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The results of inspection of samples of a product taken over the past 5 days are given below. Sample size for each day has been 100:

Day        1             2             3             4             5

Defectives           2             6             14           3             7

1. Determine the UCL for this chart
2. Determine the LCL for this chart
3. Is this process in control?

Answer 1

number of samples m=					5.00
sample size n=					100.00
total number of units =mn=					500.00
number of defects d =					32.00
hence non conforming fraction p̅=d/(mn)=					0.0640
control line (CL) = p̅=					0.0640
upper control limit(UCL) =p̅+3*(√(p̅(1-p̅)/n)=					0.1374
lower control limit(LCL) =max(0,p̅-3*(√(p̅(1-p̅)/n))=					0.0000

(Note: for np chart: upper control limit =13.74 and lower control limit =0.00)

No ,since proportion of defectives for day 4 (0.14) falls outside the control limits