The setting with the best average is not always the best setting
Two machine settings produce the same average tensile strength. One of them gives you the same number every day; the other swings with the humidity, the raw material batch, and who is on shift. On paper they tie. In production only one of them is any good.
What ordinary DOE misses. A factorial experiment estimates the effect of each factor on the average response. It has nothing to say about the spread, because the noise is treated as something to be averaged away. Taguchi turns that around: the noise is the point. You deliberately vary the things you cannot control in production — an outer array of noise factors — and look for the control settings whose output barely moves when the noise does. That is robustness, and it is free: it costs nothing extra to run a process at a setting that happens to be insensitive.
Orthogonal arrays. These let you study many factors in very few runs. The property that makes them work is balance: within any pair of columns, every combination of levels appears the same number of times, so when you compare the levels of one factor, the others are perfectly balanced out and cancel. L8 studies up to 7 factors in 8 runs. That sounds too good, and it is — see the warning below.
The signal-to-noise ratio. One number per run, combining the mean and the variation, in decibels. Larger-is-better, smaller-is-better and hit-the-target each have their own formula. Higher is always better. The method is genuinely criticised by statisticians on this point: collapsing mean and variance into one number throws information away, and the ratio can favour a setting for the wrong reason. SenSight therefore always shows the mean beside the S/N, so you can use the two-step approach instead: first choose the levels that reduce variation, then use a factor that shifts the mean without affecting the spread to bring the average onto target.
The trap that costs the most. Putting 7 factors into L8 does not give you 7 clean answers. There are only 7 columns, and the interactions have to go somewhere — straight on top of the main effects. If A×B is real, the effect you read for C is partly A×B. SenSight computes this exactly for your column assignment and names which pairs are inseparable from which factor, rather than printing a vague warning. With four factors in L8 there is no confounding at all, and that is usually the better trade.
Always confirm. The predicted optimum assumes the factors add up independently. If the recommended combination was never actually run, it is arithmetic, not evidence. Run it.
What ordinary DOE misses. A factorial experiment estimates the effect of each factor on the average response. It has nothing to say about the spread, because the noise is treated as something to be averaged away. Taguchi turns that around: the noise is the point. You deliberately vary the things you cannot control in production — an outer array of noise factors — and look for the control settings whose output barely moves when the noise does. That is robustness, and it is free: it costs nothing extra to run a process at a setting that happens to be insensitive.
Orthogonal arrays. These let you study many factors in very few runs. The property that makes them work is balance: within any pair of columns, every combination of levels appears the same number of times, so when you compare the levels of one factor, the others are perfectly balanced out and cancel. L8 studies up to 7 factors in 8 runs. That sounds too good, and it is — see the warning below.
The signal-to-noise ratio. One number per run, combining the mean and the variation, in decibels. Larger-is-better, smaller-is-better and hit-the-target each have their own formula. Higher is always better. The method is genuinely criticised by statisticians on this point: collapsing mean and variance into one number throws information away, and the ratio can favour a setting for the wrong reason. SenSight therefore always shows the mean beside the S/N, so you can use the two-step approach instead: first choose the levels that reduce variation, then use a factor that shifts the mean without affecting the spread to bring the average onto target.
The trap that costs the most. Putting 7 factors into L8 does not give you 7 clean answers. There are only 7 columns, and the interactions have to go somewhere — straight on top of the main effects. If A×B is real, the effect you read for C is partly A×B. SenSight computes this exactly for your column assignment and names which pairs are inseparable from which factor, rather than printing a vague warning. With four factors in L8 there is no confounding at all, and that is usually the better trade.
Always confirm. The predicted optimum assumes the factors add up independently. If the recommended combination was never actually run, it is arithmetic, not evidence. Run it.
Try it in the app
Try: DOE tab, Taguchi. Put 7 factors into L8 and read the confounding list, then drop to 4 factors and watch it disappear.