I-MR Chart (Individuals Chart)

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Control Chart - I Chart


Purpose

The Individuals Chart is used to observe and evaluate the behavior of a process over time and take corrective action if necessary. The Individuals Chart (I-Chart) plots the Individual values of each of a number of samples. The I Chart is usually plotted in conjunction with the MR (Moving Range) Chart.


Anatomy

spc individuals control chart

SPC Individuals Control Chart


Reference: Statistical Process Control – Ford/GM/Chrysler

Terminology

A. Upper Control Limit (UCL) – The upper range of process control. The UCL is by convention calculated to equal to the process Mean plus three Standard Deviations.

B. Center Line – Calculated as the process Mean over the period being investigated

C. Lower Control Limit (LCL) – The lower range of process control. The LCL is by convention calculated to equal to the process Mean minus three Standard Deviations.

D. Plot of process sample statistic in chronological order vs. sample number. Any excursion in this plot above the UCL or below the LCL represents an out-of-control condition and should be investigated.

E. Out of Control Point – A single process point showing the most obvious sign of an Out-of-Control situation, i.e. being beyond either the UCL or LCL.


Major Considerations

The Individuals Chart (I Chart), together with the MR Chart, is a sensitive control chart for identifying assignable causes of product and process variation.


Application Cookbook

  1. Determine purpose of the chart
  2. Select data collection point
  3. Establish sampling interval
  4. Set up forms for recording and charting data and write specific instructions on use of the chart
  5. Collect and record data. A minimum of 25 subgroups or samples of size n should be measured
  6. Compute the Process Average X
  7. If using the MR Chart - Compute the Moving Range MR
  8. Compute required Upper Control Limit UCL I
  9. Compute required Lower Control Limit LCL I
  10. Plot data points
  11. Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary.

Control Chart - MR Chart


Purpose

To observe and evaluate the behavior of a process over time, and against control limits, and take corrective action if necessary. The MR Chart plots the moving range between individual process output values, generally the difference between two successive readings.

The MR Chart is used to visualize the process dispersion, and is usually plotted in conjunction with the I Chart (Individuals Chart), which is used to visualize the process location

Anatomy


spc moving range control chart

SPC Moving Range Control Chart


Reference: Statistical Process Control – Ford/GM/Chrysler

Terminology

A. Moving Range – The Moving Range values as calculated from sequential, or chronological, readings from the process

B. Observation Number – The chronological index number for the individual moving range value being referenced

C. Lower Control Limit (LCL) – Line and numerical value representing the lower limit of the variation that could be expected if the process were in a state of statistical control, equal to the average Moving Range over the period, multiplied by a conversion factor.

D. Average of the Moving Range– Average value of the individual Moving Range values, over the period of inspection being referenced

E. Upper Control Limit (UCL) – Line and numerical value representing the upper limit of the variation that could be expected if the process were in a state of statistical control. It is equal to the average Moving Range over the period, multiplied by a second conversion factor, different from the one used to calculate the LCL.

F. Plot of the Moving Range values vs observation number. Any excursion in this plot above the UCL or below the LCL represents an out-of-control condition and should be investigated


Major Considerations

Moving Range values are correlated, because each successive point has a point in common with the preceding one. Care must be exercised in interpretation.

There will always be one less Moving Range value on the Individuals Chart.


Application Cookbook

  1. Determine purpose of the chart
  2. Select data collection point
  3. Set up forms for recording and charting data and write specific instructions on use of the chart
  4. Collect and record data. A minimum of 20 individual readings should be taken. Note that even though the measurements are sampled individually, the number of readings grouped to form the moving range determines the nominal sample size "n"
  5. Compute the Moving Range MRI between n consecutive values
  6. Compute the Average Moving Range MR
  7. Compute Upper Control Limit UCL MR
  8. Compute Lower Control Limit LCL MR
  9. Plot data points
  10. Interpret MR chart together with Individuals Chart and take corrective action if necessary

Statistical Process Control Basics

Statistical Process Control

Control Charts

Control Chart Selection

Control Limits

Capability Indices - Cpk, Etc.

Process Capability Study

Statistical Process Control Control Charts

Xbar & R (Range) Chart

Xbar & s (Standard Deviation) Chart

I (Individuals) & MR (Moving Range) Chart

p Chart

np Chart

u Chart

From Individuals Chart to Statistical Quality Control.

From Individual Chart to Free Six Sigma Tools.

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