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Share Plans (Details 3) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 25, 2015
Sep. 26, 2014
Sep. 27, 2013
Share-based Compensation Arrangement by Share-based Payment Award      
Weighted-average pre-conversion grant-date fair value (in dollars per share) $ 11.29 $ 10.24 $ 7.21
Total intrinsic value of options exercised $ 66 $ 76 $ 73
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding      
Outstanding share options at beginning of period (in shares) 15,126,365    
Granted 1,906,376    
Exercised (3,834,707)    
Expired (627,093)    
Forfeited (35,464)    
Outstanding share options at end of period (in shares) 12,535,477    
Vested and unvested expected to vest as of September 25, 2015    
Exercisable as of September 25, 2015    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]      
Outstanding share options, weighted-average exercise price at beginning of period (in dollars per share) $ 24.31    
Granted 42.52    
Exercised 23.95    
Expired 31.56    
Forfeited 28.70    
Outstanding share options, weighted-average exercise price at end of period (in dollars per share) $ 26.81    
Vested and unvested expected to vest as of September 25, 2015    
Exercisable as of September 25, 2015    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]      
Outstanding share options, weighted-average remaining contractual term at end of period (in years) 6 years 25 days    
Vested and unvested expected to vest as of September 25, 2015 5 years 11 months 28 days    
Exercisable as of September 25, 2015 4 years 5 months 23 days    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Intrinsic Value $ 116    
Vested and unvested expected to vest as of September 25, 2015 115    
Exercisable as of September 25, 2015 93    
Share Options      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]      
Total unrecognized compensation cost related to non-vested awards $ 27    
Weighted-average period for recognizing compensation cost related to non-vested options 2 years 7 months    
Tyco Employee Stock Purchase Plan      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]      
Shares available for future grant 3,000,000