Design of Experiments for PCB Process Optimisation

Process problems rarely have a single cause. Changing one parameter at a time, which is how most process work is done, cannot reveal what happens when two parameters are changed together, and it is inefficient when several parameters need to be explored. Design of experiments is a structured way to learn more from fewer runs.

Why One Factor at a Time Fails

The traditional approach holds everything constant and varies one parameter, then moves to the next. It works when the parameters act independently, and it misleads when they do not. A temperature that improves the result at one conveyor speed may make it worse at another, and a one factor at a time study will never see it.

The approach is also expensive. Exploring five parameters at three levels each would take a very large number of runs sequentially, while a designed experiment can cover the same ground in a fraction of the effort and can quantify the interactions at the same time.

The Vocabulary of an Experiment

A factor is a process parameter that is deliberately varied, such as reflow peak temperature, conveyor speed or stencil aperture size. A level is a value at which the factor is set. A response is the measured outcome, such as solder joint void percentage or paste deposit volume.

An interaction exists when the effect of one factor depends on the level of another. Interactions are the main reason designed experiments are worthwhile, because they are common in soldering and coating processes, and they are invisible to sequential testing.

Screening Designs

When there are many candidate factors and little is known about which matter, a screening design is used. It varies many factors at two levels each in a small number of runs, and it identifies which factors and interactions have a measurable effect, so that effort can be focused on those. A typical screening design covers six or seven factors in eight to sixteen runs, which is small enough to complete in a day on most processes.

Screening designs deliberately accept some ambiguity, because the effects of the higher order interactions are mixed together. That is acceptable at the screening stage, where the goal is to reduce a long list to a short one, and the remaining factors are studied more carefully afterwards.

Full Factorial and Response Surface

Once the important factors are known, a full factorial design at two or three levels gives a complete picture of the main effects and interactions. It needs more runs, but the analysis is unambiguous and the result is easy to explain to a team that has not studied statistics.

Where the goal is to find a setting rather than to identify an effect, a response surface design is more efficient. It models the curvature of the response and can locate an optimum, including the region where two factors interact strongly, at the cost of requiring the response to be measured with good repeatability.

Choosing Responses and Measurement

The response has to be measurable, relevant to the problem and repeatable. A defect count with a low rate gives almost no information in the twenty runs a typical experiment contains, while a continuous measurement such as deposit volume or pull strength gives a result from every run.

Where the obvious response is a defect rate, a surrogate is often better: paste deposit volume instead of bridging, void percentage instead of joint failure, coating thickness uniformity instead of pinholes. The surrogate has to be established as a predictor of the real outcome before it is used. Where several outcomes matter, it is usually better to nominate one primary response for the design and treat the rest as constraints that must not be violated. The measurement methods available for printing are described in this guide to solder paste inspection.

Randomisation, Blocking and Replication

The run order should be randomised, because a systematic drift in the process over the course of the experiment will otherwise be attributed to the factor that happened to be set when the drift occurred. Randomisation converts that drift into noise instead of a false effect.

Where the runs cannot be fully randomised, blocking is used. Runs made in one session, on one machine or from one batch of material form a block, and the analysis separates the block effect from the factor effects. Replication, meaning repeated runs at the same settings, provides an estimate of the experimental error that all the other conclusions depend on.

Analysing the Results

The analysis estimates the effect of each factor and interaction, and compares those estimates against the experimental error. An effect much larger than the noise is real; one of the same size is not, however appealing the explanation may be. The error estimate is what makes that judgement possible, and the verification measurements behind it follow the same logic as judging PCB quality on a finished board.

Graphs are as important as the numbers. A plot of the response against each factor shows the direction and the size of the effect, and an interaction plot shows whether the lines cross or diverge. Those pictures usually communicate the result to the production team far better than a table of coefficients.

Confirmatory Runs and Implementation

An experiment produces a prediction, not a proof. The settings identified as best should be run again, in production conditions, and the response measured to confirm that the prediction holds outside the experimental window. A result that cannot be reproduced is usually the product of a factor that was not controlled, such as a change in material, environment or operator, and the resulting defect patterns are catalogued in this guide to solder defects and board failures.

The confirmed settings then become a process change with the usual controls: documented, communicated and monitored. Because the experiment established which factors matter, monitoring can focus on those rather than on everything, which makes the control plan simpler and more likely to be followed.

Common Mistakes

The most common mistakes are running too few replicates to estimate error, changing more than one thing during a run, and choosing a response that cannot distinguish between the settings being compared. Each of these produces an experiment that consumes time without producing a conclusion.

Another is treating a designed experiment as a substitute for understanding the process. The statistics identify what changed; the physics explains why. Both are needed, and the process documentation that supports that explanation is part of the wider PCB production process flow.

FAQ

How many runs does a designed experiment need? A screening design can cover six or seven factors in eight to sixteen runs, while a full factorial with three factors at two levels needs eight runs plus replicates. The number is set by the design and by the number of replicates needed to estimate the error.

Can I run a designed experiment on a production line? Yes, and it is usually the best place to do it, because the results then apply to the real process. The runs have to be planned so that the changes are safe and traceable, and the parts produced should be identified so their quality can be verified.

What if the response cannot be measured accurately? Then the experiment cannot detect small effects, however well it is designed. Improving the measurement first, even with a simpler method such as weighing deposits instead of measuring them, is usually time well spent before investing in a large experiment.