Runs and Scans in Industrial statistics

During my Ph.D. I developed a method for computing exact probabilities
for random variables that arise when runs or scans are used. A run is a sequence of consecutive successes in a series of Bernoulli trials. A scan is a “window” of consecutive Bernoulli trials that includes at least a given number of successes. Runs and scans are applied in various fields. Although they are easy to understand and use, the random variables that arise tend to have characteristics (e.g. probability functions, moments) that are complicated for computation. The method that I developed is based on Feller’s idea for computing the distribution of the waiting time until the first run (the geometric distribution of order k). In my Ph.D. thesis I generalized Feller’s method using both probability theory and advances in computation power. Since then I have generalized the theory further, and applied it to industrial applications. 

SQC Online (Statistical Quality Control Online)
As many statisticians have pointed out, there exists an enormous gap between research advances and their adoption by practitioners. One approach to bridge the gap is to webify theoretical work, thus making it accessible to users. I have therefore webified “good old” existing statistical procedures, tables, and charts (e.g., the Military Standards 105E, MIL-STD-414, MIL-STD-1235 Sampling Plans and their civilian counterparts, ANSI Z1.4, Z1.9, ISO 2859) and a few new theoretical results. My website SQC Online, is used by many well-known companies. It uses a simple and user-friendly interface to compute probabilities, create graphs, etc., that are then used for quality control. The site webifies existing techniques (e.g. acceptance sampling plans, control charts, MTBF calculations, MIL-HDBK-217, etc) and new theoretical derivations on runs and scans. The website is mentioned and pointed to in many sites such as the NIST/SEMATECH Online Engineering Statistics Handbook.