Reliability (version 0.0-2)

mvf.ver.quad: Mean value function in the quadratic form for the Littlewood-Verall model

Description

mvf.ver.quad returns mean value function in the quadratic form for the Littlewood-Verall model.

Usage

mvf.ver.quad(theta0, theta1, rho, t)

Arguments

theta0

parameter value for theta0

theta1

parameter value for theta1

rho

parameter value for rho

t

time between failure data

Value

• The mean value function in the quadratic form for the Littlewood-Verall model.

Details

This function gives the values of the mean value function in the quadratic form for the Littlewood-Verall model, this is written as $$\mu(t) = 3 v_1 (Q_1 + Q_2),$$ where $$v_1 = \frac{(\rho - 1)^{1 / 3}}{(18 \theta_1)^{1 / 3}},$$ $$v_2 = \frac{4 \theta_0^3}{9 (\rho - 1)^2 \theta_1},$$ $$Q_1 = [t + (t^2 + v_2)^{1 / 2}]^{1 / 3}$$ and $$Q_2 = [t - (t^2 + v_2)^{1 / 2}]^{1 / 3}.$$ Further there is a verifying if the parameter theta1 satisfy the assumptions for the Littlewood-Verall model. So the paramter theta1 should net be equal zero, in equation $\theta_1 \neq 0.$

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

littlewood.verall, littlewood.verall.plot, mvf.ver.lin

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)

lit.par1 <- littlewood.verall(t, linear = TRUE)$theta0
lit.par2 <- littlewood.verall(t, linear = TRUE)$theta1
lit.par3 <- littlewood.verall(t, linear = TRUE)$rho

mvf.ver.quad(lit.par1, lit.par2, lit.par3, t)