Reliability HotWire

Issue 109, March 2010

Tool Tips

* 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.
  • Step 2: Select Taguchi OA Factorial Design.
  • 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.
    • 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.

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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