Question

A recent public relations fiasco has intensified demand for engine testing for a particular OEM of agricultural machinery. Historically, these engines are estimated to have a constant failure rate of 7 failures per 10062 hours. A local TV station is testing the engines under two different trials (25 hours and 100 hours) What is the reliability of a single engine after 25 hours AND 100 hours? What is the probability of no failed engines, a single failed engine, and more than one failed engine, if the engines are tested in batches of 5 engines? Use the Poisson method and fill in the table on the next page, for both the 25 hour test and the 100 hour test. (show one sample calculation below 0 failed 1 failed >1 failed TOTAL 100.00 % (25 hours) 100.00 % (100 hours) Two separate third party labs are also testing the engine but using some different criteria. Number of engines tested Number Failed Lab 1 282 43 Lab 2 127 25 Formulate the hypothesis comparing the two labs, using the Z test for binomial trials (difference in proportions). What significance did you find?

Answer 1

GIVEN DATA :-

HISTORICALLY 7 FAILURES PER 10062 HOURS , MEANING ONE FAILURE PER 1437.42 HOURS

FOR 1 HOUR FAILURE RATE WILL BE 0.000242

FOR 25 HOURS = 25X0.000242= 0.00605

FOR 100 HOURS SET = 0.000242X100= 0.0242

WHEN TESTED WITH TWO DIFFERENT SETS

25 HOURS , RELIABILTY WILL BE MORE THAN THE 100 HOURS SET AS FAILURE RATE WILL BE LESS FOR 25 HOURS PLATFORM AS FAILURE RATIO WILL BE LESS IN 25 HOURS SET

FOR EVEERY 1437 HOURS A FAILURE WILL OCCUR , PROBABILITY FOR A FAILURE WILL BE

P(F) = 1/1437.42

GOING BY THIS FAILURE RATE

FOR NO FAILED ENGINE THE PROBABILITY WILL BE 0

FOR 1 FAILED ENGINE 0<P(A)

FOR MORE THAN 5 FAILURES IT WILLL BE 0<P(A)<5