A fuel pump used in the manufacture of the TF0222 jet engine has been found thro

Question

A fuel pump used in the manufacture of the TF0222 jet engine has been found through extensive reliability testing to have a normal failure distribution with MTTF = 9400 operating hours and sigma = 3610 operating hours. The TF0222 is scheduled for depot overhaul at 5000 flying hours, at which time this fuel pump may be replaced. (a) Find R(5000 hr). (b) Find a 90-percent design life. (c) During depot overhaul, the option exists not to replace the fuel pump if it shows no sign of wear and is in working order. Find R(5000|5000). (d) If the TF0222 engine is configured to operate with two active redundant fuel pumps, find the redundant reliability for the second 5000 hours given the depot decides to keep the fuel pump after the first 5000-hour inspection (assuming it is still operating).

Explanation / Answer

a)P(X>5000) =P(Z>(5000-9400)/3610)=1-P(Z<-1.2188)=1-0.1115=0.8885

b)for 90% reliabilty; z=-1.2815

hence corresponding liffe =mean +z*Std deviatrion =5427.19

P(X>10000|X>5000) =P(X>10000|X>5000) =P(Z>0.1935)/P(Z>-1.4194)=0.4333/0.9221 =0.4590

d)redundant reliabilty =1-P(both of them failed)=1-P(Z<5000)*P(Z<10000) =1-0.0449=0.9551

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