A Dyadic Age-Replacement Policy for a Periodically Inspected Equipment Item Subject to Random Deterioration
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
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A periodic review replacement system is considered. The amount of deterioration over successive periods form a sequence of i.i.d. random variables. A replacement policy of the dyadic type is in effect whereby the used equipment item is discarded and immediately replaced by a new identical equipment item if at the end of a period the old equipment has service aged by an amount in excess of S or has been in operation for exactly N periods whichever comes first. Expressions for the joint distribution of the service age and the chronological age and for the distribution of the total number N sub t of replacements are derived. The derivation of the distribution function of N sub t relies on the solution to a system of linear Diophantine equations. Finally, using as criterion the minimization of the total steady-state expected cost per period, consisting of a fixed replacement cost and a linear cost of operation, optimal values of S and N are computed for a few numerical examples.
- Statistics and Probability