We have seen is in problem 2 that, despite the average heartbeat rate is quite different for humans and RAD2 population (74 beats/min versus 95 beats/min), dispersion of measurement (noise and fluctuations) makes it difficult to achieve a good probability of detection for a given false alarm rate (Pd = 35.5 %, Pfa = 1%).
Further studies have shown that these fluctuations where more due to physical activity, mood and stress than to physical characteristics and that the heartbeat rate of a specific individual can vary randomly from one measurement to the other.
To make detection more reliable, the average processing of four independent measurements for each candidate before comparing to the threshold has proved to increase dramatically the discrimination between RAD2 and human (from 35.5% to 90%).
Nevertheless, this averaging process proves to be difficult to manage (necessity to record all the measures of each individual before making a decision) and moreover it appears that some human individual where too much impressed by the test and their heartbeat could increases abnormally biasing the average process (just one high value abnormal measurement among the four can completely bias the result).
It was decided that the averaging process has to be replaced by a M out of N process ("M/N" for short) which is more resistant to abnormal behaviour of the candidates.(the weight of an abnormal measurement is only 1 among the N values whatever is its amplitude).
This process consists of comparing the elementary measurement to a first threshold and to makes a preliminary decision (0 or 1, that is to say "yes" or "no") and then to cumulate these decisions for the N tests (K being the result): a second criterion is then applied comparing K to a second threshold (M). If K exceed M (if there are more than M positive results among the N tests) a positive decision is made.
Remember that humans are characterized by a Gaussian distribution of mean value m0 = 74.3 and standard deviation s0 = 9.9, while RAD2 characteristics are: m1=95, s1=14
Help the GWG decide the best criterion: 2 out of 4, or 3 out of 4.