# Reliability

Ideally, a PUF should always be able to exactly reproduce the same response when the same challenge is applied. However, as anticipated before, since PUFs are based on variations of electrical characteristics, a number of response bits might change under either stable or variable environmental conditions, such as temperature and power supply. To this aim, the stability metric can be used to estimate the percentage number of bits in a response which change value among responses obtained from a repeatedly applied challenge. For a device d, let *M* be the number of measurements of *N* -bit responses, *r' _{d} ? (j = 1, 2,..., m),* and

*r*be the baseline reference response of the

_{d}*d*-th device. The stability, also called as

*intra-chip Hamming Distance*or Steadiness in [16], can be estimated as:

For a population of R devices, it can be averaged as

Alternatively, we can express the reliability value, which is the percentage number of bits which keep the value stable over time

A PUF with stable responses achieves a high value of reliability, thus its value should be as close as possible to 100%.