FTE

Definition

The FTE is defined as the probability that a user attempting to biometrically enroll will be unable to. For example, Craig goes to the group in his company responsible for biometric enrollments. He is quickly instructed on the use of a biometric device, and then he attempts to have his biometric trait enrolled. At this time, he is unable to be enrolled. What defines his FTE can influence this measure. If the FTE is defined as a single-attempt failure, then the FTE will likely be higher than what would be seen over a larger group of people.

The FTE is normally defined by a minimum of three attempts. This is justified by the Rule of Three . The Rule of Three in this case provides us with a confidence level for a given error rate for our FTE. It also assumes that each attempt to enroll is independent, identically distributed, and that the user population size is significantly large enough. For example, if Craig is part of a population of 300 people, then using the Rule of Three for a 95% confidence level, we would obtain an FTE of 1%. ^[1] Thus, if Craig is still unable to be enrolled after three attempts, he has had an FTE.

^[1] A.J. Mansfield and J.L. Wayman, Best Practices in Testing and Reporting Performance of Biometric Devices Version 2.01 (Queens Road, Teddington, Middlesex, UK: Centre of Mathematics and Scientific Computing National Physical Laboratory), August 2002, p. 11.

The Simple Math

When the FTE is calculated by a biometric vendor, it is generally calculated with three attempts for enrollment. Since multiple attempts may need to occur before a decision is made on a success or failure, the three or fewer attempts will be called an enrollment event. In this case, a successful enrollment event occurs if Craig can be enrolled in three or fewer attempts. An unsuccessful enrollment event occurs if Craig, on his third attempt, is still unsuccessful. Thus, the FTE is calculated as the number of unsuccessful enrollment events divided by the total number of enrollment events.

n = EnrollmentCandidate

N = TotalNumberofEnrollmentCandidates

n	Value
1	Craig
2	Matt

Event'(n) = NumberofUnsuccessfulEnrollmentEvents

Event(n) = TotalNumberofEnrollmentEvents

FTE (n) = Event'(n) / Event(n)

n = 1

FTE (Craig) = Event'(Craig) / Event(Craig)

This gives us the basis for Craig's FTE. What if we have another user, Matt? We could say that Craig is representative of our user population and just assume that the FTE will be the same for Matt. Statistically, the more times something is done, the greater the confidence in the result. Thus, if we want to have a high confidence that the FTE we calculate is statistically significant, we would need to do this for every user. We would then need to take all the calculated FTEs for each user's attempt to biometrically enroll, sum them up, and divide by the total of all biometric enrollment attempts to determine the mean (average) FTE. For example, we could take the above formulas and do them over again for each user. We would eventually get something that looks like the following:

FTE (N) = (Event'(Craig) / Event(Craig) + Event'(Matt) / Event(Matt)) / 2

If we generalize the formula, we get:

n = EnrollmentCandidate

N = TotalNumberofEnrollmentCandidates

Event'(n) = NumberofUnsuccessfulEnrollmentEvents

Event(n) = TotalNumberofEnrollmentEvents

n	Value
1	Chris
2	Matt
3	David
4	Craig
5	Peter
.	.
N	Victoria

FTE (n) = event'(n) / Event(n)

Why Is This Important?

The strength of the FTE is the amount of coverage for the population that the biometric system has. The more coverage the biometric system has, the less likely that a user will experience an FTE. Craig has a greater chance of being enrolled in a biometric system that has greater coverage than one that does not. An example of this is playing golf. In this example, the ball is a biometric enrollment attempt. The par for the hole is 3, and it represents the number of attempts before an FTE occurs. The size of the green represents the coverage provided by the biometric system. If Craig is playing a par 3 hole on a green with large coverage, his probability of putting the ball on the green is very high, and thus he has a lower probability of not making par. If the hole being played has a green with little coverage, then the probability of putting the ball on the green is lower, and the probability of not making par is higher.

A Quick Note on Biometric Systems

In the FTE description, the measure is referenced to a biometric system. This biometric system is made up of the hardware to acquire the enrollment, the algorithm for templating and comparison, and the user. An FTE could be caused by 1, 2, or all 3 of these entities. For example, if the biometric hardware is malfunctioning or is not properly maintained , this could cause an FTE. An algorithm that is not tuned properly could also reject an enrollment event because of the lack of features present, or the presence of features that are not incorporated into the algorithm. A FTE could be caused by a user who does not have the physical dexterity to provide the biometric sample, or is slow to habituate to the system.

When examining a biometric system's FTE, try to eliminate the parts of the system that can be controlled. For example, have the equipment properly cleaned and serviced. Tune the algorithm for your needs. Lastly, try reducing the human factor by choosing devices that are ergonomic, providing additional assistance to the user during enrollment, and also have properly qualified people doing the enrollments. Taking these steps will help to reduce the FTE and also increase user confidence in the system itself.