Statistical Quality Control - 9 P - Chart of Percentages and Unequal Sample Size Part-1

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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 Fraction Defectives' or 'Proportion of Defectives i.e. P - Chart
Steps
1) Calculation of fraction defection of each of the samples.
p = (No. of defective units in the sample)/(Sample size)
Or p = np/n
2) Calculation of average fraction defective
P(bar) = Σnp/Σn
3) Calculation of control limits
UCLP = P(bar) + 3√[P (1 - P)/n]
CLP = P(bar)
LCLP = P(bar) - 3√[P (1 - P)/n]
In case where the samples are of different size, the value of ‘n’ for calculation of the control limits is taken as average sample size of all the samples.
Average sample size = Σn / No. of samples (N)
For P - chart for percentage of defectives
p = (np/n) x 100
P(bar) = (Σnp / Σn)X100
Problem/Case:
The following figures give the number of defective units in 10 samples each of different sample size:
Sample No.: 1 2 3 4 5 6 7 8 9 10
sample Size: 2000 1500 1400 1350 1250 1760 1875 1955 3125 1575
Number of
Defective units: 425 430 216 341 225 322 280 306 337 305
Construct a suitable control chart and state your conclusion about the process.
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