Characterizing the measurement system reduces results variance.

Before starting an optimization process, be sure the measurement system is accurate and precise. Accuracy is defined as absence of bias in the measurement and precision as the dispersion of the measurements. To quantify precision, a gauge study can be used. Sources of dispersion are failure of the measurement instrument or gauge to exactly repeat itself (repeatability) and failure of the operator or machine to exactly reproduce the measurement technique (reproducibility). The Reproducibility and Repeatability (R&R) gauge study is defined as¹:

s² Equipment  + s² Appraiser =  s² Total (R&R)

In an experiment or optimization process, a number of samples are measured multiple times by different people. If the gauge is not precise, the measurement of the process is not real and could falsely indicate the process is off target. In this case, action is required to reduce the variance. The corrective actions include better instrumentation, operator training programs, or both¹.

Typically, 20 measurements are taken. If the experiment takes a long time or is expensive, a number of 10 to 15 is also acceptable. To assess gauge capability, the precision-to-tolerance (P/T) ratio is used:

P/T = 5.15 s Total (R&R) / (USL-LSL)
where 5.15 s is a commonly used number containing 99% of the theoretical distribution.

Some use a 99.7% interval (Six Sigma). USL and LSL stand for upper specification limit and lower specification limit.

When P/T < 0.10, the measurement system is good and acceptable; when P/T is between 0.1 and 0.3, the measurement system is just acceptable; and when P/T > 0.3, the measurement system is not acceptable. It is possible to set the P/T threshold at any proportion realistic to the process measurement needs.

Here’s an example of gauge R&R to measure amount of flux in a wave soldering process. The amount of flux sprayed on a PCB should be consistent. If the flux amount is less than specified, the number of defects (bridging, spikes, solder balls) could increase. If the amount is too high on the assembly, the flux residues are exceeding the limits and may result in electromigration.

The consistency of the spray system can be measured by spraying the flux into a cup and measuring the amount of flux on a scale. In this experiment, an assembly is fed into the solder machine, but instead of spraying the flux on the board, the flux is collected in a cup. This is repeated twice for 10 different boards. Three different appraisers followed this procedure, resulting in the following data expressed in grams (Table 1).

From these results, the P/T is given by

P/T = 5.15(0.326661)/10 = 0.1682

Based on this information, spraying flux in a cup and weighing the amount is an acceptable method. This statistical method can be used in several applications: measuring solder paste volume, flux amount, wave height, profiler performance, and so on.

Reference

1. W. Kolarik, Creating Quality Process Design for Results, McGraw-Hill, 1999.

Ursula Marquez de Tino, Ph.D., is a senior process and research engineer. Her column appears monthly.