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1 1 $begingroup$ Suppose we are given some small set of data on bundles of electrical wires and increasing voltages run through them, and we note how many of the individual wires fail. So for example, a large data set we have 6 observations, for each 6, there is $w_{i}$ number of wires, voltage $v_{i}$ and $f_{i}$ of the wires fail. And suppose we are given some of the information for example, ( note that each sample has increased voltage and we see increased proportion of failed wires). $w_{1}=14$ and $f_{1}=4$ $w_{2}=13$ and $f_{2}=4$ $w_{3}=7$ and $f_{3}=3$ $w_{4}=10$ and $f_{4}=5$ $w_{5}=12$ and $f_{5}=7$ $w_{6}=20$ and $f_{6}=13$ ie we have a parameter space such that ( $t$ is the proportion that fail) ${t_{i}: t_{1} lt t_{2} lt t_{3} lt .. lt t_{6} le 1}$ Assuming a flat prior o