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

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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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\_wittmann@gmx.de

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

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# 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.