musa.okumoto: Maximum Likelihood estimation of mean value function for...

In Reliability: Functions for estimating parameters in software reliability models

Description

musa.okumoto computes the Maximum Likelihood estimates for the parameters theta0 and theta1 of the mean value function for the Musa-Okumoto model.

Usage

musa.okumoto(t, init = c(0, 1), tol = .Machine$double.eps^0.25)

Arguments

t	time between failure data
init	initial values for Maximum Likelihood fit of the mean value function for the Musa-Okumoto model.
tol	the desired accuracy

Details

This function estimates the parameters theta0 and theta1 of the mean value function for the Musa-Okumoto model. With Maximum Likelihood estimation one gets the following equation, which have to be minimized, to get theta1. This is

\frac{1}{θ_1} ∑_{i = 1}^{n} \frac{1}{1 + θ_1 t_i} - \frac{n t_n} {(1 + θ_1 t_n) \log(1 + θ_1 t_n)} = 0.

The solution of these is then put in in the following equation in order to get theta0

θ_0 = \frac{n}{\log(1 + θ_1 t_n)}.

Where t is the time between failure data and n is the length or in other words the size of the time between failure data.

Value

A list containing following components:

theta0	Maximum Likelihood estimate for theta0
theta1	Maximum Likelihood estimate for theta1

Author(s)

Andreas Wittmann andreas\[e-mail]

References

J.D. Musa, A. Iannino, and K. Okumoto. Software Reliability: Measurement, Prediction, Application. McGraw-Hill, 1987.

Michael R. Lyu. Handbook of Software Realibility Engineering. IEEE Computer Society Press, 1996. http://www.cse.cuhk.edu.hk/~lyu/book/reliability/

See Also

musa.okumoto.plot, mvf.musa

Examples

# time between-failure-data from DACS Software Reliability Dataset
# homepage, see system code 1. Number of failures is 136.
t <- c(3, 30, 113, 81, 115, 9, 2, 20, 20, 15, 138, 50, 77, 24,
       108, 88, 670, 120, 26, 114, 325, 55, 242, 68, 422, 180,
       10, 1146, 600, 15, 36, 4, 0, 8, 227, 65, 176, 58, 457,
       300, 97, 263, 452, 255, 197, 193, 6, 79, 816, 1351, 148,
       21, 233, 134, 357, 193, 236, 31, 369, 748, 0, 232, 330,
       365, 1222, 543, 10, 16, 529, 379, 44, 129, 810, 290, 300,
       529, 281, 160, 828, 1011, 445, 296, 1755, 1064, 1783, 
       860, 983, 707, 33, 868, 724, 2323, 2930, 1461, 843, 12,
       261, 1800, 865, 1435, 30, 143, 108, 0, 3110, 1247, 943,
       700, 875, 245, 729, 1897, 447, 386, 446, 122, 990, 948,
       1082, 22, 75, 482, 5509, 100, 10, 1071, 371, 790, 6150,
       3321, 1045, 648, 5485, 1160, 1864, 4116)
      
musa.okumoto(t)

Example output

$theta0
[1] 11.93933

$theta1
[1] 0.9999431

Reliability documentation built on May 1, 2019, 9:22 p.m.