Six Sigma Control Phase: How Statistical Process Control Works ?

Control is all around us. We control the household appliances, the time schedules we follow and such mundane tasks of our everyday lives. We are intuitively aware of these principles. However putting these principles down explicitly helps us develop a formal understanding which we can then use in creating a control plan for our process. Since control is so widely used in our day to day lives, one of the best way to understand control would be to take an example. A simple example of an air-conditioner with a thermostat would help us understand the principles.

Example: Air-Conditioner with a Thermostat

Suppose you have an air-conditioner at home and you want to set the temperature to 22 degrees Celsius, how do you do it? Well, you simply use the remote to enter the desired temperature into the machine which then ensures that the temperature in the room is approximately the one you had desired. Here is what actually happens behind the scene.

The air-conditioner has a thermostat inbuilt. The thermostat is the equipment which continuously monitors the temperature of the room outside. This provides the air-conditioner with the feedback information it needs.

Let’s suppose that the temperature in the room is 30 degrees Celsius when you switch on the air conditioner and program 22 degrees Celsius as your desired temperature. The air-conditioner uses a simple algorithm to understand that tells it that since 30 degrees is greater than 22 degrees (the desired temperature), a corrective action must be taken.

The air-conditioner then keeps on cooling the room, until the thermostat tells the air-conditioner that the temperature has reached 22 degrees i.e. the desired temperature. Here the air-conditioner stops cooling. Once again as the temperature starts increasing and goes beyond a certain level, lets say 24 degrees Celsius, the corrective action is set in and the temperature is brought back to the level where it should be. Hence the thermostat can automatically control the temperature.

The Principles Deciphered from the Example:

The formal principles of what is called feedback based control in statistical language have been pinned down in the example. They are as follows:

  • Desired State of Affairs: To control a process, the desired state of affairs must be explicitly known and programmed into the control mechanism. In our example the air-conditioner knew that the desired temperature was 22 degrees Celsius and could compare whether the actual state were as desired or not.

  • Limits: It is impossible for any process to function in a straight line. Therefore control limits were built in. Temperature within the range of 20 to 24 degrees would be considered as being the desired state of affairs.

  • Feedback Mechanism: The thermostat acted as the feedback mechanism, continuously monitoring the feedback. This feedback was compared with what the desired state of affairs on a real time basis.

  • Corrective Action Plan: As soon as it was realised that the actual state of affairs did not correspond to the desired state of affairs, corrective action plan was immediately triggered.

This is exactly how a process is controlled. The output levels (Y’s) are continuously measured and so are the levels of critical inputs (X’s). As soon as a discrepancy is located, corrective action must take place.


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