Ten large samples for Machine C show it to be working normally. Describe what a control chart for Machine C would look like.
How to approach this question
1. **Recall the characteristics of a process that is "working normally" or "in control"**.
2. **Characteristic 1: Location of points**: The points should be randomly scattered around the central target line. There should be no clear trends (up or down) or long runs of points on one side.
3. **Characteristic 2: Proximity to limits**: All points must be within the action limits, and for a process that is clearly normal, you would expect all points to be within the *warning* limits as well.
4. **Combine these ideas**: Describe a chart that has ten points plotted. The points should be scattered randomly above and below the 25g target line, and none of them should be outside the warning lines at 24.5g and 25.5g.
Full Answer
For a machine to be "working normally", its control chart must show that the process is "in statistical control". This has two main features:
1. **All points are within the control limits**: Specifically, for a normally working machine, all sample means should fall between the upper and lower warning lines. No points should be in the warning or action zones.
2. **The points show a random pattern**: The points should be scattered randomly above and below the central target mass line. There should be no obvious trends, cycles, or long runs of points on one side of the target line.
Therefore, a control chart for Machine C would show ten data points, all located between the 24.5g and 25.5g warning lines, and scattered randomly around the 25g target line.
Common mistakes
✗ Describing a pattern that is out of control (e.g., points outside the limits).
✗ Only mentioning one characteristic (e.g., "the points are inside the lines") without mentioning the random scatter.
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