The manager of an accounting office is studying the problem of incorrect account numbers being entered into the computer system and wishes to produce a p chart. A subgroup of 200 account numbers is selected from each day's enteries and checked to determine the number of incorrect entries. The average proportion of such incorrect entries for the last several months is 0.12. Calculate the control limits for this process. After the control limits are calculated and drawn on the control chart and the proportions are plotted for everyday what are the signals that indicate that something has gone wrong with this process? Give at least 2 different signals with diagrams.
To calculate the control limits for a p-chart, you need to follow these steps:
Step 1: Calculate the centerline or average proportion (p-bar)
The manager mentioned that the average proportion of incorrect entries for the last several months is 0.12.
Step 2: Calculate the standard deviation (σp)
To calculate the standard deviation, you need to determine the sample size (n) and the number of defective items (d) in each subgroup. In this case, a subgroup of 200 account numbers is selected each day.
You can calculate the standard deviation using the following formula:
σp = sqrt((p-bar * (1 - p-bar)) / n)
Step 3: Calculate the control limits
The control limits for a p-chart are typically set at ±3 standard deviations from the centerline.
Upper Control Limit (UCL) = p-bar + 3σp
Lower Control Limit (LCL) = p-bar - 3σp
Once you have calculated the control limits, you can draw them on the p-chart. Every day, you will plot the proportion of incorrect entries on the chart. If any of the plotted points exceed the control limits or show certain patterns, it indicates that something has gone wrong with the process. Here are two common signals with diagrams:
Signal 1: A Single Point Outside the Control Limits
If a single data point falls either above the UCL or below the LCL, it indicates a significant deviation from the expected process.
Example Diagram:
```
|
| *
| *
|--------------X----------------
|
+---------------------------------
Day 1 Day 2 Day 3 Day 4
```
Signal 2: A Run of Points on One Side of the Centerline
A run refers to a consecutive series of data points falling on the same side of the centerline. This suggests a systematic shift in the process.
Example Diagram:
```
|
| *
| * *
|--------------X---------X--------X----X
|
+-----------------------------------
Day 1 Day 2 Day 3 Day 4
```
It's important to note that these are just two possible signals, and other patterns or trends may also indicate issues with the process.