1. Reliability and Probability in Chain-Reaction Machines

2. Reliability probability
Reliability [ri-lahy-uh-bil-i-tee], the measure of how likely it is that a device will correctly perform its purpose across the period of time intended.
Reliability

3. Probability
Probability [prob-uh-bil-i-tee], How likely it is for an event to occur
Probability

4. Reliability
Reliability [ri-lahy-uh-bil-i-tee], the probability that a device will correctly perform its purpose across the period of time intended.
Reliability

5. Reliability of a Step
The reliability of a step (the probability that a step works) is a number from 0 to 1.
If it is certain to work, then the reliability (probability of working) is
If it is certain not to work, then the reliability (probability of working) is 1

6. If it is uncertain whether or not a step will work correctly, then its reliability is some fraction between 0 and 1 (or a fraction converted to a decimal number).
0.25
0.5
0.75 1
Calculating Reliability

7. Calculating Reliability
No. of successful outcomes
Total number of trials

8. Testing the Reliability of a Step
What is the Reliability of Step A (RA)? A. B.
Ball
Plastic
Ramp
Dominoes
Table
There are 2 videos associated with this slide: Reliable and Unreliable, both located in the video folder for this module. Show both of these videos in various sequences to simulate an actual testing. E.g., Show the Reliable video 2 times, followed by the Unreliable video 2 times followed by the Reliable for 1 more time. Based on that ask students to determine the reliability of the step A.
Testing the Reliability of a Step

9. Testing the Reliability of a Step
Ball
What is the reliability of the improved step A B.
Dominoes
Barrier
Plastic
Ramp
Table
The improved Step A was performed 10 times. The ball hit the dominoes 9 of those times 9 10
No. of successful outcomes
Total number of trials =
= 0.9
Testing the Reliability of a Step

10. Performing Reliability Tests
Run the step repeatedly
Record no of trials
Record no. of successes
Each trial MUST be performed EXACTLY the same way.
NO MODIFICATIONS BETWEEN TRIALS
Don’t even change the tester
Based on the video: 1961 Chevrolet Belair Impala Ad, ask students to provide explanations for how to test for reliability. (how was it tested in the video)

11. Calculating Reliability of each step
No. of trials
No. of successful trials
No. of
failed
trials
Reliability
A) Ball rolls down ramp 10 6 4
6/10 = 0.6
Discuss how the testing can be documented with a table. Following the presentation teams will start to test the reliability of the steps in their modules. Each team will create a table to document the testing of their steps (provide each team with a poster board and markers). At the end of the presentation you can revisit this slide or slide 17 so teams have a model to refer to

12. Calculating Reliability of a Machine?
A machine - two or more steps connected in series.
Reliability of Machine = Product of the reliability of each step

13. Calculating Reliability of each step
No. of
trials
No. of successful trials
failed
Reliability
A) Ball rolls down ramp 10 6 4
6/10 = 0.6
B) Dominoes fall down 7 3
7/10 = 0.7
C) Dominoes fall on pulley ramp 8 2
8/10 = 0.8
D) Cup lifts up
E) Car rolls away
10/10 =1
Students should begin to appreciate that the overall reliability of the machine will be less than the least reliable step. It is important to get the reliability as high as possible for all steps