For k=1,…, K, a stochastic process {An,k, n =1, 2,…} is an arithmetic process (AP) if there exists some real number, d, so that {An,k +(n-1)d, n =1, 2,…} is a renewal process (RP). AP is a stochastically monotonic process and can be used to model a point process, i.e., point events occurring in a haphazard way in time (or space), especially with a trend. For example, the events may be failures arising from a deteriorating machine; and such a series of failures is distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for K independent, homogeneous APs. Two statistics are suggested for testing whether K given processes come from a common AP. If this is so, we can estimate the parameters d, [Formula: see text] and [Formula: see text] of the AP based on the techniques of simple linear regression, where [Formula: see text] and [Formula: see text] are the mean and variance of the first average random variable [Formula: see text], respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.