Circuit breaker Use the circuit breaker data from Problem 3.4.

(a) The old design has a known proportion po =  0 . 5 0fa iling by 10,000 cycles. What is the binomial estimate of the proportion of the new design failing by 10,000 cycles, based on the first sample of 18 circuit breakers?

(b) For a two-sided test for equality of these two proportions, calculate the significance level. Does this proportion for the new design differ statistically significantly from that for the old one?

(c) Use Fisher's test to compare the two samples of the new breaker with respect to the proportion failed by 15,000 cycles.

(d) For the sample sizes in (c), how big ;I difference in the proportions do you think the test will detect? A formal answer would involve calculating the OC curve of the test.

Problem

Circuit breaker A mechanical life test of 18 circuit breakers of a new design was run to estimate the percentage failed by 10,000 cycles of operation. Breakers were inspected on a schedule, and it is known only that a failure occurred between certain inspections as shown.

(a)   Make a Weibull plot with each failure as a separate point.

(b)   How well does the Weibull distribution appear to fit the data?

(c) Graphically estimate the percentage failing by 10,000 cycles.

(d) What is your subjective estimate of the uncertainty in the estimate?

(e) Graphically estimate the Weibull shape parameter. Does the plot convince you that the true shape parameter differs from unity?

(f) The old breaker design had about 50% failure by 10,000 cycles. Is the new design clearly better?

(g) Another sample of 18 breakers of the new design was assembled under different conditions. These breakers were run on test for 15,000 cycles without failure and removed from test. Do you subjectively judge the two samples consistent?