Stopping rules in the context of proofreading are studied. Previous results by Yang et al. [6] are corrected and a computational procedure to obtain an optimal rule is presented.

Consider a fixed set of n events. Let S1 denote the sum of the probabilities of occurrence of each event and S2 the sum of the probabilities of occurrence of each of the pairs of events. Using a dual linear programming method a sharp upper bound is derived for the probability of occurrence of at least m out of the n events when S1 and S2 are given. The bound improves one of the inequalities obtained by Sathe et al. (1980).

A number of extensions of the class preservation results in the Esary, Marshall and Proschan shock model have been investigated by various authors in recent years, most recently by Ghosh and Ebrahimi. In this note, generalizations are obtained using different methods for the IFR and NBUE cases when the shocking process is a regular continuous-time Markov process with stationary transition probabilites.

Jobs arrive at a buffer from which there are several parallel routes to a destination. A socially optimal policy is one which minimizes the average delay of all jobs, whereas an individually optimal policy is one which, for each job, minimizes its own delay, with route preference given to jobs at the head of the buffer. If there is a socially optimal policy for a system with no arrivals, which can be implemented by each job following a policy γ in such a way that no job ever utilizes a previously declined route, then we show that such a γ is an individually optimal policy for each job. Moreover γ continues to be individually optimal even if the system has an arbitrary arrival process, subject only to the restriction that past arrivals are independent of future route-traversal times. Thus, γ is an individually optimal policy which is insensitive to the nature of the arrival process. In the particular case where the times to traverse the routes are exponentially distributed with a possibly different mean time for each of the parallel routes, then such an insensitive individually optimal policy does in fact exist and is moreover trivially determined by certain threshold numbers. A conjecture is also made about more general situations where such individually optimal policies exist.