# U Chart

## What is U Chart?

U Chart is a statistical process control chart that is used to monitor and control the variation in the number of defects per unit during the production process. It is used to track defects or non-conformances in a sample of items, where the sample size may vary from period to period.

The U Chart plots the number of defects per unit over time, and determines if the process is stable or not. It is commonly used in manufacturing and quality control to identify and correct issues in the production line.

## When to use U Chart?

A U chart is typically used to analyze data that reflects the count of defects in a set of items. It is particularly useful for assessing the presence of special causes of variation in data. A U chart is used when the sample size is constant and the defects are measured in discrete units. Therefore, it is commonly used in manufacturing processes, quality control, and similar settings where the occurrence of defects needs to be monitored and tracked over time.

## Guidelines for correct usage of U Chart

• Count defects on each item or unit, or use P Chart Diagnostic for binary data
• Collect data in time order
• Collect data at appropriate time interval
• Collect data in subgroups that are representative of the process output and subject to the same process conditions
• Subgroups must be large enough to accurately estimate control limits
• Collect enough subgroups to obtain precise control limits

## Alternatives: When not to use U chart

If you are only able to classify items as defective or non defective, then you should use the P Chart Diagnostic.

## Example of U Chart?

The director of quality for a group of hospitals wants to assess the medication error rate. Examples of errors include delivering medication at the wrong time, delivering the wrong dose, and delivering the wrong medication. The director records the number of patients and the number of medication errors each week for 32 weeks. The average subgroup size is more than 7500. Because of the large number of patients, the director uses a U chart diagnostic test to test for over dispersion. She has performed this in following steps:

1. She worked all day and gathered the data.

1. After gathering the data, she uses mathematical formula for finding the u bar, n bar, Upper Control Limit (UCL) and Lower Control Limit(LCL).
1. Now, after calculating u bar, UCL and LCL, she analyzes the data with the help of https://qtools.zometric.com/
2. After using the above mentioned tool, she fetches the useful graph as follows:

## How to generate U Chart?

The guide is as follows:

1. Login in to QTools account with the help of https://qtools.zometric.com/
2. On the home page, one will see U Chart under control charts.
3. Click on U Chart and will reach the dashboard.
4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
5. Next, you need to select the desired Check Rules.
6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of U Chart, the window is separated into two parts.

On the left part, Data Pane is present. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.

On the right part, there are many options present as follows:

• Process mean: If process mean is provided, this value is considered to be the centerline. If not, Zometric Q-Tools calculates the centerline from the data provided.
• Check Rule 1: 1 point > K Stdev from center line: If a data point is K standard deviations from the center line, it means that it is K times the standard deviation away from the mean. This is important in statistical process control because it indicates whether a data point is within acceptable limits or whether there may be a problem with the process that needs to be addressed. Typically, data points that are more than three standard deviations from the center line are considered outliers and may require further investigation.
• Check Rule 2: K points in a row on same side of center line: If there are K points in a row on the same side of the center line in a dataset, it suggests that there may be a bias or trend in the data that is causing the values to cluster together. This could be due to a variety of factors, such as measurement error, sampling bias, or a true underlying pattern in the data.
• Check Rule 3: K points in a row, all increasing or all decreasing: If there are K points in a row, it is certain that at least one of two things must be true:
• The points are all increasing (i.e. each point has a greater y-coordinate than the one before it)
• The points are all decreasing (i.e. each point has a smaller y-coordinate than the one before it)
• Check Rule 4: K points in a row, alternating up and down:
• If the trend is upwards, it indicates that the process is becoming less consistent and more variable over time. This can be caused by factors such as equipment deterioration, operator error or changes in raw material quality.
• If the trend is downwards, it indicates that the process is becoming more consistent and less variable over time. This could be due to process improvements or tighter control measures being implemented.