Single meter failure represents a meter's accidental failure in a meter network (i.e., a set of meters installed of identical purpose) whereas multiple meter failure is more common under intended malfunctioning action (e.g., cyber-attack). All or most meters in a network may be paralyzed from a cyber-attack and stop sending/receiving any information.
An interesting research topic is to investigate the correlation between the impacts of accidental and intentional meter failure events on water distribution system pipe burst detection.
<Photo courtesy of Jay L. Clendenin / Los Angeles Times http://beta.latimes.com/local/cityhall/la-me-pipe-rupture-20140807-story.html>