1) What does it mean that a process is under statistical control? Can a production process be labeled as "out of control" because it is too good? Explain.
A process that continues to be described by the same distribution when observed over time is in statistical control and the observation in the process is within the upper and lower control limits.
If there is a tendency in the observation and their do not appear random, the process is "out of control" even though it appear in control. For example if the curve for the observation is upward rising. Type 1 and Type 2 errors.
2) What are run charts used for in process control? Why is it desirable to use both median run test and up/down run test on the same data? if neither of these tests reveals non-randomness, does that prove that the process is random? Explain
The run charts checks for tendency in the observations, for example are they consequence is 10 over or under the mean.
The use of both test is desired to ensure the reliability of the observations, when the above/below shows if there is a tendency the median, where up/down shows the observation in proportion to each other.
If none of the two test reveals non-randomness, the process is random