Linear decay functions describe a linear decay in weights over time. The decayed weight sequence is denoted Wl_i.

wl_j=[(1/k’)*j-1/k’]/s

s=sum((1/k’)*j-1/k’)

Where Wl_i represents the weight sequence of Rg[-(k’+1)]_i+1, and wl_j is the j-th element of Wl_i.

The alarm intensity wn_i is obtained by summing the element-wise products of the weight sequence Wl_i and the anomaly score sequence Rg[-(k’+1)]_i+1.

wn_i=sum(Wl_i** Rg[-(k’+1)]_i+1)

SPL routine:

Cell A4 represents the linear decay process;

Cell A5 calculates the weights wl_j.