Quality Control

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.

I have written a book on Practical Acceptance Sampling. The book is a hands-on introduction to the inspection of products and services for quality assurance using statistically-based sampling plans. In today’s era of global supply chains the path from raw materials to final product often takes place over multiple companies and across multiple continents. Acceptance sampling plans provide criteria and decision rules for determining whether to accept or reject a batch based on a sample. They are therefore widely used by manufacturers, suppliers, contractors and subcontractors, and service providers in a wide range of industries. The book introduces readers to the most popular sampling plans, including Military Standards and civilian ISO and ANSI/ASQC/BS standards. It covers the design, choice and performance evaluation of different types of plans, including single- and double-stage plans, rectifying and non-rectifying plans, plans for pass/fail and continuous measurements, continuous sampling plans, and more. Practical Acceptance Sampling is suitable for courses on quality control and for quality practitioners with basic knowledge of statistics. It offers clear explanations, examples, end-of-chapter problems and illustrations of state-of-the-art online resources. Methods are illustrated using Microsoft Excel, online calculators, and www.SQCOnline.com. However, any statistical software can be used with the book that demystifies the various procedures of sampling for the purposes of batch sentencing.