1-What does it mean that a process is under statistic control? Can a production be labeled as "out of control" because it is too good? Explain.
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 reveal non-randomness?
I don't know the answers. Statistics is not my field. Your textbook undoubtedly explains these concepts. I recommend reading it.
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1- When a process is said to be under statistical control, it means that the process is operating within the expected variation limits and is stable over time. In other words, the process is predictable, consistent, and producing outcomes that fall within acceptable boundaries.
A production cannot be labeled as "out of control" simply because it is too good. The concept of "out of control" refers to situations where a process exhibits excessive variation or instability, causing the outcomes to deviate significantly from the expected values. So, if a production consistently meets or exceeds the desired specifications, it implies that the process is performing well and producing satisfactory results. In such cases, the process can be considered in control because it is meeting or exceeding the set targets.
2- Run charts are graphical tools used in process control to monitor and analyze data over time. They can help identify patterns, trends, and shifts in the process.
The median run test and the up/down run test are two commonly used methods to assess non-randomness in run charts. Both tests are applied on the same data to provide a comprehensive analysis of potential process deviations.
The median run test determines whether successive data points are scattered randomly around the median value, or if they tend to cluster together. This test helps detect changes in the central tendency of the process.
The up/down run test, on the other hand, focuses on identifying consecutive points moving upward or downward in a systematic manner. This test can reveal if the process is consistently moving in one direction, indicating a potential shift in the process average.
Using both tests on the same data set provides a more robust analysis by examining different aspects of the process behavior. If neither of these tests reveal non-randomness, it suggests that the process is stable and operating within expected limits, exhibiting random variation. However, it's important to note that other additional analyses and control charts may be used to further investigate the process.