Backing Up Photos 1 What Can Happen to Your Masterpiece? 2 3 4 - - PowerPoint PPT Presentation

Backing Up Photos

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What Can Happen to Your Masterpiece?

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Your Photos Here

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Causes for Data Loss

• Hard drive head crash
• Ageing of media
• Cosmic rays
• Obsolescence
• Human error
• Software bugs
• Disasters (fire, earthquake, ...)

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Failure Characteristics

• Independence
• Mean Time to Failure (Failure Rate)
• Rate changes over time (bathtub curve)
• Detectable
• Repair Time

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How good are Hard Disks?

• I would not trust more than 5 years
• Much depends on:

– type of disk – on all the time? – off line vs on line?

• Hard drives often fail in batches!

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Solid State Disks (SSDs)

• Faster and more expensive than hard disks
• Can also fail
• Not that much more reliable than hard disks

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Reliability (from Wikipedia)

• SSD: Reliability varies across manufacturers and models

with return rates reaching 40% for specific drives. As of 2011 leading SSDs have lower return rates than mechanical

• drives. Many SSDs critically fail on power outages; a

December 2013 survey found that only some of them are able to survive multiple power outages.

• Hard Disk: According to a study performed by CMU for

both consumer and enterprise-grade HDDs, their average failure rate is 6 years, and life expectancy is 9–11 years. Leading SSDs have overtaken hard disks for reliability, however the risk of a sudden, catastrophic data loss can be lower for mechanical disks.

CS 245 Notes 2 13

How good are CDs and DVDs?

• You can find claims of 10-100 year life
• Much depends on:

– type of disk – exposure to heat & light – proper handling

• How do you test??

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Solutions

• Make Copies!!!
• Copies on devices with different failure

characteristics

• Check for data loss
• Repair and restore copies

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How Many Copies??

• Need model
• Example model:

– One data “object” (e.g., photo, album, ...) – Every week (say):

• bject survives with probability p
• bject is lost with probability 1 – p

– Example: p = 0.990

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State Transition Model

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• bject

OK

• bject

dead p 1 - p

Expected Time to Failure (MTF)

• Let X be time to failure (years)
• E(X) =

– with probability (1-p): 1 – with probability (1-p)p: 2 – with probability (1-p)p2: 3 – with probability (1-p)p3: 4 – with probability (1-p)p4: 5 – ...

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Expected Time to Failure (MTF)

• E(X)

= (1-p)[ 1 + 2p + 3p2 + 4p3 + 5p4 + ...]

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Expected Time to Failure (MTF)

• E(X)

= (1-p)[ 1 + 2p + 3p2 + 4p3 + 5p4 + ...]

• Let

S = [ 1 + 2p + 3p2 + 4p3 + 5p4 + ...] T = [ p + p2 + p3 + p4 + ...]

• Note that

dT/dp = S

• Now let us solve for T...

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Expected Time to Failure (MTF)

• T = [ p + p2 + p3 + p4 + ...]
• T = p[ 1 + p + p2 + p3 + p4 + ...]
• T = p[ 1+ T ]

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Expected Time to Failure (MTF)

• T = [ p + p2 + p3 + p4 + ...]
• T = p[ 1 + p + p2 + p3 + p4 + ...]
• T = p[ 1+ T ]
• T – pT = p
• T = p/(1-p)

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Expected Time to Failure (MTF)

• T = [ p + p2 + p3 + p4 + ...]
• T = p[ 1 + p + p2 + p3 + p4 + ...]
• T = p[ 1+ T ]
• T – pT = p
• T = p/(1-p)
• dT/dp = p(-1)(1-p)-2(-1) + (1-p)-1
• dT/dp = 1/(1-p)2
• E(X) = (1-p)S = (1-p)/(1-p)2 = 1/(1-p)

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Expected Time to Failure (MTF)

• E(X) = 1/(1-p)

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p MTF 0.9999 10000.00 0.999 1000.00 0.99 100.00 0.9 10.00 0.85 6.67 0.8 5.00

Multiple Copies

• Number of copies = n
• What is probability we lose data at end of year?
• Assume independence, same p

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n=3 p p p

Multiple Copies

• Probability of loss = (1-p)n
• Probability data survives = [1 - (1-p)n ]

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n=3 p p p

Multiple Copies

• New p = [1 - (1-p)n ]

– assume repairs at end of week

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p n new p MTF 0.99 1 0.99 100 0.99 2 0.9999 10000 0.99 3 0.999999 1000000 0.99 4 0.99999999 99999999.5 0.80 1 0.8 5 0.80 2 0.96 25 0.80 3 0.992 125 0.80 4 0.9984 625

Analysis Can Be More Detailed

• Many different system states
• Time varying failure/repair rates
• Malicious failures
• ...

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In Practice

• Backup your photos!!
• Use different formats and media
• Check periodically & repair
• Migrate to new media

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End