I-MR R/S(Between/Within) chart

What is I-MR R/S(Between/Within) chart?

The I-MR-R/S (Between/Within) Chart is a three-part control chart that simultaneously monitors three sources of process variation the subgroup means over time (I chart), the variation between consecutive subgroup means (MR chart), and the variation within each subgroup (R or S chart).

It is specifically designed for situations where measurements are taken in subgroups but the subgroups themselves are collected infrequently or at widely spaced intervals  such as once per shift, once per day, or once per batch. In these cases, the between-subgroup variation and within-subgroup variation must be tracked and compared separately.

Simple Definition: A three-in-one chart that separates and monitors two distinct types of variation how much measurements spread within each sample, and how much the sample averages drift between one time period and the next.

When to use I-MR R/S(Between/Within) chart?

  • Use when subgroups are collected infrequently such as once per shift, per day, or per batch — and you need to distinguish within-subgroup from between-subgroup variation.
  • Use when the within-subgroup variation and between-subgroup variation are expected to be different ,for example, measurements within a batch are similar but batches vary from each other.
  • Use when a standard Xbar-R chart fails to separate the two variation sources and control limits appear too tight or too wide relative to actual process behaviour.
  • Use for subgroup sizes of 2 or more the R/S portion of the chart monitors within-subgroup spread.

Guidelines for correct usage of I-MR R/S(Between/Within) chart

  • Interpret the R or S chart first to confirm within-subgroup variation is stable before reading the other two charts.
  • The MR chart monitors between-subgroup variation a signal here means the process average is drifting between time periods.
  • Collect at least 20 to 25 subgroups to establish reliable control limits across all three chart components.
  • Ensure subgroup formation is rational and consistent measurements within a subgroup should represent the same process condition.
  • If within-subgroup variation is very small compared to between-subgroup variation, investigate the process for systematic batch-to-batch differences as a root cause.

Alternatives: When not to use I-MR R/S(Between/Within) chart

  • If subgroups are collected frequently and variation sources are not expected to differ, use a simpler Xbar-R or Xbar-S Chart
  • If data consists of individual measurements with no subgroups, use I-MR Chart
  • If you are not interested in separating variation sources and only want to monitor the process mean, use Xbar Chart
  • If data is attribute-based, use appropriate attribute charts such as P, NP, C, or U charts

Example of I-MR R/S(Between/Within) chart?

A quality engineer at a plastic manufacturing company oversees an injection molding process. The process involves a machine that produces five parts simultaneously using a single die. To evaluate the process, the engineer collects data from 20 subgroups, each consisting of five parts. The engineer assesses both the variation within each subgroup (comparing parts produced in the same batch) and the variation between subgroups (comparing different batches). The engineer creates an I-MR-R/S chart to monitor the injection molding process. The following steps:

  1. Gathered the necessary data.

  1. Now analyses the data with the help of  https://qtools.zometric.com/ or https://intelliqs.zometric.com/.
  2. To find I-MR R/S(Between/Within) chart choose https://intelliqs.zometric.com/> Statistical module> Control Chart > I-MR R/S(Between/Within) chart.
  3. Inside the tool, feed the data along with other inputs as follows:

5.  After using the above-mentioned tool, fetches the output as follows:

How to generate I-MR R/S(Between/Within) chart?

The guide is as follows:

  1. Login in to QTools account with the help of https://qtools.zometric.com/ or https://intelliqs.zometric.com/
  2. On the home page, choose Statistical Tool> Control Chart > I-MR R/S(Between/Within) chart.
  3. Click on I-MR R/S(Between/Within) chart and reach the dashboard.
  4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet or paste (Ctrl+V) it or else there is say option Load Example where the example data will be loaded.
  5. Next, you need to map the columns with the parameters.
  6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of I-MR R/S(Between/Within) 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.

Load example: The sample data will be loaded.

Load File: It is used to directly load the excel data.

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

  • Choose Column Select the column(s) that contain your measurement data. Use Ctrl or Command + Click to select multiple columns at once if your data is spread across more than one column.
  • Observations: This setting defines how your data is physically laid out in the worksheet. Choose the option that matches your data  structure:
  • All observations for a chart are in one column — all measurements are stacked vertically in a single column, and the subgroup size field is used to define how many rows belong to each subgroup.
  • Subgroup Size Column: Only required when all observations are in one column. This column tells the chart which rows belong to which subgroup — for example, a column containing values like 1,1,1,2,2,2 groups the data into subgroups of 3. Either this field or the Subgroup Size Number must be filled, not both.
  • Subgroup Size Number: Enter a fixed number if all your subgroups are the same size. For example, entering 5 means every 5 consecutive rows form one subgroup. Use this instead of the Subgroup Size Column when subgroup size is consistent throughout the data.
  • Process mean: It is the average value of a set of measurements or observations from a process. It represents the central tendency of the process data over time and is a key indicator of the process performance. If not, Zometric Q-Tools calculates the centerline from the data provided.
  • Standard Deviation Between Subgroup: Optional. If you have a known or historically established value for the variation between subgroups, enter it here. When provided, this overrides the estimate calculated from the data, which is useful when you have a well-characterised baseline from a previous study.
  • Standard Deviation Within Subgroup: Optional. Similarly, if you have a known standard deviation for variation within subgroups, enter it here. Providing this value prevents the chart from re-estimating within-subgroup spread from the current data, ensuring consistency with your established process baseline.
  • SD Estimation method for Between subgroup: 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.
  • SD Estimation method for Within subgroup: This leaves the user with two choices for the calculation. Choosing Rbar as the estimation method or pooled standard deviation method changes the result.
      • Pooled Sd estimation method:  The pooled standard deviation is the weighted average of subgroup variances, with larger subgroups having a greater impact on the overall estimate. This method offers a more accurate estimate of the standard deviation when the process is stable.
      • Rbar Sd estimation method: Rbar represents the average of the ranges within subgroups. The Rbar method is a widely used estimate of the standard deviation, particularly effective for subgroup sizes ranging from 2 to 8.
      • Sbar Sd estimation method: Estimates process standard deviation by averaging the standard deviations across all subgroups and applying a statistical correction factor. This method is recommended for subgroup sizes greater than 8, as it uses every data point in each subgroup to produce more accurate and reliable control limits than the range-based method.
  • Length Moving Range: Defines how many consecutive subgroup means are used to calculate each moving range value. The default is 2, meaning each moving range is the absolute difference between two consecutive subgroup averages. Increasing this value smooths the estimate but reduces sensitivity to short-term shifts.
  • Use unbiasing constants for pooled sd: This option is applicable only when Stdev is estimated using Pooled Stdev method.
  • Show Decimals: Controls how many decimal places are displayed on the chart for plotted values and control limits. The default is 3, which provides sufficient precision for most industrial and quality applications. Adjust based on the measurement precision of your data and the audience reading the chart.
  • Check Rule 1: 1 point > K Stdev from center line: Test 1 is essential for identifying subgroups that significantly deviate from others, making it a universally recognized tool for detecting out-of-control situations. To increase sensitivity and detect smaller shifts in the process, Test 2 can be used in conjunction with Test 1, enhancing the effectiveness of control charts.
  • Check Rule 2: K points in a row on same side of center line: Test 2 detects changes in process centering or variation. When monitoring for small shifts in the process, Test 2 can be used in conjunction with Test 1 to enhance the sensitivity of control charts.
  • Check Rule 3: K points in a row, all increasing or all decreasing: Test 3 is designed to identify trends within a process. This test specifically looks for an extended sequence of consecutive data points that consistently increase or decrease in value, signaling a potential underlying trend in the process behavior.
  • Check Rule 4: K points in a row, alternating up and down: Test 4 is designed to identify systematic variations within a process. Ideally, the pattern of variation in a process should be random. However, if a point fails Test 4, it may indicate that the variation is not random but instead follows a predictable pattern.
  • Check Rule 5: K out of K + 1 points > 2 standard deviation from center line (same side): Test 5 detects small shifts in the process.
  • Check Rule 6: K out of K + 1 points > 1 standard deviation from center line (same side):Test 6 detects small shifts in the process.
  • Check Rule 7: K points in a row within 1 standard deviation of center line (either side):Test 7 identifies patterns of variation that may be incorrectly interpreted as evidence of good control. This test detects overly wide control limits, which are often a result of stratified data. Stratified data occur when there is a systematic source of variation within each subgroup, causing the control limits to appear broader than they should be.
  • Check Rule 8: K points in a row > 1 standard deviation from center line (either side):Test 8 detects a mixture pattern. In a mixture pattern, the points tend to fall away from the center line and instead fall near the control limits.