A Hypothesis Test of Cumulative Sums of Multinomial Parameters
Abstract
The Air Force is considering the contract renewal application of a civilian contractor hired to maintain in working order a series of radar stations. The measure of performance of interest is T, the time that a particular station is not 'on line' while being down for repair. The contract stipulates that repair service will be such that on the average 50% of all repairs will be completed before L sub 1 hours and 90% of all repairs shall be completed before L sub 2 hours. It also states that the repair contract will be renewed on the basis of a decision rule that errors by failing to renew when the case is that the contract should be renewed with a probability of alpha. The renewal of the contract depends on the making a decision based on N repair times, T sub 1, T sub 2, ..., T sub N, of the contractor as to whether or not L sub 1 is at least the 50 to the th power percentile and L sub 2 is at least the 90 to the th power percentile of F(.), the distribution function F(.) of these repair times. The usual test based on the binomial distributions of the number of repairs before L sub 1 and the number of repairs before L sub 2 suffers from two problems: 1) Its true size is at times far from the nominal size; and 2) because of the discrete of the random variables, cannot be performed at the stipulated size. This paper proposes the use of the likelihood ratio test based on the nultinomial joint distribution of the number of repairs before L sub 1 and the number of repairs before L sub 2.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1990
- Accession Number
- ADA221466
Entities
People
- D. A. Meeter
- J. H. Clair
Organizations
- Florida State University