Battery failures. In five years, 500.000 batteries were put into service at a uniform rate. In that period, 5000 of them failed and were promptly replaced

(a) How many battery-years of exposure were accumulated by the end of the five-year period?

(b) Assuming Poisson data, estimate the failure rate of such batteries.

(c) Give an upper 95% confidence limit for the true failure rate.

(d) Is the Poisson distribution appropriate? State your reasons

(e) 100.000 more units will be manufactured and go into service over the coming year. Give a prediction of the number of failures in the entire population in service in the coming year

(f) Give the formula for the variance of the prediction error for (e) in terms of the failure rate A, previous exposure 1. and future exposure s.

(g) Calculate approximate 95% prediction limits for (e)