Question

Refills of cartons with apple juice is taking place in a plant. Data for 14 days were collected and 100 cartons were checked every day for proper filling. Data is as given below. Compute the UCL, LCL and CL using an appropriate control chart. Also draw the chart. (5) S.NO. 1 2 3 4 5 6 7 8 9 1011 12 13 14 Date 16 17 18 1920 21222324 2526 27 29 30 Total X 8 2 4 1 3 3 2 4 9 7 5 8 5 9 70

Answer 1

Answer on Question #84109 – Math – Statistics and Probability

Question

Refills of cartons with apple juice is taking place in a plant. Data for 14 days were collected and 100 cartons were checked every day for proper filling. Data is as given below. Compute the UCL, LCL and CL using an appropriate control chart. Also draw the chart.

Solution

Find the mean value (Xbar)

$$\overline{x} = \frac{8 + 2 + 4 + 1 + 3 + 3 + 2 + 4 + 9 + 7 + 5 + 8 + 5 + 9}{14} = \frac{70}{14} = 5$$ $$CL = \overline{x} = 5$$ $$UCL = \overline{x} + z\sqrt{\overline{x}} = 5 + 3\sqrt{5} = 11.708$$ $$LCL = \overline{x} - z\sqrt{\overline{x}} = 5 - 3\sqrt{5} = -1.708$$

If LCL is negative then it is taken as zero.

$$CL = 5$$ $$UCL = 11.708$$ $$LCL = 0$$

Answer provided by https://www.AssignmentExpert.com