A large national producer of appliances has traced customer experience with a popular toaster oven. A survey of 5,000 customers who purchased the oven early in 2000 has revealed the following:

Number of Year Breakdowns 2000 188 2001 58 2002 63 2003 72 2004 54 2005 71

a. Using these data, estimate pk  the probability that a toaster oven fails in its kth year of operation, for k  1, . . . , 6.

b. What is the likelihood that a toaster oven will last at least six years without failure based on these data?

c. The discrete failure rate function has the form rk  pkRk1, where Rk is the probability that a unit survives through period k. Determine the failure rate function for the first five years of operation from the given data.

d. Suppose that you purchased a toaster oven at the beginning of 2004 and it is still operating at the end of 2007. If the reliability has not changed appreciably from 2000 to 2007, use the results of part

(c) to obtain the probability that it will fail during the first two months of calendar year 2008.