# Tire Reliability

Concepts

• Distributions
• Histograms
• Quality vs. Reliability

MEA Description: The Tire Reliability MEA requires the teams of students to develop a generalized procedure to determine whether a set of data regarding tire performance is demonstrating acceptable reliability. The Peterson Tire Company is aware of a few accidents caused by tire failure in one of its tire product lines. The company wishes to know if there is a reliability issue with this set of tires so that the company can fix the problem if one exists. They also intend to use the procedure for tire data on future tire product lines. The teams (1) use the data from three types of tires to develop the procedure for determining if a set of data regarding tire performance is demonstrating acceptable reliability, and (2) use the procedure to classify the reliability of the tires as well as determine if the products are correctly rated based on when failure is expected.

Implementation Strategy:

1. Individual Activity ï¿½ Individually, students read a description of what makes a product reliable, a news article on tire failure, and an interoffice memo from the client which establishes the need to create a procedure to assess product reliability from time to failure statistics for a given line of tires. Students individually begin to explore the concept of reliability and reliability curves. The focus is on establishing what differentiates reliable from unreliable products.
2. Team Activity ï¿½ In teams of 4, students develop a procedure for analyzing time to failure data to establish if a given tire is reliable and properly assigned a grade of expected life according to that reliability. This procedure is expressed in the form of a memo to the client describing the analysis and decision process. Students demonstrate their procedure on three test cases, indicating if each test case is reliable and properly graded.

Six Principles:

Principle Description How the principle is addressed in the MEA?
Model Construction Ensures the activity requires the construction of an explicit description, explanation, or procedure for a mathematically significant situation
Describe the mathematical model the students will be developing when solving this MEA:
• What are the elements?
• What are the relationships among elements?
• What are the operations that describe how the elements interact?
Given different sets of data (numbers representing days it took for a tire to fail) a procedure should be created to determine if they are exponentially distributed. A way to do this would be to create histograms for the different sets.
Reality Requires the activity to be posed in a realistic engineering context and be designed so that the students can interpret the activity meaningfully from their different levels of mathematical ability and general knowledge
Describe the context. What is the story?
What knowledge will students need to bring to this problem?
What background information must be provided?

Describe how the problem is open-ended.
Tire company has received some complaints about their tires and wants to analyze their failure rates to see if there is a general reliability problem.
Self-Assessment Ensures that the activity contains criteria the students can identify and use to test and revise their current ways of thinking
What is provided in this MEA that students can use to test their ways of thinking?
Students will have a correct set of data and a description of what it should look like, so when they use their procedure, they should be able to tell if their model works.
Model-Documentation Ensures that the students are required to create some form of documentation that will reveal explicitly how they are thinking about the problem situation
What documentation are the students being asked to produce in this MEA?
Students will receive memo from company and must reply with a memo explaining their procedure and results.
Construct Share-Ability and Re-Usability Requires students produce solutions that are shareable with others and modifiable for other engineering situations
What will indicate to the students that a sharable, reusable, or generalizable solution is desired?
The procedure should be understandable and re-usable. It should be a process that can be used on other distributions and data sets, not just the ones provided.
Effective Prototype Ensures that the solution generated must provide a useful prototype, a metaphor, for interpreting other situations
What are other examples of structurally or conceptually similar problems that would required a similar solution?
The procedure students create might be used to determine other kinds of distributions and might be helpful in other problems that involve large data sets.

Author Information:

• Original Author(s):
• Irene Mena
• Assisted by:
• Tamara Moore
• Euridice Oware
• Carla Gerberry
• Matthew A. Verleger

Files:

• MEA Documents

History:
Tested in ENGR106 - Fall 2005 Original Draft Written - Spring/Summer 2005