Source of image of graph: http://www.econ.canterbury.ac.nz/personal_pages/bob_reed/econ3003/book/chap26a.gif (Original source of graph: Viscusi, W. Kip, John M. Vernon, and Joseph E. Harrington, Jr. Economics of Regulation and Antitrust. 2nd ed. Lexington, MA: D.C. Heath and Company, 1992, page 714.)
The graph above, from a leading textbook on the economics of regulation, strikingly shows that OSHA had no discernible effect on reducing workplace accidents.
(Note: I am grateful to Susan Dudley who mentioned this graph in one of the Association of Private Enterprise Education sessions in Guatemala City, and who graciously elaborated the source in conversation afterwards.)