Industrial engineering (IE) is human effort engineering and system efficiency engineering.
Industrial engineering uses concepts and techniques from multiple sciences and engineering disciplines in design and installation of its solutions in the work and business systems. Statistics is a discipline that is used by industrial engineers in their functioning. One can say that an industrial engineer is expected to know more about statistics among all other engineers and even managers in an organization that does not have specialist statisticians. This is because, the definition of IE given IIE contains explicit mention of mathematics and statistics as tools for IE activities. But industrial engineer is not statistician. He uses selected methods of statistics which are applied in specified ways to improve the efficiency of systems.
Statistical Quality Assurance: Statistical Methods for Process Improvement - Course page by Prof. Stephen B. Vardeman, Author of Statistics for Engineering Problem Solving.
Statistics and Industrial Engineering (new link)