4 ms·

- The robot is in your house the whole 168 hours a week, not just 4. You're assuming a good cleaning robot would be absolutely useless for anything else, like c

- The robot is in your house the whole 168 hours a week, not just 4. You're assuming a good cleaning robot would be absolutely useless for anything else, like cooking, laundry, etc. - 4-year robot lifetime is overly pessimistic. If upgrade is not the reason (which has nothing to do with lifetime, it's your choice to upgrade), a robot could last way more than 4-years (especially with right-to-repair laws in place). - That said, such a robot will most likely be available for less than $21k and very soon in the near future.

espadrine 6y ago
The first point has an obvious response and the last is speculative. I find interesting to address the middle one statistically. A given machine has a number of random events that can kill it. Each possible event type i can be modeled as a Poisson process Xᵢ with, in a given year, probability λᵢ. The machine survives in a given year if no occurrence of event i happens, with probability Pr(Xᵢ = 0) = exp(-λᵢ). For instance, a device with an average lifetime of 8 years and a single possible cause of death, has λ = -ln(½^⅛) = 0.087. Given N independent event types (say, if you have on the order of N components), the yearly survival of the overall machine has probability Πᷡᵢ exp(-λᵢ). Thus the lifetime of the overall machine is ln(½)÷ln(½^(Σᷡᵢ 1÷Lᵢ)) = 1 ÷ Σᷡᵢ (1÷Lᵢ) if each component has lifetime Lᵢ. For instance, two components with an average lifetime of 8 years yield a single machine with an average lifetime of 4 years. The more death-causing event types there are, the smaller the lifetime; and a general-purpose robot inherently has more. I believe this result is counter-intuitive, and is the reason you might be led to think I am overly pessimistic.
- emiliobumachar 6y ago
  Sorry, what is the supposedly obvious response to the first point?
- Tenobrus 6y ago
  Why does your argument not show that cars would have a similar lifetime?
  - espadrine 6y ago
    It shows that cars can never reach the pricepoint of a bike for the same lifetime, because the increased number of failure points require an increased level of quality of each part to yield the same lifetime.
  - leetcrew 6y ago
    stuff goes wrong with cars all the time. most of it isn't critical to the core function of the machine. cars also undergo routine maintenance where parts are (hopefully) replaced before they fail entirely.
  - deleted 6y ago
    [deleted]
- sobellian 6y ago
  Engineers take this phenomenon into consideration and design systems with redundancy and/or easily replaceable parts. You need specific numbers for the design in order to treat this mathematically.
- deleted 6y ago
  [deleted]
- fizixer 6y ago
  > ... machine ... has ... events that can kill it ... > ... N independent event types ... So if the robot blows a $0.03 (i.e., 3 cents) electrolytic cap [0], that's an independent event type that "killed" the machine? Just trying to get a sense of how you define "machine kill" (and as I said I mentioned a big caveat of right-to-repair laws). [0] http://amzn.com/B01MSQOX0Q http://amzn.com/B01MSQOX0Q

espadrine 6y ago

The first point has an obvious response and the last is speculative. I find interesting to address the middle one statistically. A given machine has a number of random events that can kill it. Each possible event type i can be modeled as a Poisson process Xᵢ with, in a given year, probability λᵢ. The machine survives in a given year if no occurrence of event i happens, with probability Pr(Xᵢ = 0) = exp(-λᵢ). For instance, a device with an average lifetime of 8 years and a single possible cause of death, has λ = -ln(½^⅛) = 0.087. Given N independent event types (say, if you have on the order of N components), the yearly survival of the overall machine has probability Πᷡᵢ exp(-λᵢ). Thus the lifetime of the overall machine is ln(½)÷ln(½^(Σᷡᵢ 1÷Lᵢ)) = 1 ÷ Σᷡᵢ (1÷Lᵢ) if each component has lifetime Lᵢ. For instance, two components with an average lifetime of 8 years yield a single machine with an average lifetime of 4 years. The more death-causing event types there are, the smaller the lifetime; and a general-purpose robot inherently has more. I believe this result is counter-intuitive, and is the reason you might be led to think I am overly pessimistic.

emiliobumachar 6y ago
Sorry, what is the supposedly obvious response to the first point?
Tenobrus 6y ago
Why does your argument not show that cars would have a similar lifetime?
- espadrine 6y ago
  It shows that cars can never reach the pricepoint of a bike for the same lifetime, because the increased number of failure points require an increased level of quality of each part to yield the same lifetime.
- leetcrew 6y ago
  stuff goes wrong with cars all the time. most of it isn't critical to the core function of the machine. cars also undergo routine maintenance where parts are (hopefully) replaced before they fail entirely.
- deleted 6y ago
  [deleted]
sobellian 6y ago
Engineers take this phenomenon into consideration and design systems with redundancy and/or easily replaceable parts. You need specific numbers for the design in order to treat this mathematically.
deleted 6y ago
[deleted]
fizixer 6y ago
> ... machine ... has ... events that can kill it ... > ... N independent event types ... So if the robot blows a $0.03 (i.e., 3 cents) electrolytic cap [0], that's an independent event type that "killed" the machine? Just trying to get a sense of how you define "machine kill" (and as I said I mentioned a big caveat of right-to-repair laws). [0] http://amzn.com/B01MSQOX0Q http://amzn.com/B01MSQOX0Q