The U.S. National Highway Traffic Safety Administratio (NHTSA) independently tests over 2,400 types of tires annually. In 2015, they issued more than 900 recalls, affecting 51 million vehicles nationwide. Obviously, tire failure is a leading cause of accidents, injury, and death. The cost of poor quality can be in the hundreds of millions of dollars to the tire manufacturer due to lawsuits, liability claims, and the cost of recalls to fix the problem. Your safety depends on a high level of tire quality and performance. Therefore, the Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control its manufacturing processes, the company uses x- and R-charts. Twenty-five samples, each containing three radial tires, were chosen from different shifts over several days of operation. The Excel file Goodman Tire Case Data.xlsx shows data for 25 samples of three observations of tread wear in hundredths of millimeters. Lower numbers represent better performance. Engineers have determined that, over the time in which the tires were tested, the design specifications are 28 6 6 millimeters, in order to provide the 60-month lifetime the tires are designed to achieve.

Case Questions for Discussion:

1.Draw a histogram of tread wear data. What can you conclude (if anything) about the distribution of the tread wear?

2.Construct x–- and R-charts for these data. Is the production process in control?

3.Provide two examples of each of the four major categories of quality costs applicable to this situation (i.e., prevention, appraisal, internal and external failure costs).

4.What are the process capability indexes for this process to meet design specifications? What do you recommend?