A production system is working in the GOOD state and 

there is a constant probability that it falls into 

the BAD state (and remains there) at a disorder moment.  

A decision-maker observes the output $X_t$ of the system 

at each time $t = 1, 2, \ldots, n,$ and decide either 

CONTINUE ( {\it i.e.} reject $X_t$ and observe $X_{t+1}$), 

or STOP ( {\it i.e.} accept and receive $X_t$). 

The objective is to maximize the expected net value of 

the $X_{\tau}$ at the stopping time $\tau$ he decides 

during the given finite period of time $n$. Recall is not 

allowed ( {\it i.e.} the observation once rejected cannot 

be recalled later.) For uniformly distributed observations 

we derive the Optimality Equation and show that the optimal 

policy is not necessarily of a control-limit type. Also an 

example in which the optimal policy is of a control-limit type 

is shown. An analytical solution for the infinite-horizon version 

by introducing discount rate over time, where a functional 

equation must be solved, is as yet unknown.