Sound intensity required for waking up

Sound intensity required for waking up

ARTICLE IN PRESS Fire Safety Journal 42 (2007) 265–270 www.elsevier.com/locate/firesaf Sound intensity required for waking up A.M. Hasofer, I.R. Tho...

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ARTICLE IN PRESS

Fire Safety Journal 42 (2007) 265–270 www.elsevier.com/locate/firesaf

Sound intensity required for waking up A.M. Hasofer, I.R. Thomas CESARE, Victoria University, P.O.Box 14428, MCMC Melbourne, Vic. 8001, Australia Received 22 February 2006; received in revised form 11 September 2006; accepted 4 November 2006 Available online 29 January 2007

Abstract The response of sleeping subjects to sound stimuli whose intensity increases with time is analysed, using a random walk model with varying upper boundary developed in a previous paper. The data came from an experiment carried out by Ball and Bruck to compare the response time of sleeping subjects to three different auditory stimuli. The sound intensity increased steadily with time and the young adult subjects (seven males and seven females) were tested when sober and with blood alcohol levels of 0.05 and 0.08. The analysis revealed that alcohol had a very significant effect in slowing down the response of all subjects. It also revealed that sober females responded at lower sound intensities than sober males and were less affected by alcohol than males at the same blood alcohol concentration. The great advantage of using the random walk model is that it allowed the estimation of the high percentiles of the probability distribution of the sound intensity required for waking up, for each combination of gender, type of auditory stimulus and alcohol level. It also allowed the estimation of the proportion of subjects in each category that would not wake up at the maximum realisable sound intensity of 95 dbA. The analysis underscores the severity of the danger of not being sober or even low alcohol consumption for sleeping subjects in a fire and points to possible improvements in the type of sound used in fire alarms. r 2007 Elsevier Ltd. All rights reserved. Keywords: Auditory fire cues; Influence of sound type and intensity, Gender and alcohol; Stochastic modelling; Waking up percentage

1. Introduction In three previous papers [1–3] the authors have introduced a random walk model to analyse the length of time to response of sleeping subjects exposed to various simulated fire cues. The reason for developing such a model is that one of the most important aims of the study of the response time to fire cues is to estimate the high quantiles of the distribution of the response time, since it is those who respond the most slowly who are the most at risk. However, the raw experimental results based on a comparatively small number of observations cannot by themselves be extrapolated to the levels that are infrequently reached. The only alternative is to develop a theoretical model for the response to fire cues and fit it to the experimental data. In [1,2], the intensity of the auditory cues was kept constant. By contrast, in [3], which concentrated on Corresponding author. Tel.: +61 3 9216 8033; fax: +61 3 9216 8058.

E-mail address: [email protected] (A.M. Hasofer). 0379-7112/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2006.11.005

auditory cues, the intensity of the auditory stimuli was monotonically increased. This third paper [3], analysed an experiment carried out by Ball and Bruck [4] in 2003 to compare the response time of sleeping subjects to three different auditory stimuli, as well as to determine the effect of gender and alcohol consumption on responsiveness. This important new aspect of the experimentation allowed the estimation of the sound intensity required to waken the individual participants for different types of sound and different degrees of sobriety. However, in [4], only averages of the sound intensity required for the subject to wake up were studied. In [3] a modified random walk model was introduced to analyse the experiment in [4] and a methodology to evaluate the upper quantiles of the time to awakening was developed. However, in [3] the corresponding results for the quantiles of the sound intensity required for the subjects to wake up were not given, due to space limitations. It is the purpose of the present paper to present these results, which are clearly of great importance for fire safety engineering design.

ARTICLE IN PRESS A.M. Hasofer, I.R. Thomas / Fire Safety Journal 42 (2007) 265–270

266

Fourteen young adults (7 males, 7 females) were recruited. The ages of the participants ranged from 18 to 25 years. When the participant was confirmed to be in stage 4 sleep for at least 90 s a computer program was started. The computer was instructed to play the selected sound for a period of 30 s, beginning at 35 dBA. The intensity of the sound was then increased to 40 dBA for a further 30 s. The incremental pattern was continued until 95 dBA or until the participant awoke and pressed a button at their bedside, whichever occurred first. The time dependence of the sound intensity is illustrated in Fig. 1. If the participant did not respond before 30 s at 95 dBA, the sound continued for a period of 3 min. The entire process from start to finish took 9.5 min. Participants who slept through the signal were coded as awakening after 10 min. As far as the sound intensity was concerned, responses in the first 30 s period at 95 dBA was recorded as 95 dBA, responses in the second period of 30 s at 95 dBA was recorded as 96 dBA, and so on, up to 101 dBA for awakening in the final (seventh) period at 95 dBA. Nonawakening was recorded as 105 dBA (10 dBA higher than the real maximum sound intensity). For a discussion of the recording procedure just described see [4]. Participants were tested on three non-consecutive nights in three different conditions: no alcohol, 0.05 blood alcohol content and 0.08 blood alcohol content.The order of the latter two was counterbalanced. The response time analysed in this paper is the time until the subject presses a button (‘‘Behavioural response’’). Three sounds were used: 1. Female voice: This signal consisted of a female actor’s voice that warned of danger due to fire in an emotional tone and said that the person must wake up and investigate. There was a core sound of 10 s duration, repeated three times in 30 s.

Sound Intensity (dBA)

TIME DEPENDENCE OF SOUND INTENSITY

2. Australian standard alarm (‘‘ASA’’): This alarm signal was the modulating high-frequency beeping sound that is used in residential smoke alarms in Australia. 3. Temporal-three evacuation signal (‘‘T3 alarm’’): A lower frequency alarm signal that sounds the Temporal-Three pattern as laid down in International Standard 8201 (see [5]). For full details of the three sounds see [4]. A report worth reading [6] establishes a clear link between alcohol and fire fatality and supports the findings of this paper. 2. Experimental results Visual examination of the raw experimental data revealed that there was no significant difference between the two levels of blood alcohol content considered, namely 0.05 and 0.08. This is consistent with the well-known Weber–Fechner law (see e.g. Encyclopaedia Britannica) that states that human response to a stimulus is proportional to the logarithm of the stimulus. In fact, a person who has exactly 0.05 or 0.08 blood alcohol content can drive a car in most European and North American countries; people who are above those levels are judged unfit to drive. In Canada, 0.08 is the limit, so that 0.05 would be judged as ‘‘fairly sober’’. For the purpose of the present paper it was therefore decided to combine the two levels of blood alcohol content into one and to denote the condition as ‘‘Not sober’’. The main object of the research presented in this paper is to document numerically the fact that even at a relatively low blood alcohol content the proportion of people unlikely to awake to a fire alarm is significant, particularly for males. The link between alcohol and fire fatality has been clearly established in a report produced by Tridata in 1999 [6]. The means and standard deviations of the behavioural response time are given in Table 1. One interesting conclusion that can be drawn from the table is that the standard deviations are roughly

90

Table 1 Mean and standard deviation of behavioural response time (male and female)

70

Sound

Alcohol level

Male Mean

50 Female voice

100

200

300

400

500

Time (secs) Fig. 1. Time dependence of sound intensity.

Standard deviation

Mean

Standard deviation

Sober

168.43

91.95

119.43

80.55

Not sober

395.71

185.76

214.29

151.67

ASA

Sober Not sober

219.71 406.50

70.15 128.96

246.00 258.14

190.57 130.35

T3 alarm

Sober Not sober

174.57 383.71

88.43 169.32

125.43 195.5

82.35 146.19

30 0

Female

600

ARTICLE IN PRESS A.M. Hasofer, I.R. Thomas / Fire Safety Journal 42 (2007) 265–270

proportional to the means, In fact, regression of the standard deviation on the mean (with zero intercept) shows that the ratio of the standard deviation to the mean (i.e. the ‘‘coefficient of variation’’) can be taken to be approximately constant at 0.49. Analysis of variance confirms that the proportionality is highly significant. For details see [3]. This fact simplifies the development of the model in the next section, allowing the coefficient of variation to be taken as constant with the value 0.49 just derived. 3. The random walk model For the problem at hand, which is one of evaluating the distribution of the response time of a human to a specific stimulus, the required distribution was derived from an underlying stochastic process, namely the simple random walk. In the simple random walk model used and fully described in [1,2], a particle starts from some origin Z, and moves on a line at discrete points of time. At each point of time t it moves to the right by one unit with probability p and otherwise to the left by one unit (with probability q ¼ 1  p). The random walk ends in success if the particle reaches some point A4Z and in failure if the particle reaches the point zero. The model used is called a memory retrieval theory because it considers an item recognition task as testing a single probe item against a group of items in memory which has been designated as the memory search set. The retrieval process consists of comparing a collection of features of each element of the memory search set with the probe item. The term relatedness is used to describe the amount of match between them. It is assumed that all information elicited can be mapped onto a unidimensional variable, that of relatedness. In the application of the model to the response of subjects to a smoke detector alarm the probe item is identified with the stimulus induced in the sleeping subject by the sound of the alarm. This stimulus is compared with the items of the memory search set. The comparison ends either by a match, in which case the subject wakes up, or by a non-match, in which case the subject continues to sleep. The comparison process can be described as follows: Comparison of a probe to a memory-set item proceeds by the gradual accumulation of evidence, that is, information representing the goodness of match, over time. It is easiest to conceptualise the comparison process as a feature-matching process in which probe and memory-set item features are matched one by one. A count is kept of the combined sum of the number of feature matches and non-matches, so that for a feature match, a counter is incremented, and for a feature non-match, the counter is decremented. The counter begins at some starting value Z, and if a total of A counts are reached, the probe is declared to match the memory-set item (A  Z more feature matches than non-matches). But if a total of zero counts are reached, an item non-match is declared.

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The feature-matching, memory comparison process is mathematically identical (‘‘isomorphic’’) to the classical ‘‘gambler’s ruin problem’’: a gambler wins or loses a dollar with probabilities p and 1  p, respectively. His initial capital is Z and his opponent’s capital is A  Z. The game terminates either by a win, when the gambler’s capital becomes A or by the gambler’s ruin, when his capital reaches 0. In the application of the model to the response of subjects to a fire cue the probe item is identified with the stimulus induced in the sleeping subject by the cue. This stimulus is compared with the items of the memory search set. There is a fixed probability p of a match and comparisons occur at fixed steps of length d. Comparison of a probe to a memory-set item proceeds by the gradual accumulation of evidence, that is, information representing the goodness of match, over time. A count is kept of the combined sum of the number of feature matches and nonmatches, so that for a feature match, a counter is incremented, and for a feature non-match, the counter is decremented. A threshold value A is set and the counter begins at some starting value ZoA. If a total of A counts are reached (i.e. there are A  Z more feature matches than non-matches), the probe is declared to match the memoryset item and the subject wakes up. In the first two papers [1,2] the intensity of the stimuli was kept constant. As a result, a significant proportion of the subjects did not wake up. This was reflected in the random walk model in two ways: 1. The upper boundary of the random walk was kept constant. 2. A lower boundary was introduced (at 0). If the lower boundary was reached first it was assumed that the subject would dismiss the stimulus and continue to sleep, while if the upper boundary was reached first the subject would wake up. In [3] the upper boundary, i.e. the threshold, was taken to be a decreasing function of the sound intensity. It must be pointed out that the intensity of sound is actually measured in decibels. But the decibel is a logarithmic unit of sound intensity and according to the Weber–Fechner law mentioned in Section 2 human response to a stimulus is proportional to the logarithm of the stimulus. It follows that the response to a sound stimulus measured in decibels can be expected to vary linearly with the sound measurement. It was therefore decided to decrease the threshold linearly from some initial value A at the points of time where the sound intensity was increased. The decrease was fixed at one unit. A graph showing the shape of the proposed threshold shape is given in Fig. 2. The random walk in this paper is described by three parameters: 1. A, the initial value of the wake up threshold,

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DIMINISHING THRESHOLD

1.0

20

0.8 Dist. function

Threshold

19 18 17 16

0.6 0.4 0.2

15

0.0

14

0 0

50

100

100

Time (secs) Fig. 2. Time dependence of threshold.

2. the probability p of a match between the stimulus and an item of the memory set, resulting in an upward jump of one unit at each step. A non-match, that occurs with probability 1  p, results in a downward jump of one unit. The parameter p will be referred to in the rest of the paper as the recognition probability. 3. the length d of one step. This was taken to be 0.5.

300

400

500

Fig. 3. Typical distribution function of first passage time (Corresponding to the response of sober males to the T3 alarm with observed values of response time plotted for comparison).

Table 2 Threshold and recognition probability of the random walk model Male A Female A Male p

Female p

Female voice Sober Not sober

38 57

34 41

0.55 0.52

0.55 0.55

ASA

Sober Not sober

41 61

44 42

0.54 0.52

0.54 0.54

T3 alarm

Sober Not sober

39 54

34 38

0.55 0.53

0.55 0.54

Sound

4. Fitting the model to the data In order to fit the model to the data it is necessary to be able to evaluate the mean and the coefficient of variation of the time to reach the time dependent boundary (the first passage time) in terms of A, p and d. Unlike the original model described in [1], this is by no means an elementary problem. An algorithm was specifically developed by the authors to calculate the first passage time probabilities by recurrence. It is fully described in an Appendix in [3]. It turned out that calculating 4000 successive first passage time probabilities was amply sufficient to obtain reliable values for the mean and the coefficient of variation. The mean and the coefficient of variation of the time to reach the boundary were calculated for an appropriate set of values of A and p. The values of A and p corresponding to the observed values of the mean and standard deviation were then derived by interpolation. The fit is not entirely precise because of the fact that the threshold values are restricted to be integers. A typical theoretical distribution function for the first passage time, as obtained from the formulae given in [3], is shown in Fig. 3. It corresponds to the parameters A ¼ 39, p ¼ 0:55 and d ¼ 0:5 s, derived from the response to the T3 alarm by sober males. The observed values are plotted together with the theoretical distribution. It can be seen that the fit is satisfactory.

200

Time (secs)

150

Alcohol level

5. Results The results of estimating A and p from the data are given in Table 2. While the threshold varies widely (between 34 and 61), the recognition probability is confined to a narrow interval just above 0.5 (between 0.52 and 0.55). This latter result is consistent with the analysis in [2], taking into account the fact that the increasing sound intensity can be expected to do away with the lower values of p. 5.1. High quantiles of the waking sound intensity As was pointed out in the Introduction, one of the most important aims of the stochastic analysis of the response time to fire cues is to estimate the high quantiles of the distribution of the waking sound intensity, which is of great importance in fire safety engineering design. For the present model, it is first necessary to evaluate the distribution function of the first passage time for values of A and p corresponding to the observed mean and standard deviation. From the distribution function it is easy to evaluate the high quantiles of the behavioural response time. For example, for the distribution function shown in Fig. 3, corresponding to the response of sober males to the T3 alarm, the 99th percentile of the response time turns out

ARTICLE IN PRESS A.M. Hasofer, I.R. Thomas / Fire Safety Journal 42 (2007) 265–270

to be 435 s. Using the variation of the sound intensity with time as depicted in Fig. 1 it is then possible to determine the quantiles of the sound. The waking sound intensity corresponding to a response time of 435 s turns out to be 105 dBA. Table 3 gives the 90th, 95th and 99th quantiles of the waking sound intensities for each category of subjects, namely, sober/Not sober and male/female and each of the three sound types. It is clear that the results of the experiment analysed in this paper cannot be taken to be the same as what would have been observed if the various categories of subjects had been subjected to the various types of sound at various intensities that remained constant over time. The latter design of experiment would have been more representative of what actually happens when a sleeping person is subjected to the sound of an alarm. Nevertheless, they do indicate at least qualitatively the response to different sound types and intensities. For instance: 1. the female voice and the T3 alarm are consistently better than the ASA sound, 2. females are consistently more sensitive than males, 3. alcohol severely impairs the ability to respond to any kind of sound alarm. Paradoxically, the data appear to indicate that the sensitivity to sound of females is less severely impaired than that of males, although it is generally held that females are more affected by alcohol than males. However, it must be pointed out that the general view that females are more affected than males is based on the assumption that the alcohol consumption is similar. It is then argued that under those circumstances the blood alcohol concentration of females is likely to be higher because of the following reasons: 1. The female body tends to contain more fatty tissue and less water than the male body. Alcohol is not absorbed into fatty tissue but remains more concentrated in the water portion. 2. Females are often smaller than males. As a result the alcohol tends to be more concentrated in the female Table 3 Waking sound intensity (dBA): means and quantiles Sound

Alcohol level

Male

Female

269

body, producing a higher blood alcohol concentration. 3. Females break down alcohol more slowly than males because they have a lower concentration of alcohol dehydrogenase enzyme in their bodies.

This information may be found in the factsheets issued by Alcohol Concern (Waterbridge House, London SE1 0EE) which are available on their website: www.alcoholconcern.org.uk. But in the experiment analysed in this paper what was controlled was the actual blood alcohol concentration of the subjects. Thus the female subjects must have ingested less alcohol than males. What is of interest is that when all subjects had an equal blood alcohol concentration the sensitivity to sound of females appeared to be less affected than that of males. There is a serious interpretation problem about Table 3. Indeed, many of the sound intensities listed are above 100 dBA. But the highest sound intensity used in the experiment was 95 dBA. This was because it is known that sound intensities above 95 dBA may damage the auditory system of the subjects. The values listed in Table 3 were obtained by extrapolation from the observations, using the random walk model, and could not in practice be realised. The results can, however, be presented in a more easily interpretable form by listing the expected proportion of subjects in each category who will not wake up at a sound intensity of 95 dbA. This proportion is given in Table 4. As for Table 3, the numbers given must be considered as indicative only, because of the design of the experiment and the small size of the sample. But it can be expected that more extensive experimentation will confirm the preliminary results given here. The results given in the table are fully consistent with the list given above. The main new perspective gained from Table 4 is that while sober persons have a good chance of being woken up by a sound intensity of 95 dBA, about half of non-sober males will not wake up! In the opinion of the authors, this fact has not been accorded enough importance to date in dealing with fire safety. More experimentation is required to fully confirm this result and more thought must be given to deal with the severe fire risk created by not being sober. Table 4 Percentage of subjects not waking up at 95 dBA

Mean q90 q95 q99 Mean q90 q95 q99 Female voice

Sober

60

Sound

Alcohol level

Male (%)

Female (%)

Female voice

Sober Not sober

1.9 59.1

1.3 2.4

135 135

ASA

Sober Not sober

7.0 65.0

8.9 7.7

100 130

T3 alarm

Sober Not sober

2.0 33.8

1.3 5.7

75

85

105

50

75

80

100

Not sober 100

180

210

285

70

80

90

110

ASA

Sober 70 Not sober 100

90 185

105 215

130 295

75 75

95 95

105 105

T3 alarm

Sober 60 Not sober 95

80 130

85 150

105 195

55 65

75 90

80 100

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References [1] Hasofer AM. A stochastic model for the time to awaken in response to a fire alarm. J. Fire Prot Eng 2004;11(3):151–60. [2] Hasofer AM, Bruck D. Statistical analysis of response to fire cues. Fire Saf J 2004;39:663–88. [3] Hasofer AM, Thomas IR, Bruck D, Ball M. Statistical modelling of the effect of alcohol and sound intensity on response to fire alarms, eighth symposium of the international association for safety science, Beijing, China; 2005.

[4] Ball M, Bruck D. The effect of alcohol upon response to different fire alarm signals. In: Proceedings of the third human behaviour in fire conference, Belfast, 1–3 October. London: Interscience Communications; 2004. p. 291–301. [5] Proulx G, Laroche C. Recollection, identification and perceived urgency of the temporal-three evacuation signal. J Fire Prot Eng 2003;13:67–82. [6] Tridata. Establishing a relationship between alcohol and casualties of fire. Federal Emergency Management Agency, United States Fire Administration, National Fire Data Center, Arlington, VA; 1999.