Regarding the shiulder of the tyres - whereby that has been flagged as an area of concern with the tyre explosions:
Milan, January 23, 2013. Pirelli begins the 2013 Formula One season with a completely revolutionised P Zero range for dry weather and Cinturato range for wet weather. These new tyres have been developed according to the wishes of the teams and the latest rules from world motorsport’s governing body, the FIA. The most recent evolutions benefit the compounds, which have become softer, the structures, which are more flexible and the shoulders, which have been reinforced.
Pirelli
Looks like their reinforcement isn't up to standards.
Also looks like they need to revisit their laboratory procedures and throw their simulation software out.......
Computer Simulations And Thousands Of Kilometres Of Testing
The development of the 2013 P Zero and Cinturato ranges included thousands of computer simulations carried out by Pirelli’s engineers throughout the 2012 season, using sophisticated predictive software. These simulations, which were backed up by laboratory tests on the compounds, have been integrated with data collected during grands prix and the seven thousand so kilometres covered during five private tests with the Renault R30. Pirelli’s test car was driven by Jaime Alguersuari and Lucas Di Grassi at Jerez, Spa, Barcelona (for two sessions) and Paul Ricard (for a wet weather test).
Edit: interestingly Pirelli did not disclose the private Ferrari test in 2012 - in the above press release. You'd think that data was also used in the 'thousands of kilometres of testing'?