X. EXPERIMENTAL DESIGN FOR QUALITY

LECTURE PLAN STATISTICAL EXPERIMENTATION THE TAGUCHI LOSS FUNCTION EXAMPLE PROBLEMS AND EXERCISES

1. STATISTICAL EXPERIMENTATION

FACTORS AFFECTING A PRODUCT’S PERFORMANCE: - MANUFACTURING IMPERFECTIONS, ENVIRONMENTAL FACTORS, AND HUMAN VARIATIONS IN OPERATING THE PRODUCT.

GOOD DESIGN MINIMIZES THE SENSITIVITY OF DESIGNS TO SOURCES OF VARIATION IN THE FACTORY AND IN USE.   ROBUSTNESS: INSENTIVITY OF PRODUCTS TO EXTERNAL SOURCES OF VARIATION.

  DR. GENICHI TAGUCHI: THE USE OF STATISTICALLY PLANNED EXPERIMENTS FOR PARAMETER DESIGN. DESIGN EXPERIMENT: A TEST OR SERIES OF TESTS THAT ENABLES THE EXPERIMENT TO DRAIN CONCLUSIONS ABOUT THE SITUATION UNDER STUDY.

EXPERIMENTAL DESIGN TECHNIQUES DEVELOPED BY R.A. FISHER IN ENGLAND, DATE BACK TO THE 1920s.   BECAUSE OF A LARGE NUMBER OF VARIABLES, EXPERIMENTAL DESIGN WAS NOT WIDELY USED. A LARGE NUMBER OF EXPERIMENTS HAD TO BE CONDUCTED.

TAGUCHI DEVELOPED AN APPROACH TO DESIGNING EXPERIMENTS THAT FOCUSED ON THE CRITICAL FACTORS WHILE DEEMPHASIZING THEIR INTERACTIONS.   TRADITIONAL METHODS OF EXPERIMENTAL DESIGN AIMS TO OPTIMIZE THE MEAN VALUE OF AN IMPORTANT RESPONSE VARIABLE (YIELD IN A CHEMICAL PROCESS).

IN THE TAGUCHI METHOD, PARAMETER DESIGN EXPERIMENTS AIM TO REDUCE THE VARIABILITY CAUSED BY MANUFACTURING VARIATIONS.   CONTROLLING VARIABILITY IS MUCH HARDER THAN CONTROLLING THE AVERAGE VALUE.

VARIABLES THAT AFFECT PERFORMANCE CHARACTERISTICS (ACCORDING TO TAGUCHI): DESIGN PARAMETERS:NOMINAL SETTINGS CHOSEN BY THE DESIGN ENGINEER. SOURCES OF NOISE: VARIABLES THAT CAUSE PERFORMANCE CHARACTERISTICS TO DEVIATE FROM THEIR TARGET VALUES.

NOISE FACTORS CAN BE SYSTEMATICALLY VARIED IN A DESIGNED EXPERIMENT.   THE EXPERIMENTS ARE CONDUCTED EITHER THROUGH PHYSICAL EXPERIMENTS OR BY COMPUTER SIMULATION.

OTHER OBJECTIVES OF TAGUCHI EXPERIMENTS:   - IDENTIFYING THE SETTINGS OF DESIGN PARAMETERS THAT REDUCE COST WITHOUT SACRIFICING QUALITY, - DETERMINING THE DESIGN PARAMETERS THAT INFLUENCE THE MEAN VALUE OF THE PERFORMANCE BUT HAVE NO EFFECT ON ITS VARIATION, IDENTIFYING THOSE DESIGN PARAMETERS THAT HAVE NO DETECTABLE INFLUENCE ON THE PERFORMANCE CHARACTERISTICS.

SIGNAL-TO-NOISE (S/N) RATIO: MEASURES THE SENSITIVITY OF AN EFFECT (THE SIGNAL) TO THE NOISE FACTORS.   THE EFFECT (OR SIGNAL) IS MEASURED BY ITS MEAN VALUE. THE VARIABILITY OF THE SIGNAL, REPRESENTS NOISE FACTORS, MEASURED BY STANDARD DEVIATION.

S/N RATIO: THE RATIO OF THE MEAN TO THE STANDARD DEVIATION. HIGH SIGNAL-TO-NOISE RATIOS INDICATE LOW SENSITIVITY TO NOISE FACTORS.

CRITICISMS TO TAGUCHI’S APPROACH - STATISTICALLY INVALID AND MISLEADING ANALYSES, - MODERN GRAPHICAL APPROACHES TO DATA ARE IGNORED, - RANDOMIZATION IN PERFORMING THE EXPERIMENTS IS LACKING.

2. THE TAGUCHI LOSS FUNCTION

TAGUCHI APPROACH: VIEWS QUALITY BASED ON THE ECONOMIC IMPLICATIONS OF NOT MEETING TARGET SPECIFICATIONS.   QUALITY ACCORDING TO TAGUCHI: AVOIDANCE OF LOSS A PRODUCT CAUSES TO SOCIETY AFTER BEING SHIPPED, OTHER THAN ANY LOSSES CAUSED BY ITS INTRINSIC FUNCTIONS.

THE LOSS TO SOCIETY   COSTS INCURRED BY THE PRODUCT’S FAILURE TO MEET CUSTOMER EXPECTATIONS, THE FAILURE TO MEET PERFORMANCE CHARACTERISTICS, HARMFUL SIDE EFFECTS CAUSED BY THE PRODUCT.

TAGUCHI MEASURES LOSS IN MONETARY UNITS AND RELATES IT TO QUANTIFIABLE PRODUCT CHARACTERISTICS. HENCE, THE LANGUAGE OF THE ENGINEER IS TRANSLATED INTO THE LANGUAGE OF THE MANAGER.

ACCORDING TO TAGUCHI: THE SMALLER THE VARIATION ABOUT THE TARGET VALUE, THE BETTER THE QUALITY.   THE ONLY MEANINGFUL SPECIFICATION IS BEING ON-TARGET. THE LARGER THE DEVIATION THE LARGER THE LOSS.

TRADITIONAL CONFORMANCE TO SPECIFICATION LOSS FUNCTION

TAGUCHI LOSS FUNCTION

NOMINAL-IS-BEST LOSS FUNCTION

COMPUTATIONS USING THE TAGUCHI LOSS FUNCTION THE LOSS FUNCTION (A QUADRATIC FUNCTION); L(X) = k(X – T)2   WHERE X = ANY VALUE OF THE QUALITY CHARACTERISTIC, T = THE TARGET VALUE, AND k = SOME CONSTANT.

THE EXPECTED LOSS IS EL(X) = k(2 + D2)   D2 = (X – T)2 D = DEVIATION OF THE MEAN VALUE FROM THE TARGET.

3. EXAMPLE PROBLEMS AND EXERCISES

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

EXERCISES 1. A blueprint specification for the thickness of a dishwasher part at Partspalace, Inc. is 0.325 ± 0.025 centimeters (cm). It costs $10 to scrap a part that is outside the specifications. Determine the Taguchi loss function for this situation.

2. A team was formed to study the dishwasher part described in Problem 1. While continuing to work to find the root cause of scrap, they found a way to reduce the scrap cost to $5 per part. Determine the Taguchi loss function for this situation. If the process deviation from target can be held at 0.015 cm, what is the Taguchi loss?

3. An electronic component has a specification of 180 ± 5 ohms 3. An electronic component has a specification of 180 ± 5 ohms. Scrapping the component results in an $100 loss. What is the value of k in the Taguchi loss function? If the process is centered on the target specification with a standard deviation of 2 ohms, what is the expected loss per unit?

4. Ruido Unlimited makes electronic soundboards for car stereos 4. Ruido Unlimited makes electronic soundboards for car stereos. Output voltage to a certain component on the board must be 15 ± 0.2 volts. Exceeding the limits results in an estimated loss of $75. Determine the Taguchi loss function.

5. An automatic cookie machine must deposit a specified amount of 15 ± 0.1 grams (g) of dough for each cookie on a conveyor belt. If the machine either over- or underdeposits the mixture, it costs $0.015 to scrap the defective cookie. What is the value of k in the Taguchi loss function? If the process is centered on the target specification with a standard deviation of 0.05 g, what is the expected loss per unit?

6. In the production of transformers, any output voltage that exceeds 120 ± 30 volts is unacceptable to the customer. Exceeding these limits results in an estimated loss of $300. However, the manufacturer can adjust the voltage in the plant by changing a resistor that costs $2.25. Determine the Taguchi loss function. Suppose the nominal specification is 120 volts. At what tolerance should the transformer be manufactured?