An article by J.J. Pignatiello, Jr. And J.S. Ramberg in the Journal of Quality Technology, (Vol. 17, 1985, pp. 198-206) describes the use of a replicated fractional factorial to investigate the effects of five factors on the free height of leaf springs used in an automotive application. The factors are A = furnace temperature, B = heating time, C = transfer time, D = hold down time, and E = quench oil temperature. The data are shown in Table P81.

Table P8.1 A B C D E Free Height - 7.78 7.78 7.81 + - + - 8.15 8.18 7.88 + + 7.50 7.56 7.50 + + - 7.59 7.56 7.75 7.88 - - + + 7.54 8.00 + - + 7.69 8.09 8.06 7.44 + - 7.56 7.52 7.56 7.81 7.69 + + + + - - - + 7.50 7.25 7.12 + - + + 7.88 7.88 7.44 - + + + 7.50 7.56 7.50 + + - + 7.63 7.75 7.56 - + + + 7.32 7.44 7.44 + - 7.69 + - + 7.56 7.62 + + - + 7.18 7.18 7.25 + + + + + 7.81 7.50 7.59Month Chevy Malibu Ford Fusion Hyundai Sonata Honda Accord Toyota Camry VW Passat January 22,161 21,753 21,456 19,791 21,435 20,121 February 18,724 19,835 20,442 21,322 20,235 19,555 March 18,384 17,007 16,163 17,631 17,339 16,456 April 19,837 17,870 15,504 14,950 14,543 14,533 May 17,547 16,597 15,473 16,250 16,177 17,325 June 16,694 16,623 14,745 15,508 15,686 17,343Variable Type Year the year a yearling is offered for sale: 2019, 2018, 2017 When when the yearling is auctioned, categorised as: auctioned - 1 (if a yearling is auctioned in the first third of the auctions) - 2 (if a yearling is auctioned in the middle third of the auctions) - 3 (if a yearling is auctioned in the final third of the auctions) Sold whether a yearling is sold, categorised as: - yes - passed in (if a yearling does not meet the reserve price) - withdrawn (if a yearling is withdrawn from the auction) Sex the sex of a yearling: - filly (female) - colt (male) Country the country or region of the buyer of a yearling, categorised as: - Asia - Australia - New Zealand . Other State the Australian state or territory an Australian buyer comes from: - Australian Capital Territory - New South Wales - Northern Territory Queensland South Australia - Tasmania - Victoria - Western Australia Price the selling price of a yearling (i.e. the price paid by a buyer) in $NZCode Form of analysis One sample f-test on a mean One sample f-test on a proportion One sample f-test on a mean of differences Two sample t-test on a difference between two means f-test on a difference between two proportions One-way analysis of variance F-test\f