SHOW YOUR WORK (The answers are given, but you have to show how to get the answers.)

X-bar (mean chart) using Z-score

1. A beverage company would like to use a mean chart (x-bar chart) to monitor how much liquid beverage it puts into each 750 ml bottle. They know from past experience that whenever this process is under control, bottle weight is normally distributed with a mean of 750 and a standard deviation of 3.8ml. The company plans to measure samples of 49 bottles from the production line every hour, and record the mean weight of liquid beverage in the bottles.

a) If the company uses z=3.0 as its standard for establishing the mean chart, where will the upper and lower control limits be on that chart?

Answer: UCL = 751.63 ml, LCL = 748.37ml

b) For legal reasons, the company cannot tolerate more than 755 or less than 745 ml in each bottle. What is the process capability index value for this bottling process? What does it indicate about the process?

Answer: 0.4386, the process cannot support the design specification

x-bar (mean chart) using table (Mean (x-bar) and Range (R) Chart Factors) from Chapter 13 PPTs.

2. Thirty samples of 18 cans each are measured from a canning process while it is in control. The mean of the thirty sample means is 15.02 ounces and the average range is 0.14 ounces. What should the upper and lower control limits be on a mean chart to monitor this canning process in the future?

Answer: UCL 15.05, LCL 14.99

Range chart using table (Mean (x-bar) and Range (R) Chart Factors) from Chapter 13 PPTs.

3. Thirty samples of 18 cans each are measured from a canning process while it is in control. The mean of the thirty sample means is 15.02 ounces and the average range is 0.14 ounces. What should the upper and lower control limits be on a range chart to monitor this canning process in the future?

Answer: UCL 0.225, LCL 0.055

p-chart using z-score

4. The average proportion of defective is known to be 2%. What should the upper and lower control limits of a P-chart be if n = 30 and z = 3.0?

Answer: UCL 0.097, LCL 0

c-chart

5. The average number of defects is 40 per day. What should the upper and lower control limits of a C-chart be if z = 2.5?

Answer: UCL 55.8, LCL 24.2