Range Accrual

This is an instrument whose payout is dependent on the number of days the underlying stays in or out a certain range.
In contrast to a digital where the focus is on whether the underlying is above or below the strike on expiry(at one date only), a range accrual averages out the risk.
Mathematically a range accrual payoout is represented as n/N x Notional where
N = no. of business days during the tenor of the investment.
n = no. of days the underlying stays in/out of the strike.

One variant to the range accrual is the Fadar which is a type of range accrual barrier.
The payout is dependent on the number of days within a period in which the underlying stays below/above the barrier. Consider a knockout put USD/JPY barrier @85, strike 76. It pays out if USD/JPY @ expiry <76, but lapses if at anytime during the expiry USD/JPY shoots up above 85. A fadar reduces this risk by having a payout proportional to the number of days that stays below 85.
eg. N = 180 days. During the 180-day period, there're 6 days that USD/JPY hit above 85. A normal barrier pays out nothing since this barrier is breached. A fadar will have 174/180 x [76-St] x N.