The Securities and Exchange Commission's independent watchdog called for a sweeping overhaul of the agency's investigation and enforcement practices on Tuesday, after a blistering report on the S.E.C.'s failure to detect Bernard L. Madoff's extensive Ponzi scheme. Two reports, released by the S.E.C.'s inspector general, H. David Kotz, recommended dozens of changes in the way the agency evaluates tips, trains investigators and documents examinations of securities firms. The first report, which covers the S.E.C.'s inspections and examinations office, outlines 37 improvements that would revamp nearly every aspect of the division's operations, including how investigators follow up on tips and creating step-by-step procedures in identifying potential violations of securities laws. Mr. Kotz also issued 21 recommendations to the S.E.C.'s division of enforcement, including the start of a formal process for handling complaints and improving working relationships within the division. One measure would mandate that tips and complaints be reviewed by at least two individuals experienced in the subject before taking further action. The proposed changes come after Mr. Kotz's office completed an exhaustive investigation this month of the S.E.C.'s failure to detect the Madoff fraud despite many warnings and a flood of complaints from credible sources. At nearly every turn, the investigation found, the agency had failed to properly examine Mr. Madoff's firm and had not adequately followed up on tips from as far back as 1992 that could have unearthed the estimated $65 billion scheme.