S Chart

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Control Chart - S Chart


Purpose

The S Chart is used to observe and evaluate the variation of a process over time against control limits, and take corrective action if necessary. The chart plots the standard deviation of each of a number of sampled subgroups. It is usually plotted in conjunction with the Xbar Chart


Anatomy

Standard Deviation Control Chart

Measuring Variation - Standard Deviation Control Chart


Reference: Statistical Process Control – Ford/GM/Chrysler

Terminology

A. Sample StDev – The standard deviations of the process subgroups as collected in sequential, or chronological, order from the process

B. Sample Number – The chronological index number for the sample, or subgroup, whose standard deviation is 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 Standard Deviation over the period, multiplied by a conversion factor.

D. Process Average – Overall average value of the subgroup standard deviations, 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 Standard Deviation over the period, multiplied by a second conversion factor, different from the one used to calculate the LCL.

F. Plot of the sample Standard Deviation values vs sample number.


Major Considerations

This chart is a more accurate indicator of process variation, and is recommended for use with larger sample sizes (generally 10).

It is less sensitive than the R Chart in detecting special causes of variation that cause only a single value in a subgroup to be unusual,


Application Cookbook

  1. Determine purpose of the chart
  2. Select data collection point
  3. Establish basis for sub grouping
  4. Establish sampling interval and determine sample size n
  5. Set up forms for recording and charting data and write specific instructions on use of the chart
  6. Collect and record data.
  7. Compute each subgroup's Mean Xi
  8. Compute each subgroup's Standard Deviation si
  9. Compute the overall process Standard Deviation s
  10. Compute Upper Control Limit UCLs
  11. Compute Lower Control Limit LCLs
  12. Plot data points
  13. Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary

n is the subgroup size, and k is the number of subgroups LCL = 0 for n<7


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 S Chart to Six Sigma Tools.

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