LB <- 0
UB <- 10
k=0.05
ARL0 <- 200
repeat {
  RL <- NULL
  for(i in 1:100) {
    e = 0
    count <- 0
    h <- (LB + UB) / 2
    while(e < h ) {
      x <- rnorm(1)
      e <- max(k*x+(1-k)*e, 0)
      count <- count + 1
    }
    RL <- count
  }
  ARL <- mean(RL)
  if(abs(ARL0 - ARL) <= 1) break
  if(ARL < ARL0 - 1) {
    LB <- h
  } else if(ARL > ARL0 + 1) {
    UB <- h
  }
}
h
ARL