Question: A machine set to fill a bottle with 60 grams of liquid was started at 7 a.m. today. Slight variations (called chance variations) were expected. The quality control inspector made her initial check of the weights at 8 a.m. She selected five bottles from the first hour of production and weighed the contents of each bottle. The results of the first seven inspections are shown below.

8 am 60 59 60 60 60

9 am 60 60 60 60 60

10 am 60 60 60 59 60

11 am 60 59 60 60 60

12 pm 60 60 59 60 59

1 pm 60 60 59 60 59

2 pm 60 59 59 59 59

a. Develop a control chart for the sample means. What are the limits? What is the grand mean? Comment on this chart.

b. Develop a control chart for the sample ranges. What are the limits? What is the mean range? Comment on this chart.

c. As the Quality Control Inspector, what would you report to the plant manager?