Ingo,
thanks for your valuable input
Attached you will find your L18 analysed with Minitab.
Because your Response should be minimized (time to start the Engine) the S/N Ratio Formula is used for "Smaller the Better" (keep in mind that this is related to your Response the S/N Ratio goal is maximize)
The Static Parameter Design has an inner array with Control Factors and an outer array for Noise Factors. (acc. Mr. Taguchi's Definition)
The goal is 1. to minimize Variation due to Noise Factors and 2. improve the response (maximize, nominal, smaller depends on what you want --> different S/N Formulars)
The Dynamic Parameter Design includes additional to the outer array of Noise Factors also a Signal (z.B. unterschiedliche Betriebszustände).
The calculation Formulars for S/N is different and additional there will be a slope Calculation to improve the response over the whole Signal Settings.
Good point
I've corrected the attachment.
But let's come back to your L18 --> First it makes no really sense to calculate a Standard Deviation (Needed for S/N Ratio) out of 2 values.
You need minimum 3 repeated measurements for each Noise Level Setting.
Why 3 and not 4, 5, ...? The standard deviation can be calculated if 2 or more values are present, but the answer to the question "how many replications are necessary" depends on other knowledge as well (e.g. measurement system error, effect size, resolution of the measurement).
In the L18-design are three runs (run 2, 3 and 5) where exactly the same outcome is given for N1 and N2. For these runs the standard deviation is 0.
To evaluate variation a common method is to use the natural logarithm of the standard variation (ln(s)) as it has a nearly linear relationship to the factors. This method is provided as an option for Taguchi analyses in Minitab (see Analyze Taguchi Design > Options) and is used within the "Analyze Variability" menu for factorial designs. But ln(0) is not defined, because the natural logarithm can only be calculated for values >0. So there will be a lack of information from those runs with equal results (independent of the number of repeated measurements) in the analysis of variation.
But Minitab is just doing the Math Job without checking the sense.
Ok acc. what Minitab gives as Coefficiants B1 is only significant (p-value small) to use it to Maximize the S/N Ratio and if you check the Graphs you are in the lucky position that also the Mean can be reduced with B1.
But every Prediction of a DoE or PD has to be confirmed.
I hope the Factor B on Level 1 can really help to reduce Variation due to noise and reduce the Response.
I won't be too optimistic that an optimization depending on B=1 will provide a better result. If all non-significant terms in the model are removed (A, C, D, E, F, G, H) and only B remains (Analyze Taguchi Design > Terms > Selected Terms: B:B), the coefficient of determination is R²=31% (for SN-ratio) and 37% (for Mean). That's really sparse, especially for a doe.
An alternativ Approach would be the Inner outer Array PD.
The Interaction between Control Factors and Noise Factors can be investigated and used to minimize the Effect to the Response due to the Noise.
In this PD you do not need Repeated Measurements per Test Run. (I would not run any DoE without repeated Measurments but in some cases it is a Question of Money or Time)
Imho this is a better approach, but to evaluate the mean
and the variation as response variables (and optimize the process to achieve a specific target for the mean
and a minimal variation) the design has to be done at least 2 times (or more, depending on the certainty of measurement system, etc.)
If you're "only" interested in the vital factors which have an impact on the outcome (not the variation), it would be sufficient to do only 1 replication. As a rule of thumb in a screening experiment only 20% of the factors do have a real (significant) impact on the response (see Anderson & Whitcomb), so imho the number of replications can be set to 1 here (depending on the certainty of measurement system, etc.)
Attached you will find a 2 Level L16 with 7 Control Factors and One Noise Factor.
(Response --> random number so just for Info)
Shouldn't that be a design with 8 control factors (A-H) and 1 noise factor (Noise) to be comparable to the original factor structure? Imho a fractional factorial design with 9 factors (2**(9-4), resolution IV) and 32 runs would be sufficient. And I would recommend to add some centerpoints for a curvature test (see attached xls-file with 4 centerpoints).
To separate time-dependent effects and factor-setting effects, the order should be randomised as much as possible (see first sheet in the excel-file "2^(9-4) randomised". If "Noise" is a hard-to-change factor (like in a split-plot design) and (really!) can't be changed for each experiment, the runs could be partly sorted (see second sheet in the excel-file "2^(9-4) partly randomised". If any kind of non-random structure is present in a design, the analysis has to be done with respect to this changes (e.g. a split-plot design is a nested design).
Ich hoffe wir haben Dich jetzt nicht komplett abgehängt, Hannes
Viele Grüße
Barbara