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.
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], [2] and [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] and [2], the intensity of the auditory cues was kept constant. By contrast, in [3], which concentrated on 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.
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.