Reliability (version 0.0-2)

moranda.geometric: Maximum Likelihood estimation of mean value function for Moranda-Geometric model

Description

moranda.geometric computes the Maximum Likelihood estimates for the parameters D and theta of the mean value function for the Moranda-Geometric model.

Usage

moranda.geometric(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 Moranda-Geometric model.

tol

the desired accuracy

Value

• A list containing following components:
• rho
  Maximum Likelihood estimate for rho
• theta
  Maximum Likelihood estimate for theta

Details

This function estimates the parameters D and theta of the mean value function for the Moranda-Geometric model. With Maximum Likelihood estimation one gets the following equation, which have to be minimized, to get phi. This is $$\frac{\sum_{i = 1}^{n} i \phi^i t_i}{\sum_{i = 1}^{n} \phi^i t_i} - \frac{n + 1}{2} = 0.$$ The solution of these is then put in in the following equation in order to get D $$D = \frac{\phi n}{\sum_{i = 1}^{n} \phi^i t_i}.$$ 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.

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

moranda.geometric.plot, mvf.mor

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)
      
moranda.geometric(t)