While the focus of Six Sigma in a manufacturing setting is on reducing errors, the methodology can be used in an office/government setting.
Government programs certainly produce their share of errors which often show up as delays in obtaining approvals or the rejection of permits/applications due to errors. I utilized Six Sigma to analyze why it took several months to turn over a vacant apartment in a public housing program. Going into the analysis I and others assumed the delay was primarily caused by the length of time it took to paint & repair apartments. By undertaking the Six Sigma steps of Define, Measure, Analyze, Improve & Control, we determined that our real problem was the delay in certifying tenant applications as required by HUD.
As I stated in a previous reply, I do not like the statistical aspect of Six Sigma and some of the charts utilized, as they confuse and intimidate many people. Lean, which is sort of Six Sigma lite, in my opinion is a better approach for an office/government setting.
Below are some links to government agencies that have utilized Lean/Six Sigma