Question

Midnight Mocha is a 24-hour café that specializes in coffee drinks. It has a drive-through that is almost fully automated. Each mug of coffee is dispensed by the automated machinery and should provide exactly 12 ounces. Recently, customers have complained that the cups appear to have too much or too little coffee. Midnight Mocha began a quality control program. Every day for 9 days they sampled 9 cups of coffee. They computed the average amount of coffee for the 9 cups and the average for the range of values. Those values are listed below. Table has 9 readings of mean and range 1 2 3 6 7 8 9 Mean 12.1 11.9 12.2 12.1 11.7 11.9 12.1 12.1 11.9 0.18 Range 0.19 0.24 0.19 0.19 0.18 0.07 0.09 O.07 What would be the upper control limit (UCL) and lower control limit (LCL) for the means? Hint: Remember Xbar/R charts, don't forget to include sample sizes. 12.121; 11.879 12.047; 11.953 12.097; 11.903 12.052; 11.948 L5

Answer 1

Solution:

Before calculating the control limits for the means chart, X-double bar (mean of means) and R-bar (mean of ranges) will have to be calculated. X-double bar and R-bar are calculated as below:

X-double bar = Sum of means / Total Number of samples

X-double bar = (11.9 + 12.2 + 12.1 + 12.1 + 11.7 + 11.9 + 12.1 + 12.1 + 11.9) / 9

X-double bar = 108 / 9

X-double bar = 12 ounces

R-bar = Sum of ranges / Total Number of samples

R-bar = (0.19 + 0.24 + 0.18 + 0.19 + 0.19 + 0.18 + 0.07 + 0.09 + 0.07) / 9

R-bar = 1.4 / 9

R-bar = 0.1556 ounces

From the table of factors for computing control chart limits,

For n = 9 (Number of observations in a sample = 9),

A2 = 0.337

Upper Control Limit (UCL) and Lower Control Limit (LCL) for the means chart are calculated as,

UCL = X-double bar + (A2 x R-bar)

UCL = 12 + (0.337 x 0.1556)

UCL = 12.052 ounces

LCL = X-double bar - (A2 x R-bar)

LCL = 12 - (0.337 x 0.1556)

LCL = 11.948 ounces

Answer: (d) 12.052; 11.948