Het gebruik van toevalscijfers.
Authors: Enters J. H. 
Published: April 2008

The Use of Random Numbers

A table of random numbers gives a sequence of numbers in which no order can be detected; the probability of finding a certain number respectively a certain combination of numbers in a specified place in the table is the same for all numbers respectively combinations of numbers.

Tables of random numbers have been constructed by using other tables (I) or by using a mechanical device (see [2] [4]).

The randomness of these tables can be tested by means of the %2 test of goodness of fit.

In applying statistical procedures it is often essential that the required sample is taken at random from a given collection.

In applying the ratio‐delay method in making time studies it is necessary to make „snap readings” of a group of machines at random moments. This can be done by numbering the consecutive time intervals of the period in which the snap readings will be taken, choosing the required number of intervals from the available intervals by means of a table of random numbers and making observations at the beginning of each interval.

Certain properties of industrial sampling schemes may be determined experimentally by constructing, by means of random sampling numbers, lots containing a wanted percentage defectives.

A lot containing e.g. 4 % defectives is constructed by regarding pairs of numbers in the table as items in the lot and denoting the pairs 01 — 02 — 03 — 04, which are expected to occur 4 times in every 100 pairs, as „defectives”. In this way samples of n items, can easily be taken from such a lot. An application of this method is given in [7] where the sample size distribution when applying sequential tests, is discussed.

In the manner described in [I] a continuous population of a specified mathematical form can be constructed.

This has been useful when a sampling scheme had to be developed for testing the duration of life of the carbon brushes of small electric motors.

Significance tests for determining a lower boundary for the median of a distribution have been developed by Walsh [9] which seemed to be appropriate in the case.

A lower boundary for the median of the universe can for samplesize 12 be determined from the first 6 items in the sample which „end their life” (see table 2). This method however can only be applied if the probability distribution from which the samples are taken is symmetric. In the case under consideration this distribution might be supposed to be bell‐shaped but symmetry was not assured.

In order to test the outcome of min [1/2(x1+ x6), 1/2 (x3+ x4)] as a lower boundary for the median and max. [1/2 (x7+ x12), 1/2 (x9+ x10)] as an upper boundary for the median duration of life in case the universe is decidedly skew, a hundred samples of 12 items were taken from the universe depicted in fig. 1.

The frequency distribution of the 1200 items chosen in this way is given in fig. 2. In the figs. 3 and 4 frequency distributions are given of the lower and upper boundaries estimated by means of the above mentioned formules.

The test chosen has, according to Walsh, a two sided significance level of 0.011. It appeared from the sampling experiment that the estimation of the lower boundary was wrong in 2% of the cases while the upper boundary was never lower than the median of the universe.

This divergence was so small that the test could without difficulties be applied to the problem in question.