Your current design uses a fan with times to fail described by a Weibull distrib

Question

Your current design uses a fan with times to fail described by a Weibull distribution with a shape parameter, beta = 2 and a scale parameter eta = 9, 780 hours. At what number of hours would you predict 5% of the fans to fail? A new fan vendor says their fan has times to fail described by a Weibull distribution with a shape parameter beta = 1.25 and a scale parameter eta = 12,000 hours. The new fan vendor says his fan's 1 year reliability (1 year of operation is 2, 080 hours) will be better than the competitors fan you are currently using. Do you agree? Describe in terms of the Weibull parameters why?

Explanation / Answer

Please find below the number of hours vs cumulative probability: Hence from the table below at 2300 hours 5% of fans fail

1,000   0.01040049485
1,100   0.01257081791
1,200   0.01494237743
1,300   0.01751369959
1,400   0.02028318914
1,500   0.02324913103
1,600   0.02640969218
1,700   0.02976292339
1,800   0.03330676131
1,900   0.03703903058
2,000   0.04095744602
2,100   0.04505961503
2,200   0.04934303994
2,300   0.0538051206
2,400   0.05844315702
2,500   0.06325435202
2,600   0.06823581411
2,700   0.07338456036

New fan is bettter than old fan because the scale parameter has increased now.

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