frbs {bs} | R Documentation |
Failure rate function for the BSD with shape parameter alpha and scale parameter beta.
frbs(x, alpha = 1, beta = 1)
x |
Vector of quantiles. |
alpha |
Shape parameter. |
beta |
Scale parameter. |
One of the useful indicators in lifetime analysis is the hazard function (h.f.), which is defined by
h_T(t) = frac{f_T(t)}{1- F_T(t)},, t > 0,, 0<F_T(t)<1,
where f_T(cdot) and F_T(cdot) are the pdf and cdf, respectively; see e.g. Johnson, Kotz, and Balakrishnan (1994, p. 640). The behavior of h_T(t) allows one to characterize the aging of the units. For example, if the failure rate is increasing (IFR class), then the units age with time. If h_T(t) is decreasing (DFR class), then the units improve in performance with time. Finally, if h_T(t) is constant, then the lifetime distribution is necessarily the exponential one.
Another aging indicators are the following:
The failure rate average (FRA) of T is given by
FRA(t) = frac{H_T(t)}{t} = frac{int^{t}_{0} h_T(t),dt}{t},, t>0,
where H_T(t) is the cumulative hazard function. An analysis for FRA(t) on t permits to obtain the IFRA and DFRA classes.
The survival function (s.f.) and the conditional survival of T are defined by
R_T(t) = 1- F_T(t) quad {rm and} quad R_T(t|x) = frac{R_T(t+x)}{R_T(x)},, t >0,, x> 0,, R_T(cdot) > 0,
respectively, where F_T(cdot) is the cdf of T. Similarly to h_T(t) and FRA(t), the distribution of T belongs to the new better than used (NBU), exponential, or new worse than used (NWU) classes, when R_T(t|x) < R_T(t), R_T(t|x) = R_T(t), or R_T(t|x) > R_T(t), respectively.
Failure rate function for the BSD.
Víctor Leiva <victor.leiva@uv.cl>, Hugo Hernández <hugo.hernande@msn.com>, and Marco Riquelme <mriquelm@ucm.cl>.
Hoyland, A. and Rausand, M. (1994). System Reliability Theory. John Wiley and Sons. N. Y.
## Reliability indicators: ## Reliability function rfbs(3,0.5,1.0) ## Conditional reliability function crfbs(3,0,0.5,1.0) ## Conditional reliability function (age component=0) crfbs(3,x=0,0.5,1.0) ## Conditional reliability function (age component=0) crfbs(3,x=2,0.5,1.0) ## failure rate frbs(3,0.5,1.0) ## failure rate average frabs(3,0.5,1.0)