Risk calculations

By Eric Crampton 09/11/2012

Engineering checks on the block of shoppes nearest our house has resulted in their being yellow-stickered. So long to the Bridge Street Bakehouse, the local fish and chip shop, and the local dairy.

Most surprising, at least to me, was that the shoppe owners only found out about it yesterday and were given until 5 PM to clear out. I’d stopped there on Tuesday for milk; guess it was to have been my last visit.

A Canterbury Earthquake Recovery Authority spokeswoman said the building’s structure was compromised.

”Visually, the building appeared to be OK. However, upon further detailed investigation by the owner’s engineers, the structural integrity of the building was found to be badly compromised,” she said.

“With a building in such a condition, there is no choice but to put public safety first. The owner must now decide the building’s future.”

South Brighton Dairy owner Sam Yang said he had no other options.

”We don’t know the future. If we shut down, we lose everything.”

He would try to return the store’s stock while asking friends to help him store what he could not return.

He had been unable to get insurance cover for his business since last year, when his insurance company refused to renew his policy.

”It’s hard to find another place to start a new business,” he said.

”They should have given us more time to get rid of the stock. This is not like a house. This is a business.”

Under what conditions does it make sense for CERA to force an immediate closure rather than letting the dairy have a week to clear out the stock? If the risk of an additional earthquake sufficiently large to bring down the dairy exceeds the ratio of the cost imposed upon the dairy by the hasty shutdown divided by the value of statistical lives that would be lost in case of catastrophic failure.

Let’s ballpark things. VSL in New Zealand is $3.67 million. Most times I visit the dairy, it’s me and Sam there; sometimes, another customer walks in while I’m there. It’s busier in high summer when the ice cream traffic picks up. Let’s call it $10m in expected VSL costs. The probability of a collapse-causing quake, times that $10m, has to exceed the cost that CERA imposes on Sam by not giving him a week to clear out some stock. Let’s denote that cost as c. If c is $10,000, then p > 0.1% for the next week, or 5.2% for the year. If c is $5,000, halve p.

At last GNS update, the odds of a 7+ quake were below 1%, 3% chance of a 6.5-6.9, and 9% chance of 6.0 to 6.4. That’s then a 13% chance of a 6+ quake in the next year. I don’t know the risk decay rate over the year, but let’s say there’s a 0.25% chance over the next week. The expected VSL cost is then $25,000. If Sam could have avoided at least $25k in cost by having the extra week, then it was inefficient that he be shut down. If the engineering reports said it was certain the building would come down in another 6+ quake and that it were certain that the collapse would kill everyone inside. If the engineering reports said there were only a 50/50 shot of the building’s coming down in a 6+, then Sam would have needed to be able to avoid $12.5k in cost to rule out the short-notice closure.

I would love to know how CERA’s running its risk assessments. Because there are hundreds of earthquake-prone buildings in Wellington that could fall down when Wellington gets its earthquake, and our baseline risk in Christchurch is no more than that in Wellington and falling every day [Note that the SciBlogs link is more than a year old; earthquake hazard in Christchurch has dropped more over the period]. Why do earthquake-prone buildings in Wellington get 10-20 years to undertake repairs while our local dairy gets a couple hours? Wellington’s yellow stickers advise building visitors of the building’s risk and to make their own judgment. Shame Sam couldn’t have had that kind of yellow sticker.