Workers in an operations facility gathered the above data during their work. Ass

Question

Workers in an operations facility gathered the above data during their work.  Assume calculations are based on 200 obs.  What is pbar, the UCL and the LCL?  Is this process in control?

Number of Proportion Sample Defectives Defective p UCL LCL 1 2 0.100 0.15 0.1450 0.1450 2 3 0.150 0.15 0.1450 0.1450 3 4 0.200 0.15 0.1450 0.1450 4 2 0.100 0.15 0.1450 0.1450 5 1 0.050 0.15 0.1450 0.1450 6 2 0.100 0.15 0.1450 0.1450 7 3 0.150 0.15 0.1450 0.1450 8 4 0.200 0.15 0.1450 0.1450 9 2 0.100 0.15 0.1450 0.1450 10 6 0.300 0.15 0.1450 0.1450 Total 29

Explanation / Answer

CL= SUM OF DEFECTIVES / SUM OF ALL SAMPLES =

= 29 /176=0.164

UCL =P+3SQUARE ROOT OF [P X(1-P)  /100]

UCL = 0.164+3SQUARE ROOT OF [0.164 X(1- 0.164)  /100]=0.1751

LCL =P-3SQUARE ROOT OF [P X(1-P) /100]==0.1529

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