Probability: Concept and Its Application

After reading this article you will learn about the concept of probability and its application.

Concept of Probability:

The basic idea in the theory of probability is the law of large numbers. Probability concept states that certain mass phenomenon have a tendency towards regularity in behaviour i.e. if sample is drawn from the mass of universe (population) without any bias, the sample is quite likely to display those characteristics that are found in the whole mass. Therefore, inferences drawn from the study of such a sample can be relied upon as being representative of the ‘whole mass’.

Universe:

‘Universe’ means a group of items from which a sample is drawn.

Sampling enables us to draw conclusions about a mass of items based upon the careful study of a small number of items. This number of items is known as ‘sample’. The chief applica­tion of the theory of probability is in Statistical Quality Control.

Inspection of each individual item of production to determine whether it meet specifications or not may be too expensive and monotonous. Therefore, samples are regularly taken at random from a lot and information from the study of samples tell us the extent to which specifications are being met.

Application of Probability:

1. Probability of Finding Defectives in a Sample:

Let us take a lot size of 1000 units out of which 100 are known to be defective. Now, if a sample of n units is taken and if it is used to study the true character of the lot, i.e. how many units are defective, we expect to receive after inspection 0.9 n good units and 0.1 n defective.

Therefore, the probability that a unit taken from the lot at random would be a good one is 0.90 and that it would be defective is 0.10. Similarly the chances that the two units taken in succession would be all right are 0.90 x 0.90 or the chances that three good units in a lot would be 0.90 x 0.90 x 0.90, i.e. (0.90)³. So in this way we can conclude that the probability in a sample of n units will have no defective is given by qⁿ.

Here q = actual proportion of good units in the lot.

n = sample size.

2. Normal Curve and Standard Deviation:

Frequency Distribution can be applied in following fields of Quality Control:

1. To determine performance of incoming material.

2. To determine the amount of variation from that expected.

3. To determine the performance of new product to facilitate its design.

4. To determine the operating accuracies of machine tools and other processing equipment’s.

5. To examine the difference between the dimensional characteristics of parts produced by two machine tools or two moulds.

6. To examine the accuracy of fits between mating parts.

7. To determine the effect of tool wear on a machine tool.