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Guarantor Financial Information (Condensed Consolidating Statements of Cash Flows) (Details) - USD ($)
$ in Millions
 9 Months Ended
Sep. 30, 2016
Sep. 30, 2015
Dec. 31, 2015
Dec. 31, 2014
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities $ 1,008.3 $ 280.2    
Net cash provided by (used in) discontinued operating activities 94.1 (27.2)    
Net Cash Provided by (Used in) Operating Activities 1,102.4 253.0    
Cash flows from investing activities:        
Capital expenditures (127.5) (173.3)    
Acquisition of businesses, net of cash acquired (9.2) (952.0)    
Proceeds from sale of property, plant and equipment 2.6 14.8    
Proceeds from Sale of Equity Method Investments 423.0 0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 0.0    
Net cash provided by (used in) continuing investing activities 288.4 (1,110.5)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 150.6 (339.1)    
Debt issuance costs (2.1) 0.0    
DividendsPaid 245.6 227.4    
Dividends paid to noncontrolling interests (13.8) (9.0)    
Repurchase of ordinary shares (250.1) (233.4)    
Other, net 30.6 54.6    
Net proceeds (repayments) in debt 0.0 0.0    
Net cash provided by (used in) continuing financing activities (631.6) (76.1)    
Effect of exchange rate changes on cash and cash equivalents 8.6 (120.1)    
Net increase (decrease) in cash and cash equivalents 767.8 (1,053.7)    
Cash and cash equivalents 1,504.6 651.5 $ 736.8 $ 1,705.2
IR Ireland [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (51.3) (51.2)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (51.3) (51.2)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (160.2) 0.0    
Net cash provided by (used in) continuing investing activities (160.2) 0.0    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 0.0    
Debt issuance costs 0.0      
DividendsPaid 245.6 227.4    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares (250.1)      
Other, net 30.6 54.6    
Net proceeds (repayments) in debt 676.6 457.4    
Net cash provided by (used in) continuing financing activities 211.5 51.2    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.0    
Cash and cash equivalents 0.0 0.0 0.0 0.0
IR Irish Holdings [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 0.0 (1.2)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 0.0 (1.2)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (19,535.7) 3.5    
Net cash provided by (used in) continuing investing activities (19,535.7) 3.5    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 0.0    
Debt issuance costs 0.0      
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0      
Other, net 0.0 0.0    
Net proceeds (repayments) in debt 19,535.7 (2.3)    
Net cash provided by (used in) continuing financing activities 19,535.7 (2.3)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.0    
Cash and cash equivalents 0.0 0.0 0.0 0.0
IR Lux International [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (11.4) (10.6)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (11.4) (10.6)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (2.4) 73.4    
Net cash provided by (used in) continuing investing activities (2.4) 73.4    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 0.0    
Debt issuance costs 0.0      
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0      
Other, net 0.0 0.0    
Net proceeds (repayments) in debt 13.9 (63.9)    
Net cash provided by (used in) continuing financing activities 13.9 (63.9)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.1 (1.1)    
Cash and cash equivalents 0.1 0.0 0.0 1.1
IR Global [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (206.7) (93.1)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (206.7) (93.1)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.1    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (242.8) 259.9    
Net cash provided by (used in) continuing investing activities (242.8) 260.0    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 0.0    
Debt issuance costs (2.1)      
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0      
Other, net 0.0 0.0    
Net proceeds (repayments) in debt 440.2 (166.9)    
Net cash provided by (used in) continuing financing activities 438.1 (166.9)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents (11.4) 0.0    
Cash and cash equivalents 0.0 0.0 11.4 0.0
IR New Jersey [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 569.4 (1,314.8)    
Net cash provided by (used in) discontinued operating activities 99.5 (27.3)    
Net Cash Provided by (Used in) Operating Activities 668.9 (1,342.1)    
Cash flows from investing activities:        
Capital expenditures (56.3) (94.7)    
Acquisition of businesses, net of cash acquired (9.2) (448.1)    
Proceeds from sale of property, plant and equipment 0.0 0.2    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 65.7 55.8    
Net cash provided by (used in) continuing investing activities 0.2 (486.8)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 7.6 7.5    
Debt issuance costs 0.0      
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0      
Other, net 0.0 0.0    
Net proceeds (repayments) in debt (120.2) 1,411.0    
Net cash provided by (used in) continuing financing activities (127.8) 1,403.5    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 541.3 (425.4)    
Cash and cash equivalents 541.3 0.0 0.0 425.4
IR Lux Finance [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (20.8) (14.2)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (20.8) (14.2)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 243.7 (228.0)    
Net cash provided by (used in) continuing investing activities 243.7 (228.0)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 143.0 (355.3)    
Debt issuance costs 0.0      
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0      
Other, net 0.0 0.0    
Net proceeds (repayments) in debt (79.9) (112.9)    
Net cash provided by (used in) continuing financing activities (222.9) 242.4    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.2    
Cash and cash equivalents 0.1 0.2 0.1 0.0
Other Subsidiaries [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 729.1 1,765.3    
Net cash provided by (used in) discontinued operating activities (5.4) 0.1    
Net Cash Provided by (Used in) Operating Activities 723.7 1,765.4    
Cash flows from investing activities:        
Capital expenditures (71.2) (78.6)    
Acquisition of businesses, net of cash acquired 0.0 (503.9)    
Proceeds from sale of property, plant and equipment 2.6 14.5    
Proceeds from Sale of Equity Method Investments 423.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (930.4) (1,522.5)    
Net cash provided by (used in) continuing investing activities (576.5) (2,090.5)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 8.7    
Debt issuance costs 0.0      
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests (13.8) (9.0)    
Repurchase of ordinary shares 0.0      
Other, net 0.0 0.0    
Net proceeds (repayments) in debt 95.8 (164.5)    
Net cash provided by (used in) continuing financing activities 82.0 (182.2)    
Effect of exchange rate changes on cash and cash equivalents 8.6 (120.1)    
Net increase (decrease) in cash and cash equivalents 237.8 (627.4)    
Cash and cash equivalents 963.1 651.3 725.3 1,278.7
Consolidation, Eliminations [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 0.0 0.0    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 0.0 0.0    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 20,562.1 1,357.9    
Net cash provided by (used in) continuing investing activities 20,562.1 1,357.9    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 0.0    
Debt issuance costs 0.0      
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0      
Other, net 0.0 0.0    
Net proceeds (repayments) in debt (20,562.1) (1,357.9)    
Net cash provided by (used in) continuing financing activities (20,562.1) (1,357.9)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.0    
Cash and cash equivalents $ 0.0 $ 0.0 $ 0.0 $ 0.0