Taguchi Methods for Robust Design and the P-Diagram

In previous articles in this series I introduced Designed Experiments (Article 28) and Taguchi Methods (Article 32).   In this article I will introduce the Parameter Diagram, aka P-diagram, and explain how the P-diagram is used in conjunction with Designed Experiments as part of the robust design process.

The P-diagram is used to classify all of the variables associated with a product as signals (inputs), responses (outputs), control factors or noise factors.  Control factors are parameters that can be specified by the designer, either as fixed values or adjustable values, while noise factors are beyond the control of the designer.  Examples of noise factors are environmental factors such as temperature, humidity, and vibration.  The objective of the designer when creating a robust design is to determine parameter settings that produce the desired responses while at the same time reducing the sensitivity of the design to noise factors that are not easily controlled.

As an example, consider the hand braking system on an All-Terrain Bicycle.  Input signals include braking force applied to the hand brakes and the steering inputs.  The ideal output responses are safe stopping distances and ease of stopping.   The types of errors that may occur include difficulty stopping on a wet surface, brake levers located in a position that makes them hard to use, and delay in braking action when brakes are applied.

The control factors include brake type, brake pad material and tire material.

The noise factors include tire wear, brake pad wear, tire pressure, ambient temperature, road condition (wet, snow, ice) and road type (asphalt, loose gravel, concrete).   Noise factors would also include piece to piece manufacturing variation in the brake system components and the tires.

The objective of the designer of the bicycle is to design a system that stops the bicycle safely under all anticipated customer usage conditions.  Customer usage conditions include foreseeable misuse such as overloading, the use of aftermarket parts or improper maintenance.   A Designed Experiment could be used in this case to evaluate the impact of different brake types, different brake materials and different tire materials on stopping distance and ease of stopping.   The objective of the designer is to choose the combination of control factors that gives the best response while being as insensitive as possible to the noise factors.

Your comments or questions about this article are welcome, as are suggestions for future articles.  Feel free to contact me by email at roger@keyperformance.com.

About the author:  Mr. Roger C. Ellis is an industrial engineer by training and profession.  He is a Six Sigma Master Black Belt with over 50 years of business experience in a wide range of fields.  Mr. Ellis develops and instructs Six Sigma professional certification courses for Key Performance LLC.   For a more detailed biography, please refer to www.keyperformance.com.