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The Delphi method: a complement to research
National Research
Conseil national
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1084
1
N21a
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Council Canada
de recherches Canada
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IILDG
ITHE DELPHI METHOD
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A COMPLEMENT T O RESEARCH by T.Z. HarmathyANALYZED
Reprinted from Fire and Materials Vol. 6, No. 2,1982 p. 76
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7 9DBR Paper No. 1086
Division of Building Research
En p r e n a n t d e s d g c i s i o n s r e l a t i v e s 3 l a s b c u r i t g i n c e n d i e , l e concepteur s e rend souvent compte que c e r t a i n e s donn6es s o n t a l g a t o i r e s . Comme d e s donn6es s t a t i s t i q u e s d E t a i l l 6 e s n e s o n t que rarement d i s p o n i b l e s , l e concepteur d o i t compter s u r t o u t s u r son jugement d ' e x p e r t . En a p p l i q u a n t l a d t h o d e Delphi, de t e l l e s d g c i s i o n s peuvent l t r e f o r n u l 6 e s e t o p t i m i s 6 e s , _ _ Lea- mi-
- - W e
Delphi s o n t d g c r i t si l l u s t r g e p a r un ex/ f e u q u i d o i t &re ea
The Delphi Method-A Complement to
Research
T.
Z. HarmathyDivision of Building Research, National Research Council of Canada, Ottawa, Ontario KIA OR6, Canada
In making fire safety decisions the designer often finds that some input variables concerning his problems are chance variables. As detailed statistical data are rarely available the designer must rely largely on his expert judgment. With the application of the Delphi method such decisions can be optimized and formalized. The essence of the Delphi method is described and its use illustrated through an example related to the assessment of fire resistance requirements.
In trying to make sound decisions concerning fire safety, designers often find that some design variables are chance variables. Since fire safety design must address reasonably adverse conditions that may arise in practice, each of these chance variables must be examined to determine if it has any extreme value that indicates such a condition. It will be found that there is such an extreme value for some variables while for others there is not. If there is not, a conscientious designer will attempt to assign a design value to that variable on considerations aimed at minimizing the over-all costs of fire safety. In this effort, one will look for supporting statistical data, and will usually find that they do not abound. It seems to be one version of Murphy's law that statistical data never come broken down in the manner necessary for the solution of a particular problem. For lack of statistical data, design- ers will do one of two things: If theoretically oriented they will proceed with a probabilistic analysis, but at the end substitute their own estimates for factual input information. Clearly, a decision arrived at in this way is jnst a sophisticated statement of subjective judg- ment. If, on the other hand, they are practically oriented, they will skip all mathematical considera- tions and make design decisions based on experience. One thing wrong with making these kinds of decisions is that experience may lead two persons to two very different results. Realizing that they cannot be 100% right in their judgments, the next best thing they can do is to 'seek a formalization of the decision-making process so that all should arrive at identical design decisions. This is where the Delphi technique can be of use.
A specific example will be used to illustrate the problem: the calculation of fire resistance require- ments for the boundary elements of a compartment.
The input variables that have to be defined for the calculation are as follows:' AF = floor area of com-
partment, (mZ
,
A, = total area of compartmentI
boundaries, (m ), hc = height of compartment, (m), = average thermal inertia of compartment boundaries, J m-*
c ' ' ~
KT'
(k
is thermal conductivity, p density, c specific heat), @ = ventilation factor char- acterizing the rate of air flow into the compartment, (kg s-l), and L = specific fire load (mass of combusti- bles per unit floor area) (kg m-').The values for the first three variables are available from the building plans; the value of the fourth is calculable from the planned use of building materials. The last two are chance variables. If the designer can somehow obtain appropriate design values for these two variables, the calculation of the fire resistance requirement for the compartment boundaries can pro- ceed as follows. (Note: This is the calculation techni- que used in the author's laboratory. It has been de- scribed in several other publications, e.g. in Ref. 2. Strictly speaking, it is only applicable if the fire load consists of wholly cellulosic materials. The validity of the following discussion is, however, not tied to the calculation technique employed.)
First, calculate the total fire load, G, i.e. the total mass of combustibles in the compartment:
Then calculate the fraction of the fuel energy that is released inside the compartment.' (It is well known that the fuel will decompose in the fire and a fraction of the energy of the gaseous decomposition products will be released in the flames emerging from the compartment .)
6 = { 0 . 7 9 m whichever is less.
1
In the third step, calculate the so-called normalized heat load, H, the total heat absorbed by the compart- ment boundaries during the fire incident, divided by the thermal inertia of the boundaries. (The normalized heat load has been shown1 to be a quantitative de- scriptor of the destructive potential of-fire.)
Finally, calculate the fire resistance requirement (in h) from an equation that is an approximate expression of the relation between the normalized heat load absorbed by a specimen building element in standard fire test and duration of the test fire. (That relation is shown graphically in Fig. 1.)
z = 0.11
+
0.16x
IO-~H+
0.13 x ~ o - ~ H ' It must still be decided how to define the two chance variables, the ventilation factor and the specific fireTHE DELPHI METHOD-A COMPLEMENT TO RESEARCH
L E N G T H OF E X P O S U R E TO S T A N D A R D T E S T F I R E . T h
Figure 1. Normalized heat load imposed on a construction during a standard fire resistance test2
load. The minimum rate of flow of air that enters the burning compartment is determined by the dimensions of the ventilation opening, e.g., doors or windows. The actual flow rate is usually higher, dependent on the prevailing draughts in the building, perhaps am- plified by winds. As mentioned earlier, the first task is to determine whether one can define an air flow rate that would represent an adverse condition from the point of view of the destructive potential of fire with- out imposing unrealistic requirements on the design. By plotting the normalized heat load, H , against va- rious values of the air flow rate, as quantified by the ventilation factor, @, one will find that H steadily decreases as @ increases. This means that the destruc- tive potential of a fire is highest when @ is lowest, which occurs if there are no draughts in the compart- ment. This minimum, most adverse value of @ is determined by the dimensions of the ventilation open- ing. It is denoted by @*, and referred to as ventilation parameter
@ * = ~aAvd(ghv)
where pa is the density of (atmospheric) air (kg m-3), A, is the area of the ventilation opening (m2), and hv the height of the ventilation opening (m). g is the gravitational acceleration (m sP2).
From plots of H against @ one will also see that at such an adverse ventilation condition the destructive potential of the fire is rarely more than twice that which may arise at very high, draught-augmented ven- tilation. It is a reasonable suggestion, therefore, that the value of the ventilation parameter, @*, be accepted as input value in the design.
Let attention now be turned to the other chance variable, the specific fire load, L , the mass of com- bustibles per unit floor area. The specific fire load is known to depend mainly on the type of occupancy, but even for similar occupancies it may vary markedly in a seemingly unpredictable manner, as shown in a cumulative plot of fire load in Fig. 2.
Again, one has to ask, can an adverse value for the specific fire load be defined? The answer is yes. Clear- ly, the amount of combustible materials that can be
put in a compartment is limited by the volume of the compartment. L,,, is about 900 kg mP2. Adopting this as a design value would, however, be grossly unrealistic. If the room is filled completely with com- bustible materials, they will not have access to air and therefore will not burn. It is estimated that, even if the compartment is used as a storage room, the maximum amount of combustibles that can burn during a fire is about 150 kg m-2. But even this value would be ex- cessive for design. Statistical data indicate that, de- pending on the type of occupancy, the mean fire load is between 15 and 45 kg m-2, and rarely exceeds 100 kg mP2.
Perhaps 100 kg mP2 should be selected as design value for specific fire load'L? Definitely not, for two reasons. First, the reader is reminded that for Q,
(ventilation factor) a design value representing an absolutely adverse condition, @*, has already been selected. It would be an unduly conservative step to select another design value connected with an utmost adversity. Second, unlike ventilation, the fire load has a strong influence on the destructive potential of fire, and therefore the fire resistance requirement is ex- pected to be very sensitive to the selected value of the fire load.
Then how should the selection be made? If the mean value is selected, the design may be inadequate in up to 50% of the cases. If a value much higher than the mean is selected, the cost of fire protection may be greatly increased. In Sweden, the fire load that is applicable to 80% of the cases is usually chosen as the design value. (The meaning of this 80th percentile, LgO, is illustrated in Fig. 2, together with the mean fire load, L,.)
The most appropriate way of deciding on the design value of L would be on the basis of cost-benefit studies. The algorithm for such calculations is well e~tablished.~ Yet information needed for performing the calculations is either not available or very poorly defined. One would need reliable information on the probability of fire occurrence, the probability of fire developing beyond the flashover stage, the occupant load, the fraction of occupants still in the building when structural failure occurs, the target life safety level, the cost of the building, the service life of the
S P E C I F I C F l R E L O A D . L k g rn-'
Figure 2. The customary presentation of information on spe- cific fire load.
T. Z. HARMATHY
I building, the value of the building contents, the cost of
repair, the incremental cost of fire protection, the interest rate, and so on. But let it be assumed that there is a magic storehouse from which one can pick any information needed. Which value would be pick- ed, for example, for the probability of fire occurrence? The national average? That applicable to the city; to the district; to the income level of the prospective occupants; to the expected racial origin of the occu- pants? How about the interest rate? What will that be during the next 50 years? Or even in the next month? The plain truth is that after a detailed probabilistic study the input data will usually be selected in such a way as to yield a result which, based on the designer's background, was in mind all the time.
It would be self-deception to deny the fact that in this field, and in some others, it is largely expert opinion that motivates the designers' decisions. There is nothing wrong with that, provided a technique can be devised that ensures some degree of uniformity in the design. One way of achieving such uniformity is as follows. First, a simple algorithm is devised for the calculation of the chance variable in question. For specific fire load, a possible algorithm may be
According to this, the design fire load is taken as the value pertaining to a Pth percentile in the cumulative fire load plot for the relevant occupancy (Fig. 2). P
consists of a base value, Po, and a number of positive or negative contributions, Pi. The base value should reflect expert judgment on the basic level of safety. For example, if Po = 80 is selected, compartment boundary failures are allowed in up to 20% of the cases if there is no intervention by the fire department. This base value should also reflect some fundamental uncertainties in the insight into the problem, for exam- ple, the simplified nature of the way the fire resistance requirements are calculated, and the possible dimen- sional and constructional differences that may exist in supposedly identical building elements, among them that used as a fire test specimen.
The base value will be modified by positive or negative contributions reflecting considerations relat- ing to the value at stake (as determined by the size of building), the probability of fire occurrence (as in- fluenced by use and by the degree of compartmenta- tion), the probability of fire reaching the fully de- veloped stage (as influenced by the use of combustible linings, the expected interior design, the nearness of a fire department, etc.), the use of active protective measures (detection, sprinklering, self-closing doors, etc.), some aspects of life safety, and some aspects of re-usability of the building after fire.
Table 1 shows a scheme for the tabulation of in- formation to be used in the calculation of the design value of P. Naturally, this tabulation is an illustration only and has no objective validity.
To remain within rational bounds, certain limita- tions may be imposed on the so calculated values of the specific fire load. For example, 20 I P I 95. This limitation means that, notwithstanding the calculated value of P , the design fire load should always be
higher than the 20th but never higher than the 95th percentile.
It is quite obvious that such a tabulation, if prepared properly according to the Delphi method, will help solve not only the problem of how to define uniquely the design fire load but will also provide a rational way of making trade-offs between, say, fire resistance re- quirement and sprinklering, or fire resistance require- ment and fire detection, or fire resistance requirement and self-closing doors, and so on. Experience shows that hard-fact statistical data for determining the de- sign fire load are rarely available even in the simplest conditions. How can one ever hope to acquire statis- tical data that would allow an insight into the complex problem of how to trade off the design fire load for, say, fire detection in a five-storey residential building located in an urban area two miles from the nearest fire station?
The Delphi method has been mentioned several times. The following description of the method is based on Dalkey's report.4 (A few phrases and sent- ences of that report are reproduced verbatim in the following.) The method is 'based on the adage, two heads are better than one, or more generally, n heads are better than one'.
In assembling the n heads, expertise is the only criterion. No consideration must ever be given to balancing the Delphi group from the point of view of affiliation or interests.
'The Delphi procedures have three features: anony- mity, controlled feedback, and statistical group re- sponse.' Anonymity of the participants ensures that the group decisions will not be influenced by 'domi- nant individuals'. The exercise is conducted 'in a sequ- ence of rounds, between which the results of the
Table 1. Basic percentile, Po, and contributive percentiles,
P;
Basic percentile: Po = 80 Contributive percentiles, Pi
Characteristic features 4
1 Building height (storeys) 1-3
2-1 0 10-50 >50
2 Average compartment area (m2) 0-25
25-100 100-500 >500
3 Nature of compartment boundaries Dividing element
Key element
Fire from one direction only Fire from more than one direction 4 Fire safety features
Fire detection Self-closing doors Sprinklering
THE DELPHI METHOD-A COMPLEMENT TO RESEARCH
previous round are communicated to the participants'. This is a 'device for reducing noise'. The 'use of statistical definition of the group response is a way of reducing group pressure for conformity; at the end of the exercise there still may be significant spread in individual opinions'. Those who are interested in a thorough discussion on the value of the Delphi method are asked to refer to a book by Linstone and ~ u r o f f
.'
The Rand Corporation conducted extensive inves- tigations, with the participation of university students, concerning various features of the method such as effect of size of the group, accuracy and reproducibil- ity of decisions, forms of feedback, improvement of decisions by iteration, and so on. The method is already widely used to make decisions on subjects that depend on an unmanageable number of variables or on poorly defined or unavailable information of a
statistical nature. It is believed that the provision of fire safety is an ideal area for application of the method. It can be used as a tool to complement research in certain areas, for example, the area de- scribed earlier or the area of fire risk assessment, or better, assessment of potential for harm of p r ~ d u c t s , ~ and also to make a variety of other uninfluenced design decisions.
Clearly, a dedicated Delphi group could provide an invaluable service to fire technology by establishing the consensus necessary to bridge some grey area in fire science.
Acknowledgement
This paper is a contribution from the Division of Building Research, National Research Council of Canada, and i s published with the approval of the Director of the Division.
REFERENCES
1. T. 2. Harmathy, Fire severity: basis of fire safety design. group opinion. Report RM-5888-PR, Rand Corporation, San- Paper presented at the International Symposium on Fire ta Monica, California (June 1969).
Safety of Concrete Structures, Fall Convention of ACI, San 5. H. A. Linstone and M. Turoff, The Delphi Method: Techni- Juan, Puerto Rico (21-26 September 1980). ques and Applications, Addison Wesley, London (1975). 2. J. R. Mehaffey and T. 2. Harmathy, Fire Technol. 17, 221 6. T. 2. Harmathy, Fire Mater. 4, 173 (1980).
(1981).
3. T. T. Lie, Can. J. Civil Eng. 6, 617 (1979).
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