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#statistics #SQC #control #chart #npchart #problem #solution #free #tutorial
Control Charts for Attributes i.e. for for presence or absence of any characteristic. It is based only a 'yes-or-no' type of conclusion based on whether the item complies with the specification.
P - Chart, np - Chart and C - Chart are the control charts for attributes.
For this purpose we need to define 'defect' in the item - i.e. a presence or absence of a particular characteristic. Then we just need to draw samples and count the number of defective units in each sample.
Control Chart for Number of Defectives, i.e. np - Chart
Generally, the data for constructing p-Chart are used to construct np-Chart subject to the following two conditions:
(1) The size of all the samples MUST BE equal.
(2) The range of the number of defective units of all sample should be such that both the least number of defective units and the highest number of defective units are suitable to plot on a normal graph paper, on suitable and proper scale.
If both of the above conditions are satisfied, then it is easier to construct np-Chart than constructing p-Chart for the same data and that too without affecting the final conclusion, i.e. even if we construct np-Chart, instead of p-Chart, the conclusion remains the same as it would be if we had constructed p-Chart.
Steps
i. p(bar) = Σnp / Σn
ii. np(bar) = (n)(p(bar))
UCLnp = np(bar) + 3 √ np(1 - p)
CLnp = np(bar)
LCLnp = np(bar) - 3 √ np (1 - p)
Problem/Case:
An inspection of 10 samples of size 400 each from 10 lots revealed the following number of defective units: 17, 15, 14, 26, 9, 4, 19, 12, 9 and 15. Construct a suitable control chart and state your conclusion about the process.
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16 сен 2024
