Be sure to look at the Blackboard Module for this week for various hand-in mechanisms!


C25 In Class Exercise: Serial and Parallel Reliability

This is a group assignment that should be completed in class.

Overall question hint: Wolfram Alpha can be a useful resource. An Excel (or other) spreadsheet is sometimes helpful, but be EXTREMELY careful of numerical round-off errors for very low probilities that will cause incorrect answers. Some calculators can have problems as well. Always use Wolfram Alpha or another high-precision calculation tool to check your answers. Remember that we just learned about the pitfalls of floating point math. Don't let them bite you here!

This is a group exercise. You should divide up work once you see how things work. Note that the individal boxes A through H have the same reliability in both problems.

Consider the below reliability calculation example:

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Exercise #1: Calculate the reliability of the whole system for mission length t given above.
Hints:

  1. Break the calculation up into steps
  2. Work from the "inside out," for example starting with nodes E and F.
  3. Generally you'll alternate a step that is computing R(t) of a component, or a step that computes R(t) for chunks of the system already analyzed
  4. Keep the reliability for each block on the whiteboard/blackboard for use in the next exercise
  5. Use Wolfram Alpha if there are a lot of 9s involved
  6. Keep track of each step on your hand-line slide as a way of showing your work. Paste numbers in from Wolfram Alpha. (Don't use a spreadsheet -- you'll get too much round off error). Here are some steps to get you started:

Exercise #2: Calculate the reliability of the belows system using the same failure rates as above:

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Here are some steps to get you started (note overlap with the previous problem for individual box reliabilities:

Hand in:


C26 In Class Exercise: Critical Systems

This is a group assignment that should be completed in class.

Find an on-line video of a failure mode, software defect, product recall, or other video of a problem relevant to a topic selected from the list below. DO NOT make your own video of a hazard! (Hint: use keywords such as "defect," "recall," "safety," "fire," "explosion," and "glitch" when searching.) Include on your hand-in slide:

Topic assignments for this question are as below, based on the last digit of your group number. (For example, if your group number is 17 you are a "7" and do the train crash.) If you have a strong preference not to do a particular topic such as a personal experience with a failure of this type, just let the instructor know and do either the topic before or the topic after.


Homework #25: Dependability

Overall question hint: Wolfram Alpha can be a useful resource. An Excel (or other) spreadsheet is sometimes helpful, but be EXTREMELY careful of numerical round-off errors for very low probilities that will cause incorrect answers. Some calculators can have problems as well. Always use Wolfram Alpha or another high-precision calculation tool to check your answers. Remember that we just learned about the pitfalls of floating point math. Don't let them bite you here!

25-1. Consider a two-engine passenger aircraft. Such aircraft are designed to be able to fly and land even if only one engine is working. Assume that each engine has an in-flight failure rate of one failure per 51,000 hours. The FAA requires an aircraft to have a probability of catastrophic failure (e.g., both engines fail) of less than 1e-9 (one catastrophic failure per billion hours). Assume random independent failures.

25-2. Consider a safety interlock switch on an access door to a piece of hazardous equipment (for example, a high-powered industrial milling machine that will damage any hand that is inserted through the open door while the equipment is running). The door has a switch that detects whether the door is open and a safety microcontroller that checks whether one or more door switches is open. If any door switch detects that the door is open the safety microcontroller performs a safety shutdown. Assume that the switches fail on average at 50,000 hours, and the safety microcontroller fails on average at 1,000,000 hours. Assume the system runs 24 hours per day, 7 days/week for a 10 year product life. Assume that a failure of either the switch or the safety microcontroller makes the system dangerous. Assume that no repairs made to the system. Assume random independent failures.

Supplemental Material:


Homework #26: Critical Systems

26-1. (10 points) For all the topics assigned below, list the MOST dangerous failure mode you can think of for that type of device. Rate the failure mode according to a loose SIL scale:

If it's a tie, it's OK to list two or three important failure modes. For each item include BOTH a summary of the item name AND the failure mode so graders don't have to cross-reference the problem assignment when grading. (e.g., "Aircraft engine: .. failure mode... SIL 4"). You should consider the effect of the failure mode assuming that there is a mitigation failure. In other words, if there is defective safety design, how bad could the failure be in a reasonable deployment situation?

It is possible some answers will be something you heard in class, but if you can think of a worse failure mode you should list that instead. It is fine to use the internet to go fishing for ideas (but if you find an in idea on the Internet cite the URL with your answer). Grading is based on whether it is a reasonable choice, not whether we can think of one that is even worse than what you say. 1 point per item.

Supplemental Materials: