Taguchi Method II

Introduction to Taguchi Method (Part II)

By Issa Bass

Introduction to Taguchi Method I

Variability Reduction
Since the deviation from the target is the source of financial loss to society, what needs to be done in order to prevent any deviation from the set target?

The first thought might be to reduce the specification range and improve the online quality control, to bring the specified limits closer to the target and inspect more samples during the production process in order to find the defective products before they reach the customers. But this would not be a good option since it would only address the symptoms and not the root causes of the problem. It would be an expensive alternative because it would require more inspection which would at best help detect nonconforming parts early enough to prevent them from reaching the customers.

The root of the problem is in fact the variation within the production process, i.e. the value of sigma, the standard deviation from the mean.

Let’s illustrate this assertion with an example. Let’s suppose that the length of a screw is a Critical-To-Quality (CTQ) characteristic and the target is determined to be 15” with a LCL of 14. 96 and a UCL of 15.04. The following sample was taken for testing:

15.02
14.99
14.96
15.03
14.98
14.99
15.03
15.01
14.99

All the observed items in this sample fall within the control limits even though all of them do not match the target. The mean is 15 and the standard deviation is 0.023979. Should the manufacturer decide to improve the quality of the output by reducing the range of the control limits to 14.98 and 15.02, three of the items in the sample would have failed audit and would have to be reworked or discarded.

Let’s suppose that the manufacturer decides instead to reduce the variability (the standard deviation) around the target and leave the control limits untouched. After process improvement, the following sample is taken:

15.01
15
14.99
15.01
14.99
14.99
15
15.01
15

The mean is still 15 but the standard deviation has been reduced to 0.00866 and all the observed items are closer to the target. Reducing the variability around the target has resulted in improving quality in the production process at a lower cost.

This is not to suggest that the tolerance around the target should never be reduced; addressing the tolerance limits should be done under specific conditions and only after the variability around the target has been reduced.

Since variability is a source of financial loss to producers, customers and society at large, it necessary to determine what the sources of variation are so that actions can be taken to reduce them. According to Taguchi, these sources of variation that he calls Noise factors can be reduced to three:

The Inner Noise
Inner noises are deteriorations due to time. Product wear, metal rust or fading colors, material shrinkage and product waning are among the Inner Noise factors.
The Outer Noises which are environmental effects on the products.
They are factors such as heat, humidity, operating conditions or pressure. These factors have negative effects on products or processes. In the case of my notebook, at first the LCD would not display until it heats up so humidity was the noise factor that was preventing it from operating properly. The manufacturer has no control over these factors.
The Product Noise or manufacturing imperfections
Product noises are due to production malfunctions, they can come from bad materials, inexperienced operator or bad machine settings.

But if the online quality control is not the appropriate way to reduce production variations, what needs to be done to prevent deviations from the target?
According to Taguchi, a pre-emptive approach must be taken to thwart the variations in the production processes. That pre-emptive approach that he calls Off-line Quality control consists in creating a robust design, in other words designing products that are insensitive to the noise factors.

Concept Design
The production of a product starts with the concept design, which consists in choosing the product or service to be produced and defining its structural design and the production process that will be used to generate it. These factors are contingent upon among other factors the cost of production, the company’s strategy, the current technology and the market demand. So the concept design will consist in:

Determining the intended use of the product and its basic functions
Determining the materials needed to produce the selected product
Determining the production process needed to produce it

Parameter Design
The next step in the production process is the parameter design. After the design architecture has been selected; the producer will need to set the parameter design. The parameter design consists in selecting the best combination of control factors that would optimize the quality level of the product by reducing the product’s sensitivity to noise factors. Control factors are parameters over which the designer has control. When an engineer designs a computer, he has control on factors such as the CPU, System board, LCD, memory, LCD cables…. etc. He determines what CPU best fits a motherboard, what memory stick and what wireless network card to use and how to design the system board that would make it easier for the parts to fit in. The way he combines those factors will impact the quality level of the computer.

The producer wants to design products at the lowest possible cost and at the same time have the best quality result under current technology. To do so, the combination of the control factors must be optimal while the effect of the noise factors must be so minimal that they will not have any negative impact on the functionality of the products. So the experiment that leads to the optimal results will require the identification of the noise factors because they are part of the process and their effects need to be controlled.

One of the first steps the designer will take is to determine what the optimal quality level is. He will need to determine what the functional requirements are, assess the Critical-To-Quality characteristics of the product and specify their targets. The determination of the CTQs and their targets depends among other criteria on the customer requirements, the cost of production and current technology. The engineer is seeking to produce the optimal design, a product that is insensitive to noise factors!
The quality level of the CTQ characteristics of the product under optimal conditions depends on whether the response experiment is static or dynamic.
The response experiment (or output of the experiment) is said to be dynamic when the product has a signal factor that steers the output. For instance when I switch on the power button on my computer, I am sending a signal to the computer to load my Operating System. It should power up and display within 5 seconds and it should do so exactly the same way every time I switch it on. If, as in the case of my computer, it fails to display because of the humidity, I conclude that the computer is sensitive to humidity and that humidity is a noise factor that negatively impacts the performance of my computer.

The response experiment is said to be static when the quality level of the CTQ characteristic is fixed. In that case, the optimization process will seek to determine the optimal combination of factors that enables to reach the targeted value. This happens in the absence of a signal factor, the only input factors are the control factors and the noise factors. When we build a table, we determine all the CTQ target and we want to produce a balanced table with all the parts matching the targets.

The optimal quality level of a product depends on the nature of the product itself. In some cases, the more a CTQ characteristic is found on a product, the happier the customers are, in other cases the less the CTQ is present, the better it is. Some products require the CTQs to match their specified targets.
According to Taguchi, to optimize the quality level of his products, the producer must seek to minimize the noise factors and maximize the Signal-To-Noise (S/N) ratio. Taguchi uses log functions to determine the Signal-To-Noise ratios that optimize the desired output.

The Bigger-The-Better
If the number of minutes per dollar customers get from their cellular phone service provider is critical to quality, the customers will want to get the maximum number of minutes they can for every dollar they spend on their phone bills.
If the lifetime of a battery is critical to quality, the customers will want their batteries to last forever. The longer the battery lasts, the better it is.

The Signal-To-Noise ratio for the bigger-the-better is:

S/N = -10*log (mean square of the inverse of the response)

The Smaller-The-Better
Impurity in drinking water is critical to quality. The less impurities customers find in their in their drinking water, the better it is.
Vibrations are critical to quality for a car, the less vibration the customers feel while driving their cars the better, the more attractive the cars are.

The Signal-To-Noise ratio for the Smaller-The-Better is:

S/N = -10 *log (mean square of the response)

The Nominal-The-Best.
When a manufacturer is building mating parts, he would want every part to match the predetermined target. For instance when he is creating pistons that need to be anchored on a given part of a machine, failure to have the length of the piston to match a predetermined size will result in it being either too small or too long resulting in lowering the quality of the machine. In that case, the manufacturer wants all the parts to match their target.

When a customer buys ceramic tiles to decorate his bathroom, the size of the tiles is critical to quality, having tiles that do not match the predetermined target will result in them not being correctly lined up against the bathroom walls.

The S/N equation for the Nominal-The-Best is:

S/N = 10 * log (the square of the mean divided by the variance)

Tolerance Design.
Parameter design may not completely eliminate variations from the target. That’s why tolerance design must be used for all parts of a product to limit the possibility of producing defective products. The tolerance around the target is usually set by the design engineers; it is defined as the range within which variation may take place. The tolerance limits are set after testing and experimentation. The setting of the tolerance must be determined by criteria such as the set target, the safety factors, the functional limits, the expected quality level and the financial cost of any deviation from the target.

The safety limits measure the loss incurred when products that are outside the specified limits are produced.

With being the loss incurred when the functional limits are exceeded and A being the loss when the tolerance limits are exceeded.

tolerance specifications for the response factor will be:

With being the functional limit.

Example:
The functional limits of a conveyor motor are +/- 0.05 of the response RPM. The adjustments made at the audit station before a motor left the company cost $2.5 and the cost associated to defective motors once it has been sold is on average $180.
Find the tolerance specification for a 2500 RPM motor.

Solution:
We need first of all to find the economical factor which is determined by the loss incurred when the functional limits or/and the tolerance limits are exceeded.

Now we can determine the tolerance specification. The tolerance specification will be the value of the response factor plus or minus the allowed variation from the target.

Tolerance specification for the response factor:

The variation from the target:

2500 * 0.0059 = 14.73

The tolerance specification will be 2500 +/- 14.73.

About the author
Issa Bass is the managing editor of SixSigmaFirst. He can be reached at issa@sixsigmafirst.com

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