Recently I've had a need to include robust and complex math calculations in my c# applications such as polynomial curve fitting, calculus and advanced statistics. I am pleased to say I've found an excellent .NET math code library called NMath from CenterSpace Software. The company is extremely customer friendly, has both email and phone support, and has an easy to use object model. Check them out if you need this kind of functionality.

Two common ways of visualizing a distribution of tested UUTs is to use a Histogram  or a BoxPlot as shown below. Of special importance are points that fall outside the expected population, otherwise known as outliers. If the population comes from a passing universe, outliers may still be of concern since they may pose a reliability or intermittent problem. For example, a junction leakage of a power FET may indicate a surface leakage issue that may, in time, fail in the end applications. Another example is an outlier in a "tested good" power supply module. This may indicate improperly built magnetic components that may eventually fail intermittently or produce internal hot spots leading to eventual failure.

In the Histogram, the red area are the Histogram bins and the top section are the individual data points. Statistical outliers can be determined as follows:

• Compute the mean and standard deviation of the total population.
• Identify any point from the main population that falls outside +/- 3 standard deviations. These are considered outliers.

A BoxPlot is shown in the bottom chart. Here the outliers, or unusual points are defined as points falling outside a percentile range such as 10%/90%, although other choices can be made such as 1%/99%.

Note that the main difference between the two types of distribution charts is that a Histogram deals with bins of data and the BoxPlot deals in percentiles.

LabVIEW has many statistical function that enable adding SPC to your application. I use the functions extensively in my applications and am glad I don't have to revert to a third party tool or write my own. Here are a few of my favorites:

• Histogram.vi - Creates histogram bins from raw data
• Continuous Random.vi - Creates a distribution of data points based on a few key parameters. For example, a normal distribution can be created by specifying the sample size, mean and standard deviation. I use this when implementing Monte Carlo analysis.
• Statistics Express VI - This express VI contains numerous statistics parameters all in the same VI.