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A company manufactures valves for industrial use. Ten samples of 15 valves each were taken from the production line and tested. The results are as follows SAMPLE NUMBER DEFECTIVES SAMPLE NUMBER DEFECTIVES 2 [6] 10 2 3 4 5 1 12] 0 [3] 0 [4] 0 [5] 6 7 8 3 [81 1 [9] 0 110] 10 a. Compute the fraction defectives for each sample. (3 decimal places0 b. Compute for the center line [a]. Upper Control Limit [b], Lower Control Limit [c] c. What comments can you make about the results? Is the process in-control. What action should be taken? [d]

math   Statistics-And-Probability   
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SampleSample (n)Number defectivesFraction defectives 0 10 2 0.300 0.500 0.000 0.000 0.000 0.333 0.000 0.375 2 0 0 0 2 4 4 10 10 64 0.000 0 10 Total Σηί 64 .d 10 Central line CL-0.15625 ni 64 p (1-p) Upper Control Limit (UCL)-p+3E1-2 0.15625 (1-0.15625 = 0.15625 +3 -0.15625 +3(0.143525) =0.15625+0.430574 6.4 , UCL =0.586824p (1-p) Lower Control Limit (LCL)-p-32 0.15625 (1-0.15625 0.1 5625-3 6.4 -0.15625 3(0.143525) -0.15625-0.430574 LCL=-0.27432 → 0 When the lower control limit id negative then it is rounded up to zero. (c) This process is in control since the fraction defectives for all ten samples are lies within control limits. The process is in control it means there is chance cause of variation present in manufactuing process

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