## TTT function

### Description

There are several behaviors that the failure rate function of a random variable T can take. In this context, the graph of total test time (TTT curve) proposed by Aarset (1987) may be used for obtaining empirical behavior of the function failure rate.

### Usage

TTT(x, lwd = 2, lty = 2, col = "black", grid = TRUE,...)


### Arguments

 x Data vector; lwd Thickness of the TTT curve. The argument lwd must be a nonnegative real number; lty The argument lty modifies the style of the diagonal line chart TTT. Possible values are: 0 [blank], 1 [solid (default)], 2 [dashed], three [dotted], 4 [dotdash], 5 [longdash], 6 [twodash]; col Color used in the TTT curve; grid If grid = FALSE graphic appears without the grid; ... Other arguments passed by the user and available for the function plot. More details in par.

### Note

The graphic TTT may have various forms. Aarset (1987) showed that if the curve approaches a straight diagonal function constant failure rate is adequate. When the curve is convex or concave the failure rate function is monotonically increasing or decescente respectively is adequate. If the failure rate function is convex and concave, the failure rate function in format U is adequate, otherwise the failure rate function unimodal is more appropriate.

The TTT curve is constructed by values r/n and G(r/n), wherein

 G(r/n) = \frac{[\sum_{i=1}^{r} T_{i:n} + (n-r)T_{r:n}]}{\sum_{i=1}^{n}T_{i:n}}, r = 1, \ldots, n, T_{1:n} = 1, \ldots, n. 

### Author(s)

Pedro Rafael Diniz Marinho (pedro.rafael.marinho@gmail.com);

Marcelo Bourguignon (m.p.bourguignon@gmail.com).

### References

Aarset, M. V. (1987). How to identify bathtub hazard rate. IEEE Transactions Reliability, 36, 106-108.

### Examples

data(carbone)
TTT(carbone, col = "red", lwd = 2.5, grid = TRUE, lty = 2)