Non-Parametric Tolerance Limits
Murphy, R. B.
Ann. Math. Statist., Tome 19 (1948) no. 4, p. 581-589 / Harvested from Project Euclid
In this note are presented graphs of minimum probable population coverage by sample blocks determined by the order statistics of a sample from a population with a continuous but unknown cumulative distribution function (c.d.f.). The graphs are constructed for the three tolerance levels .90, .95, and .99. The number, $m$, of blocks excluded from the tolerance region runs as follows: $m$ = 1(1)6(2)10(5)30(10)60(20)100, and the sample size, $n$, runs from $m$ to 500. Thus the curves show the solution, $\beta$, of the equation $1 - \alpha = I_\beta(n - m + 1, m)$ for $\alpha = .90, .95, .99$ over the range of $n$ and $m$ given above, where $I_x(p, q)$ is Pearson's notation for the incomplete beta function. Examples are cited below for the one- and two-variate cases. Finally, the exact and approximate formulae used in computations for these graphs are given.
Publié le : 1948-12-14
Classification: 
@article{1177730154,
     author = {Murphy, R. B.},
     title = {Non-Parametric Tolerance Limits},
     journal = {Ann. Math. Statist.},
     volume = {19},
     number = {4},
     year = {1948},
     pages = { 581-589},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177730154}
}
Murphy, R. B. Non-Parametric Tolerance Limits. Ann. Math. Statist., Tome 19 (1948) no. 4, pp.  581-589. http://gdmltest.u-ga.fr/item/1177730154/