In the present paper an attempt is made to accurately understand the spread and progress of fire by dividing the spread of a fire within a single building into several phases and by relating them to one another from the point of view of theory of probability.
At first, a more adequate form of fire spread model for application by collecting and classifying data of actual housing fires is composed as a stochastic state-transition system. The system of differential equations which describes the behaviour of this stochastic state-transition corresponding fire spread is derived and its solution is obtained. Similarly the equation of survival probability for each phase at each time is solved.
Secondly, as a simplified measure of the above stochastic fire spread system, the average arrival time and the average extinguishment time for each phase are obtained from the above solution.
Finally, the unknown parameters in our model are estimated with data consisted of a total of 335 fire-cases randomly sampled from actual fires. And the behaviour of the value of survival probability for each phase is obtained.

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In order to make to accurately understand the spread of fire in building, the stochastic model of fire-spread has been formulated and the unknown parameters in this model have been estimated in previous paper.
In this paper, the instantaneous extinguishment rate and instantaneous transition rate for each phase are estimated with the result of the previous paper at first. The behaviour of existence probability for each phase is obtained with the above estimated parameters, and the differences between the properties of fire-spread process in Phases 1 through 3 and one of the process in Phase 4 and subsequent phases are clarified.
Secondly, the differences in fire-spread process among the building types of structure are shown by estimating parameters for each type of structure and it is clear that when the trend of fire-extend up to a flashover is viewed probabilistically, a fire extends most quickly in building of wooden construction and a fire in a building of fireproof construction extends most slowly.
Finally, a model for fire escape is formulated and an equation of relation between the average escape time and a parameter in this model is obtained. With those result, the escape-failure probability which is one of measures of danger to human life is obtained. A comparison of the escape-failure probabilities for each type of structure with the result in previous chapter reveals that wooden construction is more dangerous to human life than fireproof construction.

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For evaluating the flammability of cable-like polymers, a new test method was developed. In this method, the rate of downward flame spread along the polymer surface was measured by means of a moving wire technique, in which the flame was stopped on a special position by winding up the cable in the same speed with the flame spreading rate, under the external pre-heating by an electric furnace and the oxidative gas flow. The technique is convenient for making the polymer burn continuously without a change of flame condition, and the rate can be obtained from the winding speed of cable.
While, through a simple flame spread equation, the flame spreading rate of cable-like polymer V in such condition can be related to the oxygen concentration in atmosphere Y₀, the pre-heating temperature T_a and the pyrolysis temperature for polymer burning T_p as
V = α · (T_p − T_a )^-b · Y₀ⁿ
Where b and n denote multipliers concerning the dependences of temperature and oxygen, respectively, and α denotes the geometrical factor of specimen.
Therefore, by plotting log V vs. log Y₀ for experimental results, one may evaluate the flammability of polymers discriminating between the effects of oxygen concentration, heating temperature and specimen shape.
Results obtained by using various types of PVC electric cable showed that this method was valid as our expectation. Also, from the application of this method to “grouped cables”, it was found that they exhibited a peculiar behavior, which was different from the case of one cable, in the atmosphere of high oxygen concentration. Experimental results and discussions were given in the present paper.
In addition, this evaluation method may be applied to not only electric cables, but general polymeric materials if they can be formed like cables.

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The recent experiments by Terai & Nitta showed an example of fire plume that can hardly be expressed by the well-known model of plume by Yokoi-Morton^5),6).
In this paper, the physical structure of Terai-Nitta's plume is investigated theoretically on the basis of some qualitative characteristics of their experimental results. The principal result of this paper is that the experimental results by Terai & Nitta can be expressed by the mathematical model represented by (42)∼(45), in which the eddy coefficient is assumed as constant.

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Many reports are available on the extinction of wood fire, especially on wood crib fire, still they are not enough for systematic appreciation of extinction phenomena and mechanism, we need basic rules that govern extinction.
In order to investigate these problems, in this research, water was dripped on the top flat surface of crib, then one could avoid the drain-off ideally until the extinction is almost achieved, reducing one difficult item for analysis.
By this method, it was found that there is very clear relation among the extincted number of layers N_e , water application rate P and the period of water application t as follows;
N_e = αP^mtⁿ
where α is a function solely of the weight loss ratio φ and m, n are constants respectively.
The mass balance equilibrium can then be written as;
I = p − (r +e)
where I is the rate of mass increase, r is the burning rate during extinguishing, and e is the evaporation rate of water.
And also, it was found that I is merely a function of p neither depending on φ nor t, namely,
I = ap−b ≈ap−r_M
where a, b are constants.
and r could be given properly by the following equation;
r = r_M N₀−N_e /N₀
Here r_M is the burning rate just before water application, and N₀ is the number of layers.
Then e was derived as follows;
e = p (1−a)+r_M αP^m/N₀ tⁿ
and because the total water evaporated E is the integration of e with respect to t, then;
E = ∫^te₀edt = [p (1−a) + r_M /n+1]t_e
Furthermore, the fuel lost during extinguishing can be obtained by integrating r as follows;
ΔM = ∫^te₀rdt = n/n+1 r_Mt_e ≈ n/n+1 r₀t_e
ΔM was experimentally measured and showed good agreement with the calculated value.
The relative difficulty of extinction, such as by carbon formation or crib height, could also be calculated quantitatively.
The critical water application rate P, was defined as;
M₀(1−φ−c)/r_M > (N₀/α)^1/nP^−m/n
where M₀ is the original crib weight, and c is the char yield.
and also showed good agreement with measured values in constant flaming combustion area.

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