Engineering statistics combinesengineering andstatistics usingscientific methods for analyzing data. Engineering statistics involves data concerningmanufacturing processes such as: component dimensions,tolerances, type of material, and fabrication process control. There are many methods used in engineering analysis and they are often displayed ashistograms to give a visual of the data as opposed to being just numerical. Examples of methods are:^{[1][2][3][4][5][6]}

1. Design of Experiments (DOE) is a methodology for formulating scientific and engineering problems using statistical models. The protocol specifies a randomization procedure for the experiment and specifies the primary data-analysis, particularly in hypothesis testing. In a secondary analysis, the statistical analyst further examines the data to suggest other questions and to help plan future experiments. In engineering applications, the goal is often to optimize a process or product, rather than to subject a scientific hypothesis to test of its predictive adequacy.^[1][2][3] The use ofoptimal (or near optimal) designs reduces the cost of experimentation.^[2][7]
2. Quality control andprocess control use statistics as a tool to manage conformance to specifications of manufacturing processes and their products.^[1][2][3]
3. Time and methods engineering use statistics to study repetitive operations in manufacturing in order to set standards and find optimum (in some sense) manufacturing procedures.
4. Reliability engineering which measures the ability of a system to perform for its intended function (and time) and has tools for improving performance.^{[2][8][9][10]}
5. Probabilistic design involving the use of probability in product and system design
6. System identification usesstatistical methods to buildmathematical models ofdynamical systems from measured data. System identification also includes theoptimaldesign of experiments for efficiently generating informative data forfitting such models.^[11][12]

Engineering statistics dates back to 1000 B.C. when theAbacus was developed as means to calculate numerical data. In the 1600s, the development of information processing to systematically analyze and process data began. In 1654, theSlide Rule technique was developed byRobert Bissaker for advanced data calculations. In 1833, a British mathematician namedCharles Babbage designed the idea of an automatic computer which inspired developers atHarvard University andIBM to design the first mechanical automatic-sequence-controlled calculator calledMARK I. The integration of computers and calculators into the industry brought about a more efficient means of analyzing data and the beginning of engineering statistics.^[13][6][14]

A factorial experiment is one where, contrary to the standard experimental philosophy of changing only one independent variable and holding everything else constant, multiple independent variables are tested at the same time. With this design, statistical engineers can see both the direct effects of one independent variable (main effect), as well as potentialinteraction effects that arise when multiple independent variables provide a different result when together than either would on its own.

Six Sigma is a set of techniques to improve the reliability of a manufacturing process. Ideally, all products will have the exact same specifications equivalent to what was desired, but countless imperfections of real-world manufacturing makes this impossible. The as-built specifications of a product are assumed to be centered around a mean, with each individual product deviating some amount away from that mean in a normal distribution. The goal of Six Sigma is to ensure that the acceptable specification limits are sixstandard deviations away from the mean of the distribution; in other words, that each step of the manufacturing process has at most a 0.00034% chance of producing a defect.

• Atkinson, A. C.; Donev, A. N.; Tobias, R. D. (2007).Optimum Experimental Designs, with SAS. Oxford University Press. pp. 511+xvi.ISBN 978-0-19-929660-6.
• Box, G. E., Hunter, W.G., Hunter, J.S., Hunter, W.G., "Statistics for Experimenters: Design, Innovation, and Discovery", 2nd Edition, Wiley, 2005,ISBN 0-471-71813-0
• Logothetis, N.; Wynn, H. P (1989).Quality Through Design: Experimental Design, Off-line Quality Control, and Taguchi's Contributions. Oxford U. P.ISBN 0-19-851993-1.
• Rao, Singiresu (2002).Applied Numerical Methods of Engineers and Scientists. Upper Saddle River, New Jersey: Prentice Hall.ISBN 013089480X.
• The Editors of Encyclopaedia Britannica."Slide Rule".Encyclopaedia Britannica. Encyclopaedia Britannica Inc. Retrieved17 April 2018.
• Montgomery, Douglas; Runger, George; Hubele, Norma (21 December 2010).Engineering Statistics (5 ed.).ISBN 978-0470631478.

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