After decades of partial solutions to fire threats in nursing homes, regulators are finally requiring sprinkler systems for the 2,466 facilities that still don't have them fully installed.  On Aug. 13, the Centers for Medicare and Medicaid Services issued a rule declaring that the $144 billion long-term care industry has five years to install the systems. Some 1.4 million residents live in 16,000 U.S. nursing homes.  The government, which has adopted fire standards developed by the nonprofit National Fire Protection Association since 1971, was spurred to action by the deaths of 31 nursing home residents in incidents in Nashville and Hartford, Conn., in 2003.  "It is 35 to 40 years overdue," said Janet Wells, director of public policy for the National Citizens' Coalition for Nursing Home Reform, a Washington group that works to protect residents' rights.  The Department of Health and Human Services recently began listing on a Medicare Web site, under "nursing home compare," whether a facility has sprinklers, when fire-safety inspections took place, and the number of deficiencies found and corrected.