For given values of m, alpha, and P, this function solves the necessary sample size such that the
r-th (or (n-s+1)-th) order statistic is the [100(1-alpha)%, 100(P)%] lower (or upper) tolerance
limit (see the Details section below for further explanation). This function can also report all combinations of order
statistics for 2-sided intervals.
np.order(m, alpha = 0.05, P = 0.99, indices = FALSE)If indices = FALSE, then a single number is returned for the necessary sample size such that the
r-th (or (n-s+1)-th) order statistic is the [100(1-alpha)%, 100(P)%] lower (or upper) tolerance
limit. If indices = TRUE, then a list is returned with a single number for the necessary sample size and a matrix
with 2 columns where each row gives the pairs of indices for the order statistics for all permissible [100(1-alpha)%, 100(P)%]
2-sided tolerance intervals.
See the Details section below for how m is defined.
1 minus the confidence level attained when it is desired to cover a proportion P
of the population with the order statistics.
The proportion of the population to be covered with confidence 1-alpha with the order statistics.
An optional argument to report all combinations of order statistics indices for the upper and lower limits
of the 2-sided intervals. Note that this can only be calculated when m>1.
For the 1-sided tolerance limits, m=s+r such that the probability is at least 1-alpha that at least the
proportion P of the population is below the (n-s+1)-th order statistic for the upper limit or above the r-th order statistic
for the lower limit. This means for the 1-sided upper limit that r=1, while for the 1-sided lower limit it means that s=1.
For the 2-sided tolerance intervals, m=s+r such that the probability is at least 1-alpha that at least the
proportion P of the population is between the r-th and (n-s+1)-th order statistics. Thus, all combinations of r>0 and
s>0 such that m=s+r are considered.
Hanson, D. L. and Owen, D. B. (1963), Distribution-Free Tolerance Limits Elimination of the Requirement That Cumulative Distribution Functions Be Continuous, Technometrics, 5, 518--522.
Scheffe, H. and Tukey, J. W. (1945), Non-Parametric Estimation I. Validation of Order Statistics, Annals of Mathematical Statistics, 16, 187--192.
nptol.int
## Only requesting the sample size.
np.order(m = 5, alpha = 0.05, P = 0.95)
## Requesting the order statistics indices as well.
np.order(m = 5, alpha = 0.05, P = 0.95, indices = TRUE)
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