Accession Number : AD0675424

Title :   RENEWAL FUNCTIONS FOR GAMMA AND WEIBULL DISTRIBUTIONS WITH INCREASING HAZARD RATE.

Descriptive Note : Technical paper,

Corporate Author : RESEARCH ANALYSIS CORP MCLEAN VA

Personal Author(s) : Soland,Richard M.

Report Date : AUG 1968

Pagination or Media Count : 52

Abstract : Four-decimal-place tables, accurate to within a unit in the last place, are given of the expected number of renewals and variance of the number of renewals for an ordinary renewal process and the variance of the number of renewals for an equilibrium renewal process. Results are tabulated for the cases in which the underlying lifetime distribution is gamma (Table 1) or Weibull (Table 2). In each case the value of the location parameter is assumed to be zero and the scale parameter is chosen so that the mean lifetime is one. For both cases results are given for distributions with shape parameter alpha = 2(0.25) 4(1) 6. Values are given for time t = 0.01(0.01) 2 in the gamma case and for time t = 0.01(0.01) 4 in the Weibull case. Also given are the asymptotic expressions for the three renewal functions and tables indicating the minimum time t such that the absolute percentage error of the asymptotic formula is less than a specified value for all times greater than or equal to t. The mathematical formulation is given, along with a description of the method of computations and an example illustrating the use of the tables. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, TABLES(DATA)), (*SPARE PARTS, SPECIAL FUNCTIONS(MATHEMATICAL)), PROBABILITY, LIFE EXPECTANCY, PROBABILITY DENSITY FUNCTIONS, INVENTORY CONTROL

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE