# I-MR Chart

## What is I-MR Chart?

I-MR chart (Individual-Moving Range chart) is a type of statistical process control chart used to monitor and control processes over time by tracking variation in a single variable. It consists of two charts: the Individual chart shows the data points of a single variable over time, and the Moving Range chart shows the differences between consecutive data points in the individual chart.

The I-MR chart is particularly useful for analyzing data sets with small sample sizes, where it is not possible to create traditional control charts such as X-bar and R or X-bar and S charts. It helps to identify any process instability, trends, and shifts in the data over time.

## When to use I-MR Chart?

I-MR chart is used in statistical process control (SPC) to monitor and control the variation of a single process variable over time. It is commonly used for continuous data that is measured over time, such as production rates, customer satisfaction scores, or machine speeds. I-MR chart is particularly useful for detecting special causes of variation that may indicate a problem with the process or equipment. It is commonly used in manufacturing industries, healthcare, and service sectors.

## Guidelines for correct usage of I-MR Chart

• Data should be continuous, collected at appropriate time intervals, and in time order.
• Use attribute control chart for count data, and Xbar-R/S chart for subgroup data.
• Have at least 100 total observations for more precise control limits.
• Data should be moderately normal, consider Box-Cox transformation if data is very skewed.
• Observations should not be correlated with each other, as it can lead to narrow control limits and false out-of-control signals.

## Example of I-MR Chart?

The pH of 25 successive batches of liquid detergent is measured by a quality engineer who aims to evaluate whether the manufacturing process is under control.. She evaluates in following steps:

1. She worked all day and measured the size of all the camshafts produced in a day by all machines.

1. Now, she analyzes the data with the help of https://qtools.zometric.com/
2. Inside the tool, she feeds up the data. Also, she chooses average moving range as the sd estimation method and keeps 2 as the value of length moving range.
3. After using the above mentioned tool, she fetches the useful graphs as follows:

## How to generate I-MR 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 I-MR Chart under control charts.
3. Click on I-MR Chart and 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 choose Sd estimation method and length moving range along with 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 I-MR chart, the window is separated into two parts.

On the left part, Data Pane is present. In the Data Pane, each row makes one subgroup. 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.
• Process sd: 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.
• Sd estimation method: This leaves the user with two choices for the calculation. Choosing average moving range as the estimation method or median moving range method changes the result.
• Average moving range Sd estimation method: It involves calculating the difference between consecutive values in a data set and then taking the average of those differences.
• Median moving range Sd estimation method: The MMR is calculated by taking the median of the moving ranges between consecutive data points.
• Length moving range: In an I-MR chart, the length moving range (LMR) is the difference between the largest and smallest values within a subgroup or sample. It is used to calculate the control limits of the chart and to evaluate the variability or dispersion of the process being monitored.
• 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.
• Check Rule 5: K out of K + 1 points > 2 standard deviation from center line (same side): According to the statement, if K out of K+1 data points fall on the same side of the center line and are more than two standard deviations away from it, it suggests that the process might be out of control, and special causes should be investigated to identify and fix the problem.
• Check Rule 6: K out of K + 1 points > 1 standard deviation from center line (same side): In this statement, K represents the number of consecutive observations that are above the center line (on the same side) and are greater than one standard deviation away from it. This indicates a potential shift in the mean of the process. The K+1 point serves as a reference point to compare the K consecutive observations against.
• Check Rule 7: K points in a row within 1 standard deviation of center line (either side): If K points in a row are within 1 standard deviation of the center line, it suggests that the data points are clustered around the expected value, and there is no significant trend or deviation from the expected pattern.
• Check Rule 8: K points in a row > 1 standard deviation from center line (either side): If K points in a row are more than 1 standard deviation away from the center line, it suggests that there may be a trend or pattern in the data that is moving away from the expected value.