AN OPTIMAL SEARCHING PLAN FOR A PROBLEM IN MAINTENANCE ANALYSIS
Abstract
A system of R is to be searched for a single object located in one of them by inspecting the boxes one at a time. Given for box i (i=1,...,R) are a prior probability P sub i that the object is there, a known positive probability alpha sub i that if it is there, the object is not detected on a given inspection of the box, and probability zero that the object is detected if it is not there. A searching plan is a specified (infinite) sequence the nth term of which indicates the box to be inspected at the nth stage of the search, and it is of interest to determine, if possible, some 'optimal' plan. With the further assumption that all inspections are in a reasonable sense independent, it is shown that a plan which instructs the searcher to inspect at each stage, the box in which the object is most likely to be found is optimal in the sense of minimizing the expected total number of inspections required to find the object. In addition, the optimal plan is shown to be ultimately periodic if all alpha sub i's are equal, and when R=2, that it can be approximated by an ultimately periodic plan that does not require exact knowledge of the probabilities alphas sub 1 and 2.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1964
- Accession Number
- AD0610429
Entities
People
- Milton C. Chew Jr.
Organizations
- Carnegie Institute of Technology