mvf.ver.quad: Mean value function in the quadratic form for the...

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

Description

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

Usage

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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

Details

This function gives the values of the mean value function in the quadratic form for the Littlewood-Verall model, this is written as

μ(t) = 3 v_1 (Q_1 + Q_2),

where

v_1 = \frac{(ρ - 1)^{1 / 3}}{(18 θ_1)^{1 / 3}},

v_2 = \frac{4 θ_0^3}{9 (ρ - 1)^2 θ_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 θ_1 \neq 0.

Value

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

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

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

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)

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)

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