter-comparisons of outcome rates. We found and showed how all the data agreed with the learning theory when the accumulated experience is accounted for. Here, learning includes both positive and negative feedback, directly or indirectly, as a result of prior outcomes or experience gained, in both the organizational and individual contexts as in [5]. Our purpose here and now is to try to introduce some predictability and insight into the risk or occurrence of these apparently random events. In seeking such a general risk prediction we adopt a fundamental theoretical approach that is and must be testable against the world's existing data.
B.R Duffey, W.J. Saull - RISK PREDICTION FOR MODERN TECHNOLOGICAL SYSTEMS
R&RATA # 2 (Vol.1) 2008, June
2. What we must predict
We have shown how outcomes develop in phases from a string or confluence of factors too complex to predict but always avoidable. The bright feature is that we now know that a universal learning curve (ULC) exists and we can utilize that to predict outcome rates and track our progress as we improve. We can therefore start to manage the risk, but only if we include the human element.
We need to make it entirely clear what we do not propose. We will not use the existing idea of analysing human reliability and errors on a task-by-task, item-by-item, situation-by-situation basis. In that approach, which is commonly adopted as part of probabilistic safety analysis using event sequence "trees", the probability of a correct or incorrect action is assigned at each significant step or branch point in the hypothesized evolution of an accident sequence. The probability of any action is represented and weighted or adjusted by situational multipliers, representing stress, environment and time pressures. We suggest, at least for the present, that it is practically impossible to try to describe all the nuances, permutations and possibilities behind human decision-making. Instead, we treat the homo-technological system (HTS) as an integral system. We base our analysis on the Learning Hypothesis, invoking the inseparability of the human and the technological system. Using the data, we invoke and use experience as the correct measure of integrated learning and decision-making opportunity; and we demonstrate that the HTS reliability and outcome probabilities are dynamic, simply because of learning.
The basic and sole assumption that we make every time and everywhere is the "learning hypothesis" as a physical model for human behaviour when coupled to any system. Simply and directly, we postulate that humans learn from their mistakes (outcomes) as experience is gained. So, the rate of reduction of outcomes (observed in the technology or activity as accidents, errors and events) is proportional to the number of outcomes that are occurring.
That learning occurs is implicitly obvious, and the reduction in risk must affect the outcome rate directly. To set the scene, let us make it clear that the probability of error is quite universal, and can affect anyone and everyone in a homo-technological system (HTS). There are clear examples of highly skilled well-trained operators, fully equipped with warning and automated systems. So all the people involved (from maintenance, ground control, management, airline operator and the pilots) are working in an almost completely safe industry (ACSI).
Two aircraft examples are very basic to safety: loss of fuel while in flight, and mid-air collision. Given all the systems put in place to avoid these very obvious and fundamental risks, the outcomes still occurred. But despite all the effort, procedures and warnings, there is loss of control through loss of understanding,
communication and information in the most modern of aircraft which were maintained to the highest
standards. We need to estimate their chance of occurrence of the outcomes, and define the risk by finding the probability of the outcomes due to the human errors embedded in the HTS.
Let us start with the learning hypothesis applied and applicable to any integrated (total) HTS. Thus, the human error or technological system failure or outcome rate, X, is equivalent to a dynamic hazard function h(s) which varies with experience, s, as given by the Minimum Error Rate Equation (MERE):
dX/ds = - k (X -Xm) (1)
where k is the learning rate constant, and Xm the minimum obtainable rate. The failure or outcome rate as a function of experience, X(s), is then obtained by straightforward integration as,
X(s) = Xm + (Xo - Xm) e" ks (2)
where the outcome or failure rate X = h(s), the hazard function; Xm is the minimum obtainable rate at large experience; and X0 is the initial rate at some initial experience, sO.
Here, it will be remembered that the failure or outcome rate is the summation of all the ith rates in the technological system, so that effectively:
Me) - Xm = Si (Xi - Xm) (3)
Since the MERE result describes and agrees with a wide range of actual data, we hypothesize that this is indeed the correct form for the human error or outcome rate in a HTS with learning. This form has been used to derive the ULC, validated by obtaining failure rates from the world accident, injury and event data.
