**** Please show all your work to all parts of the problem **** 5- The data give

Question

**** Please show all your work to all parts of the problem ****

5- The data given below contains the number of defective products found in a sample of 25 randomly selected from each hour’s production for 20 hours.

a- Construct a control chart for the proportion of defective products.

b- Is the process in control?

c- Conduct a runs analysis for this control chart.

DATA:-

Sample Proportion Defective 1 0.2 2 0.24 3 0.16 4 0.28 5 0.04 6 0.12 7 0.24 8 0.2 9 0.16 10 0.2 11 0.32 12 0.12 13 0.08 14 0.04 15 0 16 0.04 17 0.04 18 0.08 19 0.12 20 0.12

Explanation / Answer

First find mean and std dev for the sample

Control means within 3 sigma times from the mean

mu-3sigma = 0.078032

mu+3 sigma = 0.201968

Comparing with our sample chart,

0.04 is below control level and

0.24, 0.28, 0.32 are above contol level.

Here is the control chart

Sample Proportion Defective 1 0.2 2 0.24 3 0.16 4 0.28 5 0.04 6 0.12 7 0.24 8 0.2 9 0.16 10 0.2 11 0.32 12 0.12 13 0.08 14 0.04 15 0 16 0.04 17 0.04 18 0.08 19 0.12 20 0.12 Mean 0.14 Std dev 0.092376 Std error 0.020656

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