Proportion of defectives, Pbar
= Total number of defectives / ( Sample size x Number of sample)
= ( 4 + 7 +3 + 5+5+5 +5 +4 +2 +12)/ ( 50 x 10 ) = 52/ 500 = 0.104
Sample size = n = 50
Z value for 99.73 % variation = NORMSINV ( 0.9973) = 2.7821
Upper control limit for P chart, UCLp
= Pbar + Zvalue x Square root ( Pbar x ( 1 – Pbar)/n)
= 0.104 + 2.7821 x Square root ( 0.104 x 0.896 /50)
= 0.104 +2.7821 x 0.0431
= 0.104 + 0.1199
= 0.2239 ( 0.224 rounded to 3 decimal places )
UCLp = 0.224
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