Accession Number : AD0764136

Title :   Multivariate Geometric Distributions Generated by a Cumulative Damage Process.

Descriptive Note : Technical rept.,

Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF

Personal Author(s) : Esary,James D. ; Marshall,Albert W.

Report Date : MAR 1973

Pagination or Media Count : 33

Abstract : Two (narrow and wide) multivariate geometric analogues of the Marshall-Olkin multivariate exponetial distribution are derived from the following cumulative damage model. A set of devices is exposed to a common damage process. Damage occurs in discrete cycles. On each cycle the amount of damage is an independent observation on a nonnegative random variable. Damages accumulate additively. Each device has its own random breaking threshold. A device fails when the accumulated damage exceeds its threshold. Thresholds are independent of damages, and have a Marshall-Olkin multivariate exponential distribution. The joint distribution of the random numbers of cycles up to and including failure of the devices has the wide multivariate geometric distribution. It has the narrow multivariate geometric distribution if the damage variable is infinitely divisible. (Author)

Descriptors :   (*MULTIVARIATE ANALYSIS, DISTRIBUTION FUNCTIONS), (*RELIABILITY, MATHEMATICAL PREDICTION), RANDOM VARIABLES, THEOREMS

Subject Categories : Statistics and Probability
      Mfg & Industrial Eng & Control of Product Sys

Distribution Statement : APPROVED FOR PUBLIC RELEASE