Question

1. In an attempt to measure the reliability of a new brand of light bulbs, the manufacturer selected a random sample of 14 light bulbs. The time of failure for these light bulbs is organized from lowest to highest and is presented in the following table.

Sample	Hours of operation before Failure
1	35
2	90
3	100
4	150
5	700
6	1010
7	1040
8	1190
9	1200
10	1250
11	1270
12	1280
13	1300
14	1450

a) What is the failure rate for testing period of 450 hours? (1 point)

b) What is the failure rate for testing period of 900 hours? (1 point)

c) What is the failure rate for testing period of 1350 hours? (1 point)

d) Match the failure rates determined in parts a, b, and c with the three basic stages of the product life cycle (early, middle, late). Do the failure rates correspond to the general idea behind a bathtub function? (1 point)

e) Which of the two time measures (MTBF and MTF) would be more appropriate in this instance and why? Determine the appropriate average amount of time per failure (either MTBF or MTF) for each of the testing periods in parts a through c. (1 point)

Answer 1

Solution:

Failure rate is number of failures per unit time.

a] For the given data, it can be observed that before the for testing period of 450 hours, there are 4 bulbs were failed,

failure rate =4/450= 0.008889

failure rate per hour is 0.008889 that is 8.89 failures per 1000 hour

b] For the given data, it can be observed that before the for testing period of 900 hours, there are 5 bulbs were failed,

failure rate =5/900= 0.005556

failure rate per hour is 0.005556 that is 5.56 failures per 1000 hour.

c] For the given data, it can be observed that before the for testing period of 1350 hours, there are 13 bulbs were failed,

failure rate =13/1350= 0.00963

failure rate per hour is 0.008889 that is 9.63 failures per 1000 hour