The statistics of records in sequences of independent, identically distributed (i.i.d.) random variables (r.v.'s) is a classical subject of study. In this presentation I will show new results on the analysis of records drawn from independent r.v.'s with a drifting mean. In particular, the probability distributions of number of records and records time in a Linear Drift Model (LDM) with a Gumbel underlying distribution. In addition, I am going to introduce a statistical test based on the number of records to detect a non i.i.d. model. The i.i.d. classical model is a particular case of the LDM with the big difference that in a general LDM, record events are drawn from uncorrelated r.v.'s with a time dependent distribution which is more common in practical applications. These results are illustrated by analysis of numerical simulations using the software R.