Question 1
A Quality Analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of twenty ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:
Day WEIGHT (ounces)
Monday 23 22 23 24
Tuesday 23 21 19 21
Wednesday 20 19 20 21
Thursday 18 19 20 19
Friday 18 20 22 20
If he uses upper and lower control limits of 22 and 18 ounces, on what day(s), if any, does this process appear to be out of control?
Question 2
A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:
Machine Measurements
Number1 17 15 15 17
Number2 16 25 18 25
Number3 23 24 23 22
For upper and lower control limits of 23.29 and 16.71, which machine(s), if any, appear(s) to have an out-of-control process mean?
Question 3
A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:
Machine Measurements
Number1 17 15 15 17
Number2 16 25 18 25
Number3 23 24 23 22
What is the estimate of the process mean for whenever it is under control?
Question 4
Specifications for a piece of material used in the manufacture of a bed mattress require that the piece be between 81.02 and 84.98 inches.
The process that produces the piece yields a mean of 83 and a standard deviation of 0.9 inches. The distribution of output is normal. What percentage of the pieces will meet the length specs?