Wednesday, May 2, 2012

How to Make IR Control Charts

Suppose you support a batch process. The way you likely measure performance is to sample each batch and measure different parameters. These measurements are ideal for plotting on an IR control chart - one control chart for each parameter and each batch would be represented by one point on the control chart.

If you have statistical software like JMP, then you can just click around on the menu

JMP IR control chart menu


JMP control chart dialog

control charts appear like magic:

control chart IR

But suppose Wall Street bankers crashed the economy by securitizing AAA-rated subprime mortgages and you are the collateral damage; forking over $1,250 for a single-user annual license or $1,895 for a single-user perpetual license of JMP isn't in the cards. What do you do?

Good news. William Shewhart developed control charting principles long before computers so if worse comes to worse, you could probably create a control chart from graph paper and a grease pencil.

Here's what you do:
  1. Get the data into a column
  2. Compute moving range
  3. Multiply MR by 3 and divide by 1.128
We're not going to do it with a grease pencil and graph paper. We're going to do it with a spreadsheet.

Step 1: Get the data into a column

We haven't talked about this yet, but data for analysis needs to be structured. If you look at the numbers in a column and they represent what the column headers describe, then you got it right.

columnar data

Step 2: Compute the Moving Range

moving range for control charts

This is where you take the absolute value of the difference between measurements. =B3-B2 would be the formula that you'd drag in column C. The average of the moving range is used to determine the width of the control limits.

Step 3: Compute distance to control limits

To get the distance to each control limit, compute 3 * Average( MovingRange ) / 1.128.

computing control limits

In this case, the average of the moving range is 3.90. Take 3.90 * 3 / 1.128 = 10.37.

The Upper Control Limit (UCL) is the 296 + 10.37 = 306

The Lower Control Limit (LCL) is the 296 - 10.37 = 286

What you do is calculate limits for every parameter you measure; apply it to a steady process and lock the limits and monitor the process against the locked-down limits to detect drift.

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