A manufacturer of washing machines conducted a life test during which it monitored 12 new machines for a period of 3 years and recorded the time to a major repair for each. At the end of the 3-year testing period, two machines had not yet required a major repair. The failure times (in months) of the remaining 10 washing machines were 14, 28, 9, 13, 6, 20, 10, 17, 30, and 20. Assume the life length (in years) of the machines has a Weibull failure time distribution with unknown parameters α and β.

a. Construct a table for the data listing the number of machines surviving (that is, without major repair) at the end of each year.

b. Apply the method of least squares to the data in the table of part a to derive estimates of α and β.

c. Find a 95% confidence interval for α. If you have access to a regression computer package, find a 95% confidence interval for β.

d. The manufacturer guarantees all machines against a major repair for 2 years. Using the least-squares estimates of α and β, find the probability that a new washer will have to be repaired under the guarantee.