Description Usage Arguments Details Value Author(s) References See Also Examples
musa.okumoto
computes the Maximum Likelihood estimates for the parameters theta0
and theta1
of the mean value function for the Musa-Okumoto model.
1 | musa.okumoto(t, init = c(0, 1), tol = .Machine$double.eps^0.25)
|
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 |
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.
A list containing following components:
theta0 |
Maximum Likelihood estimate for |
theta1 |
Maximum Likelihood estimate for |
Andreas Wittmann andreas\_wittmann@gmx.de
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/
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | # 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)
|
$theta0
[1] 11.93933
$theta1
[1] 0.9999431
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