By K. A. Brownlee
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Additional info for Industrial Experimentation
E. that there is less variability in problem is The test of significance for this type of their product. as Bartlett s test. known generally in the table below represents the value of the property x of six consecutive batches off machines 1 to 10. The figures in column 2 actually are originally each had transformed by shifting the zero to simplify the arithmetic Column 2 : 2200 added on to them. a 2 S where denotes -x) S(x), S(x ), ((x)) /6 and S(x summation, are merely the steps in calculating the variances for the ten machines.
Is not perfectly reproducible and gives rise to a variance a I in the final product. For stage B of the process, each 300 Ib. batch is split into three 100 Ib. units and operation B performed on these units. Operation B is also not perfectly repro ducible and gives rise to a variance a | in the final product. The problem consists of observing the total variance in the final product and analysing it into its two components a^ and Having done this, we will then be able to decide which is the part of the process which requires the more careful control in order to (b) <TB- reduce the total variability.
The incident can be of any type (we are con sidering spontaneous ignitions in a manufacturing process) and can include the occurrence of defective articles in their mass production. In this latter case we is must pay due regard to the proviso that the probability of obtaining an incident any one instant (in the terminology of this example of obtaining a defective on In practice the approximation is good selecting any particular article) is small. enough if the percentage defective is less than 10%.