A First Passage Problem in a Random Walk with a Quality Control Application
随机游走的首次到达问题及其质量控制应用
SUMMARY This paper is concerned with a first passage problem for a discrete time random walk which arises in a quality control scheme proposed by the author. There are two barriers, one of which is absorbing and the other such that the random walk particle is immediately returned to the origin upon reaching it. An explicit expression is derived for the probability distribution of the time to absorption when the barriers are symmetrically placed on either side of the origin.