Thorndike nomogram
The Thorndike nomogram is a two-dimensional diagram of the Poisson distribution . In this nomogram , the values of the distribution function (this is the probability sum) can be approximately determined graphically. It is named after Frances Thorndike who developed this nomogram in 1926. In October 1926, the Thorndike nomogram was published under the title " Application of Poisson's Probability Summation ".
Practical meaning
The most important applications of the Thorndike nomogram are in quality assurance . Especially in industrial series production, the Thorndike nomogram is an important tool for assessing the quality situation, for sampling and for control card technology. The Thorndike nomogram enables simple solutions to problems of the type "number of defects per unit". A typical problem of this kind would be the number of solder defects per television set. What is less well known is that such problems often occur outside of technology or industry, for example the number of knotholes per table top or the number of pigment spots per patient.
Advantages and disadvantages
The advantage of the Thorndike nomogram is that you do not have to be a mathematician to use it, nor do you have to have any special theoretical knowledge of statistics. Results can only be achieved very easily in a few seconds with the nomogram printed on paper (or a photocopy) plus pencil and ruler. A small disadvantage is that the results only have an approximate accuracy - the small deviations from the mathematically exact values, however, are mostly of no relevance in practice.
Alternatives
- For small numbers, the Poisson distribution can be calculated using a formula.
- For larger numbers, you can use pocket calculators or, even better, programmable pocket calculators.
- The values can be read from certain statistical tables.
- There are special computer programs for calculating the Poisson distribution.
Formula symbols in the Thorndike nomogram
The formula symbols used in quality assurance differ in part from the formula symbols in specialist mathematical books. The following notation is common in quality assurance:
- The distribution function has the symbols G . The more understandable name of the distribution function is probability sum - this is the probability of finding up to x errors in a sample. The term “up to x errors” becomes clearer when one imagines that e.g. B. up to 2 knotholes in a table top would still be permitted. The furniture specialist is then not interested in the probability that there are exactly 2 knotholes in the tabletop - they are interested in the probability that there are up to 2 knotholes in the tabletop and this is equal to the sum of the probabilities for 0 knotholes, for 1 knothole and for 2 knotholes - just up to 2. The numerical values of the distribution function G can be read on the scale on the left edge of the Thorndike nomogram. Attention: The scale is not shown in percent (%). A probability sum of 1% results in a value of 0.01 on the scale.
- The expected value for the number of errors in the sample has the symbol µ. Another expression for this expected value is the “mean number of errors per sample”. The scale for µ is at the bottom of the Thorndike nomogram. The scale for the mean number of errors in the sample µ ranges from 0.2 to 30 for most of the Thorndike nomograms.
- The number of errors in the sample has the symbol x . The number of errors in the sample can logically only assume natural numbers (including zero). Up to x = 20 there is a line in the Thorndike nomogram for each x value. From x = 20 in steps of two, later in even larger steps. Attention: the x-values are below the lines!
functionality
You take
- Printed or copied Thorndike nomogram
- Transparent ruler, length approx. 25 cm
- Pointed pencil HB
- Eraser for corrections
- Front / top lighting
- The µ value is marked on the scale at the bottom of the Thorndike nomogram
- Draw a thin, straight line with the pencil from the µ-value perpendicular to the line of the given x-value
- From the intersection of the pencil line with the x line, draw a thin pencil line horizontally to the left up to the G scale.
- The value of the distribution function, i.e. the probability sum, can be read off at the point of intersection with the G-scale.