Reliability and Probability in Chain-Reaction Machines

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

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

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

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

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 ¼ ½ ¾ 1 Calculating Reliability

Calculating Reliability No. of successful outcomes Total number of trials

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

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

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)

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

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

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