# Reliability engineering design values from tests AS/NZS1170

To get design values (the strength of something, for example) designing to Australian/ New Zealand loading code you do $n$ tests and estimate the coefficient of variation of your parent population, $V_{sc}$,). With that, you get $k_t$ from lookup table below and divide you lowest test value(arguably ought to be the mean?) by $k_t$. I have tried to work out what these $k_t$ values are - where they come from. Getting nowhere.

I think it 'works' on the principle that you want $\gamma$ confidence that the estimated strength, $R_{p,cover}$, covers the parent population $p$-fractile, $R_p$, so $P(R_{p,cover} < R_p) = \gamma$ NOTE: I am precising from an old uni text book!

So, assuming that the parent population mean equals test population mean, $\bar{R}$

Parent population Standard deviation, $s$

COV, $V_{sc}=s/\bar{R}$

$R_{p,\gamma}=m+\kappa(p,\gamma).s$, so $x_{p}=\bar{R}(1+\kappa(p,\gamma).V_{sc})$, so:

$k_t = \bar{R}/R_{p,\gamma} = \frac{1}{1+\kappa(p,\gamma).V_{sc}}$

The problem I am having is what an earth $\kappa(p,\gamma)$ is, to match the values in the lookup table. I do not know what $p$ and $\gamma$ are, though I have an inkling that they are 0.05 and 95% respectively.

I am working in R, gist here