Tabel en nomogram voor het aflezen van jaarlijkse groeipercentages van grafieken op semi-logaritmisch papier

Summary A table and a nomogram are given to find the growth rate of a regression line drawn on so-called semi-logarithmic graph paper. The growth rate is determined by: a) the slope of the regression line, b) the length ratio between the logarithmic and the metric unit, in other words, the number of years on the time axis (if a year is the time unit) corresponding in length to one cycle on the logarithmic axis (say, 1 to 10, or 100 to 1000). With an example, the use of the table and nomogram is explained.     

Tabel en nomogram voor het aflezen van jaarlijkse groeipercentages van grafieken op semi-logaritmisch papier

Summary  A table and a nomogram are given to find the growth rate of a regression line drawn on so-called semi-logarithmic graph paper. The growth rate is determined by: a) the slope of the regression line, b) the length ratio between the logarithmic and the metric unit, in other words, the number of years on the time axis (if a year is the time unit) corresponding in length to one cycle on the logarithmic axis (say, 1 to 10, or 100 to 1000). With an example, the use of the table and nomogram is explained.     

Een nomogram voor betrouwbaarheidsgrenzen van quantielen en overschrijdingskansen bij normaal verdeelde grootheden

A nomogram for confidence intervals and exceedance probabilities.
In this paper two problems are considered regarding the probability β that an observation on a normally (μ, σ²)-distributed random variable exceeds a given value W:

If μ and σ² are unknown, the two problems are as follows:
1)if Wis given, to determine a confidence interval for β and
2)if β is given, to determine a confidence interval for W.
For these two essentially equivalent problems graphs are given from which the confidence intervals can be determined. The graphs are given in terms of:

and are based on an approximation for the distribution of x¯ +k s .     

Maxima voor de eenzijdige overschrijdingskans en voor de grootte van de gemiddelde overschrijding bij discontinue en continue, eentoppige verdelingen

The well-known inequality of Bienaymé-Tschébyschef (for short B-T), generalized by Camp and Meidell (for short C-M) for continuous, unimodal distributions gives specific limits for total probabilities outside the ± to limits.
In many cases however, especially in the field of industrial applications we are interested only in the probability of one tail of the distribution, which of course must be smaller than the limits given by the B-T and C-M formula.
For these cases the maximum probability of surpassing the to limit on one side equals under B-T conditions and under C-M conditions instead of the two-sided values of 1/t² and 47/9 · 1/t² respectively (cf e.g. Uspensky: "Introduction to mathematical probability", 1937, p. 198) These results set upper limits for the value of

Alternatively we may also set an upper limit for the integral

which measures in terms of σ the average amount by which the limit + tσ is exceeded. This problem is also discussed and under C-M conditions an upper limit

is derived.
Some practical applications of these results are considered.     

Mogelijkheden en moeilijkheden bij het toepassen van de sequentietest

Summary  (Possibilities and Difficulties in Applying Sequential Sampling)
The application of sequential sampling schemes may be much simplified by chasing H and b ( in Barnard's notation ) in such a way that H/(b+ 1) = integer and (b + 1) = integer. A decision to accept can now be taken only after each (b + 1) items and samples of (b + 1) items may therefore be chosen from the batch.
A handicap of H/(b + 1) points is now allowed to the batch. One point is added to the score whenever no defectives are found in the sample; 0, 1, 2, points are subtracted whenever respectively 1, 2, 3. … defectives are found in a sample. The acceptance boundary is 2H/(b + 1) points; the rejection boundary is 0 points.
For given 1 in 20 producer's and consumer's risk points ( p ₁% and p ₂%), values of H and b are given in table 1 and fig. 3.     

Enkele opmerkingesn over de mogelijkheid van toepassing van mathematisch-statistische methoden bij tijdstudieproblemen en in het bijzonder bij het Bedaux-systeem

Summary  (Some remarks on the possibility of applying mathematical-statistical methods to time-study problems and in particular to the Bedaux system.)
Time and motion study are based on observations of the workman's movements and an estimation of his efficiency.
The time spent on a certain action in mass-production is not constant but shows a considerable variation, due to various causes. The time-study-man who investigates this action and expresses it in a rate, causes still more variations by certain inaccuracies in using the stopwatch and calculating the rate itself. Considered from a statistical point of view, these cumulating variations result in a standard-error in the calculated rate; this gives rise to some interesting phenomena.
A more statistical approach tot the whole problem is shown in this article to be possible.
In the discussion, the application of the Beaux-system is assumed, but the conclusions hold good for all time study systems.     

Statistisch onderzoek van contrôle-analyse cijfers: (De verdeling van het droge stofgehalte van het brood tijdens de tweede wereldoorlog)

Summary  (Statistical investigation of the distribution of data for the solids of bread (in loaves analysed in the Food Inspection Laboratory in Amsterdam))
The distributions of the data of the solids of bread as analysed during the years of the war are investigated. The means and the standard deviations are calculated, also χ², kurtosis and skewness supposing the distributions to be normal. An example of calculation is given in table I. Actual numbers for different years are given in table II and in table III. The distributions were tested on normality because former investigations showed that the distribution of under survey prepared loaves did not deviate significantly from the normal.
It is found that generally the investigated distributions cannot be regarded as normal. Though symmetric they show leptokurtosis and the χ²-test for the goodness of fit of normal equation gives values of P 0,01 (or a little more). Similar distributions were found by Clancey¹⁾ in his investigation of numbers of chemical analyses of industrial products (about 10% of the distributions showed this shape, some 10% were truncated leptokurtic curves) and by us for the fat percentage of meals from the governmental eating-houses. The distributions are represented on probability-paper. This way of representing results gives a clear view of the variations of the mean and the standarddeviation in the course of the years (fig. 1). The deviations of the shape of the normal straight line on probability paper by special causes is investigated (fig. 3, fig. 4, fig. 5, fig. 6 to be compared with fig. 2). With this "spectrum" of possibilities of deviations from the normal distribution in mind the special cause for the leptokurtic shape in our special case has been discussed.     

Over de spreiding bij het droge-stofonderzoek van brood

The accuracy of the determination of the amount of solids in bread.
Of a loaf with a nominal weight of 800 grams only about 480 grams remains after complete drying. This so-called 'amount of solids in bread' is regularly checked by samples. From a batch of loaves a group of at least 5. but usually more, are taken at random and weighed. From this group one is selected with a weight as nearly as possible equalling the average weight of the whole group; for two slices of this sample loaf the decrease in weight upon drying is determined in the laboratory, and is considered as representative for the entire batch.
The accuracy of these determinations is analysed on the basis of 35 samples which were investigated in 3 different laboratories. The standard error is estimated at 5 grams per loaf. The influence of various factors, such as the method of sampling which may be altered in many ways, is briefly considered, while in a final section the results obtained are discussed from a practical point of view.     

De bewerking van de resultaten van veldproeven door herleiding van de opbrengstcijfers in beide richtingen van het proefveld

Summary  (The treatment of the results of field experiments by reducing the yields in two directions)
Ir J. J. Dijkveld Stol has shown that good results have been obtained by reducing the yields of field experiments both in columns and in rows.
The mathematical foundation of this method is discussed in the preceding article and it is shown, that the method gives good results if the same supposition may be made as necessary for the application of the methods of Fisher, Knut Vik and the method of the differences.
The variance of Dijkveld Stol's method is identical with Fisher's error variance.     

Eenvoudige mathode voor het interpreteeren van statistisch contröle-materiaal

A simplified method for the working out of statistical control data by means of a suitable abacus is described and explained. A practical example for a population corresponding to the Normal (Gaussian) Curve is given. This method can also be applied to Frequency Distributions not obeying the Law of Gauss, provided they can be represented by a known mathematical function.
A simplified method for the compilation of statistical data concerning weights by means of a balance provided with numerators, is described.
The possibility of the application of a system of numerators to automatic dosing machines is discussed, by means of which control, based on random sampling, could be replaced by weighing dosages individually.     

Typologie van den statisticus Hoe men hem ziet en hoe hij

In the popular conception the statistician is a man who collects and groups figures which he publishes in the form of tables and graphs. The real statistician in the modern sense of the word, i.e. the man who does not collect the material but analyses it and draws his conclusions from it, is as yet practically unknown to the general public. It is desirable that more publicity should be given to the characteristic qualities required for this calling, so that those most fitted for i may be drawn towards it.
The aspiring statistician should be taught to think in statistical terms and not along functional or determinist lines, as the mathematician does. The statistician is only interested in individual phenomena insofar as they enable him to draw conclusions of a more general character out of a certain amount of isolated cases. A true sense of proportion is very important as it plays a major part in the framing, the working out and the conclusions to be drawn from the solution of the problems. As the sphere of his activities is so extensive, the statistician should be able to adapt himself quickly to new situations.
Those who are endowed with these varying talents can rely on finding a very useful task as a statistician.     

Poisson-proces met interrupties, een waarschijnlijkheids-model voor het machinaal dunnen van bieten.

Starting from the assumption that {even in case of dense precision sowing), the occurence of beet plants in a row can be taken as a realisation of a Poisson proces, the influence of mechanical thinning is studied.
The distribution of the distance between two plants, originally exponential, is changed by mechanical thinning in a way, dependent on the lengths of the intervals a (the potential survivor-zone) and b (the length of the thinningblade).
The distribution of the distance between plants after mechanical thinning, is examined, and the "best" way of thinning, leading to the distribution of the distance between plants with the smallest variance, is derived.     

Een berekeningsmethode voor de logistische curve

Summary  " Simple estimation of the parameters of the logistic curve ."
By means of an appropriate transformation of the dependent variable Y _t into a simple function of Y _t, which depends only linearly on time, one of the parameters can be estimated in the usual way. A second transformation leads to the estimation of the two remaining parameters. As a numerical illustration two examples are presented.     

Een simpele grafische iteratiemethode voor het schatten van een betrekkingtussen kwantitatievestochastische variabelen.

A simple graphical iteration procedure for estimating a relation between quantitative stochastic variables.
For the estimation of a relation which will predict values of one stochastic variable from known values of a number of other ones, a simple graphical iteration procedure, applicable under rather general conditions, is demonstrated by means of an example. The method amounts to plotting the values of the dependent variable against one (or one pair) of the initial variables, after correction for the influences of the other initial variables as far as these have already been estimated. An approximation (or improved approximation) for the influence of the variable considered can then be made.     

Een berekeningsmethode voor de logistische curve

Summary “Simple estimation of the parameters of the logistic curve.” By means of an appropriate transformation of the dependent variable Y_t into a simple function of Y_t, which depends only linearly on time, one of the parameters can be estimated in the usual way. A second transformation leads to the estimation of the two remaining parameters. As a numerical illustration two examples are presented.     

THE BIAS OF THE MULTIPLIER MATRIX WHEN SUPPLY AND USE TABLES ARE STOCHASTIC

The literature on stochastic input–output (I–O) analysis has paid considerable attention to the bias in the Leontief inverse. This paper extends previous studies by assuming supply and use tables (SUTs rather than I–O tables or input coefficients matrices) to be stochastic. This is a natural starting point because SUTs have become the basic data sources for I–O applications. In a Monte Carlo simulation experiment, a given SUT is randomized in two different ways and the effects are determined for eight different multiplier matrices. The analysis is carried out for Spain, Italy, the Netherlands, Germany and Finland, using their SUTs for 2006. The findings indicate that, in general, biases are statistically significant but negligibly small. This corroborates earlier findings obtained for stochastic I–O tables.     

Polygonal designs with blocks of size k≤10

The use of polygonal designs is motivated by the desire to avoid the selection of contiguous units in a sample from an ordered finite population. However very little is known about polygonal designs that have block size 5 or more. We present new polygonal designs with blocks of sizes 5 through 10, including the first designs with block sizes 9 and 10. For block sizes 5 through 7, we identify, with one possible exception, all values for the number of varieties for which a polygonal design exists. Received January 2001     

Toespraak door de directeur van de Stichting "Kwaliteitsdienst voor de Industrie"

Adress of the Director of the Foundation Industrial Quality Service.
The increasing of productivity also has an important qualitative aspect, To promote the qualitative increase of productivity the "Kwaliteitsdienst voor de Industrie" (Industrial Quality Service) wants to organize courses through which the statistical quality control methods can for each separate branch of industry be made available to those who are able to apply these methods, but who cannot spare the time and the energy required to take fully note of the mathematical and statistical backgrounds.