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How can I assign factors to specific
columns of a Taguchi orthogonal array in DOE++?
Taguchi orthogonal arrays (OA) are highly
fractional orthogonal designs based on a design matrix proposed
by Dr. Genichi Taguchi. These designs allow you to consider
a selected subset of combinations of multiple factors at
multiple levels. Orthogonal arrays are balanced to ensure
that all levels of all factors are considered equally. For
this reason, the factors can be evaluated independently
of each other despite the fractionality of the design.
To create a Taguchi OA design that meets your needs using
DOE++’s Design Wizard:
- Step 1: Select Factorial Design.
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- Step 2: Select Taguchi OA Factorial Design.
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- Step 3: Specify the type of design.
- In a Single Level Factor Design, all factors
have the same number of levels. Select the appropriate
number of levels and then select a design. For example,
you might select 3 Level Design and choose the
L27
(3^13) design, as shown next. This design involves
27 experimental runs, using 3 levels for 13 factors.
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- In a Mixed Level Factor Design, some factors
have one number of levels and the remaining factors
have another number of levels. Select the appropriate
combination of levels (2 and 3, 2 and 4, 2 and 8,
or 3 and 6) then select a design. For example, you
might select Mixed 2 Level and 4 Level Design and
choose the L16 (2^9*4^2) design, as shown next.
This design involves 16 experimental runs, using
2 levels for 9 factors and 4 levels for 2 factors.
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The View Available Designs button opens a table that
displays the available single level or mixed level Taguchi
OA designs. These tables provide information about the available
combinations of the number of factor levels and the number
of runs. In the design notation, the value immediately following
L represents the number of runs used in the design. Within
the parentheses, each base value represents a number of
levels and each exponent represents a number of factors.
For example, the L8(27) design involves 8 experimental runs,
using 2 levels for each of 7 factors. The L8(24 x 41) involves
8 experimental runs, using 2 levels for each of 4 factors
and 4 levels for 1 factor.
The Factors field allows you to further limit the number
of factors to be used in the experiment. The number of factors
available for use in the experiment will be determined by
the design you have selected. For example, if you have chosen
the L27 (3^13) 3 level design, you can select to use from
2 to 13 factors. If you choose to use fewer than the full
13 factors, the number of experimental runs will be reduced
accordingly. In the Design Wizard shown next, 4 factors
will be used.
Click Factor Properties to open the Factor Properties
window, which allows you to specify full information about
each factor, including the column of the Taguchi orthogonal
array in which it appears. In the Factor Properties window
shown next, the first factor is assigned to the first column,
the second factor is assigned to the second column, the
third factor is assigned to the fifth column and the fourth
factor is assigned to the eighth column.
What tools are available to help me design
a reliability demonstration test?
Frequently, manufacturers will need to demonstrate
that a certain product has met a goal of a specified reliability
at a given time with a specified confidence. When designing
the test that will be used to demonstrate the reliability
goal, there are several factors that must be taken into
consideration: the number of units that will be tested,
the duration of the test and the number of allowable failures
(e.g. 0 for a "zero failure test"). Several statistical
tools are available to help with the test planning and the
appropriate tool will depend on whether you are testing
a non-repairable item or a repairable system.
Non-Repairable Items
The Design of Reliability Tests (DRT) utility in ReliaSoft’s
Weibull++
software offers a choice of three methods:
- Parametric Binomial: When you specify the goal with
a given confidence level (in terms of reliability at
a given time or MTTF), the expected failure distribution
and the number of allowable failures, the utility can
calculate:
- The number of test units for a given test
time.
- OR
- The amount of test time for a given number of units.
- Non-Parametric Binomial:
- When you specify the number
of units and the number of allowable failures, the utility
can calculate the reliability that can be demonstrated
at a given confidence level.
- When you specify the
reliability goal with a given confidence level and the
number of allowable failures, the utility can calculate
the number of units that need to be tested.
- When you
specify the reliability goal, the number of allowable
failures and the number of units under test, the utility
can calculate the confidence level of the demonstrated
reliability.
- Exponential Chi-Squared: When you specify
the goal with a given confidence level (in terms of
reliability at a given time or MTTF) and the number
of allowable failures, the utility can calculate the
amount of test time required. NOTE: Since it is based
on the exponential distribution, this calculation assumes
a constant failure rate.
Repairable Systems
The Repairable
Systems DRT utility in ReliaSoft’s
RGA 7 software is
based on the non-homogeneous Poisson process (NHPP)
so it is suitable for tests involving repairable systems.
- When you specify the goal with a given confidence
level (in terms of cumulative MTBF, instantaneous MTBF,
cumulative failure intensity or instantaneous failure
intensity) and the number of allowable failures, the
utility can calculate:
- The number of test units for
a given test time.
- OR
- The amount of test time for
a given number of units.
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