Shaw was born in Uddingston, Scotland, on 28 May 1904 to David Perston Shaw and Helen Brown Shaw MBE who became MP for Bothwell in 1931. She attended St Leonard's School in St Andrews and Laurel Bank School in Glasgow. She went on to study at the University of Edinburgh before studying for her postgraduate certificate at Bryn Mawr College in Bryn Mawr, Pennsylvania. Shaw met Dr Lillian Gilbreth at Bryn Mawr College and became Gilbreth's research assistant. Shaw then began working at Gilbreth, Inc. until 1930 when she returned to the UK. She became a personal officer at Metropolitan-Vickers before becoming chief supervisor of women workers in 1933 and was the company's chief motion-study investigator between 1930 and 1945. She was also a consultant to the Associated Electrical Industries group of which Metropolitan-Vickers is part of. Shaw joined the Women's Engineering Society in 1935, and during the thirteenth annual conference of the Women's Engineering Society, Shaw gave a presentation on her study of motion at the Science Museum in Kensington, London. In late 1936, Shaw helped produce a film which demonstrated the application of motion study concerning food preparation in the home. On 31 May 1937, she was selected by the National Institute of Industrial Psychology to lecture on modern developments in the study of time and motion. Later in 1937, Shaw served as an opponent of a motion put "That the Introduction of Female Apprentices to these works is to be deplored". As a result of her opposing voice and the speech of Dorothy Garafitt, a recently accepted apprentice, the motion lost by a margin of 17 votes. Shaw married John H. Pirie the following year. Shaw was recruited by the Minister of Aircraft Production, Stafford Cripps, in 1942 and during World War II, she worked on the Production Efficiency Board as an advisor to the aircraft industry. In 1945, Shaw started the Anne Shaw Organisation Ltd. Of which she was the chairman and managing director until 1975. Between 1964 and 1979, she was also the director of Wescot Ltd. She published Purpose and Practice of Motion Study in 1952 and Introduction to the theory and application of work study in 1994. Shaw died on 4 February 1982 in Macclesfield, Cheshire, aged 77. In 2017, Shaw was inducted into the Scottish Engineering Hall of Fame.
