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The computer glitch that led to quite a muddle: Just parked this ex-BBC material here without any silly comments from me so that come the day I can recall what was reported / said.
Mr Pester argued that the migration of billions of customer records was successful "to the penny".
The underlying engine of the bank was working well, he said, and most customers could log in normally, although there was an immediate angry reaction from those customers who could not make payments or get into the system.
He said that he could be trusted to carry on the work of the bank, and MPs heard that he would not be quitting.
"They should trust me because I will ensure I will bring TSB out of the problems we're in. I have promised customers they will not be out of pocket," he said.
"[The buck] stops with me. Of course I take absolute responsibility for what has happened to TSB customers."
Mr Pester gave evidence alongside TSB chairman Richard Meddings, and Miquel Montes, chief operating officer at TSB's Spanish owner, Sabadell, who also sits on the TSB board.
During evidence, the TSB bosses said:
- The IT work was not rushed through owing to financial incentives
- Tests before the switch were "misleading" as they did not foresee the problems with the system's capacity
- A law firm has been called in to carry out an independent review of the saga
- Waiting times on phones was "very, very poor"
Mr Pester said that the "accessibility" problems for customers would "not be simple to fix". He admitted that only just over half of complaints had been "acknowledged".
Nicky Morgan, who chairs the committee, said: "What we are hearing is the most staggering example of a chief executive who seems unwilling to realise the scale of the problems that are being faced."
What the IT issue is all about
TSB shut down services for two days from the evening of Friday 20 April to move customer data from former owner Lloyds to a new IT system managed by Sabadell.
As soon as the new system was switched on during Sunday evening, customers reported seeing other people's account details alongside a range of other difficulties.
Access to accounts via online banking and the bank's app was patchy in the following days, while those who did manage to get into their accounts encountered some extraordinary errors.
In a letter to MPs, Mr Pester also revealed the extent of "widespread" failures of technology in the branch network. Problems were still experienced in 40% of branches by last Friday.
Frustrated customers also faced average waits of up to an hour for those telephoning the bank.
Last Thursday, experts from computing giant IBM were called in to try to help solve the crisis.