[ Exercise 12 ]
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It
is a fact that engineers select an appropriate variable and
treat the transformed observations as though they are normally
distributed with a constant variance.
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Those
methods neither require previous knowledge of how the variables
are distributed nor stipulate availability of the censored
data.
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The
procedure for analyzing singly censored data in a replicated
experiment is as follows:
Step 1: Distinguish the experimental results as the uncensored
(complete) data and the censored (incomplete) data.
Step 2: Find the relationship between the two values by performing
regression analysis.
Step 3: Estimate the two variables.
Step 4: Rank the estimated censored data.
Step 5: Find the regression models for response average and
standard deviation for each trial.
Step 6: Identify the factors that significantly affect the
response average and standard deviation.
Step 7: Determine the optimal factor/level combination.
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The
derived model extends an earlier concept [1] and helps industrial
managers in determining a feasible number of replenishments.
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Experimental
design is used in this method to arrange the design parameters
and noise factors in the orthogonal arrays and to compute
the signal-to-noise (SN) ratio based on the quality loss for
each experimental combination.
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The
relative importance of each response can be transformed into
a fuzzy number through means of establishing a formal scale
system that can convert linguistic terms into their corresponding
fuzzy numbers and expressing the relative importance of each
response by the linguistic term.
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The
Taguchi combines experimental design techniques with quality
loss considerations and minimizes the average quadratic loss.
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The conventional approach happens to be cumbersome, complicated
and time consuming.
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The two-step procedure not only identifies those factors that
significantly affect the signal-to-noise (SN) ratio, but also
finds the levels that maximize SN.
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Logethetis
(1988) proved that strong non-linearities exist and also recommended
using the B technique.
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This
work not only proposes an effective procedure based on the
rank transformation of responses and regression analysis,
but also discusses the singly censored data.
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The
following steps describe the procedure:
Step 1: Calculate the normalized decision matrix.
Step 2: Calculate the weighted normalized decision matrix.
Step 3: Determine the ideal and negative-ideal solution.
Step 4: Calculate the separation measures.
Step 5: Calculate the relative closeness to the ideal solution.
Step 6: Rank the preference order.
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