from concatenating M samples to the Mτ0 observation time over the MT0 with the dead-time distributed among the M measurement blocks rather than at the end of the measurement. This rendered the need for the B3 bias. The bias functions are evaluated for a particular µ value, so the α–µ mapping needs to be done for the dominant noise form as found using noise identification. Alternatively, the µ value of the dominant noise form may be inferred from the measurements using the bias functions. B1 bias function The B1 bias function relates the M-sample variance with the 2-sample variance (Allan variance), keeping the time between measurements T and time for each measurements τ constant. It is defined as where The bias function becomes after analysis B2 bias function The B2 bias function relates the 2-sample variance for sample time T with the 2-sample variance (Allan variance), keeping the number of samples N = 2 and the observation time τ constant. It is defined as where The bias function becomes after analysis B3 bias function The B3 bias function relates the 2-sample variance for sample time MT0 and observation time Mτ0 with the 2-sample variance (Allan variance) and is defined as where The B3 bias function is useful to adjust non-overlapping and overlapping variable τ estimator values based on dead-time measurements of observation time τ0 and time between observations T0 to normal dead-time estimates. The bias function becomes after analysis (for the N = 2 case) where τ bias function While formally not formulated, it has been indirectly inferred as a consequence of the α–µ mapping. When comparing two Allan variance measure for different τ, assuming same dominant noise in the form of same µ coefficient, a bias can be defined as The bias function becomes after analysis Conversion between values In order to convert from one set of measurements to another the B1, B2 and τ bias functions can be assembled. First the B1 function converts the (N1, T1, τ1) value into (2, T1, τ1), from which the B2 function converts into a (2, τ1, τ1) value, thus the Allan variance at τ1. The Allan variance measure can be converted using the τ bias function from τ1 to τ2, from which then the (2, T2, τ2) using B2 and then finally using B1 into the (N2, T2, τ2) variance. The complete conversion becomes where Similarly, for concatenated measurements using M