Midnight Mocha is a 24-hour café that specializes in coffee drinks. It has a dri
ID: 416859 • Letter: M
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 range of values. Those values are listed below. 5 7 8 9 Mean 11.9 12.2 12.0 12.1 11.7 11.9 12.112.1 12.0 Range 0.19 0.240.18 0.19 0.190.18 0.07 0.09 0.07 Use formulas with table values to determine control limits. What would be the upper control limit (UCL) and lower control limit (LCL) for the means? (2 decimals) UCL 12.05 LCL 11.99 What would be the upper control limit (UCL) and lower control limit (LCL) for the range values? (2 decimals) UCL How many of the observations for the means are out of control? (maintain 2 decimals in comparisons) How many of the nine observations for the ranges are out of control? LCL = Answer 1: 12.05Explanation / Answer
Means of X= (11.9+12.2+12+ 12.1+11.7+11.9+ 12.1+12.1+12)/9= 108/9= 12
R= (0.19+0.24+0.18+ 0.19+0.19+0.18+ 0.07+0.09+0.07)9= 1.4/9= 0.155
UCL of X = X double bar+A2 R bar= 12+0.33*0.155= 12.051
LCL= X double bar- A2 R bar= 12-0.33*0.155= 11.94
UCL of R= D4R bar= 1.816*0.155=0.2814
LCL of R= D3R bar= 0.184*0.155=0.0285
the out of control means are= 3
the out of control of range are= 0