Question

Consider a set of products is produced with 100 sample size per batch. An observation for the non-conforming unit as shown in Table 6. Construct a P-Chart and deduce whether the process is in control or not.

Table 6 Sample 1 2 3 4 5 6 Number of non-conforming unit 16 25 12 26 10 6 Sample Size 100 100 100 100 100 100

Answer 1

No. of non - conforming Sample size (N.) Proportion Defective (Difu) Sample cenit (Di) 16 100 0.25 25 100 0.12 12 100 on I wo 0.26 26 1oo 0.1 10 10 o 100 0.06 6 The distribution of fraction non conforming, Pi binomial distribution 0.16 +0.25 +0.12 + 0.26+0.1 +0.06 mean=pa I E Pi= G 0.1583 À (1-P) 0.0365 Standard deviation (SD) = P (1-P) 0.2678 UCL - P +3 n Centre line -> P = 0.1583 LCL - P 3P (1- 0.0488

Plotting the chart: P chant UCL = 0.2678 0.16 ä 0.12 Centre line P = 0.1583 0.08 L CL=0.0488 0.047 0.004 V Sample no. que charactenistics of a process in control are! . Most points are near overage A few points are nean near control limits beyond No points are the control limits Here in the plot, 2 points are close to close to control overage line. 2 points are limits. No point. is beyond the control limit and patter is zigzag. Then proces is in control. can say the
From the chart above the process is in control.

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