Transcript design experiment

X. EXPERIMENTAL DESIGN
FOR QUALITY
LECTURE PLAN
1. STATISTICAL EXPERIMENTATION
2. THE TAGUCHI LOSS FUNCTION
3. 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.
a. Determine the Taguchi loss function
for this situation.
b. 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. Scrapping
the component results in an $100 loss.
a. What is the value of k in the Taguchi
loss function?
b. 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. 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.
a. What is the value of k in the Taguchi loss
function?
b. 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.
a. Determine the Taguchi loss function.
b. Suppose the nominal specification is
120 volts. At what tolerance should the
transformer be manufactured?