ENGM 620
Fall 2012
Solutions, Ch 13
24. The Collier Company tested 200 products for 100 hours each. In this time, they experienced 12 breakdowns. Computer the number of failures per hour. What is the MTBF?
200 products * 100 hours each = 20,000 product hours
12 breakdowns in 20,000 product hours = an average of 0.0006 breakdowns per hour = λ
MTBF = 1/ λ = 1667 hours
28. Suppose there are 42 pumps used in a refinery. These pumps are continuously being used with a 2% chance of failure over 50,000 hours. If repair time is 10 hours to install a new rebuilt pump, how many pumps should be kept on hand to keep the chance of a plant shutdown to less than 1%.
R(T) = e-lT
.98 = e-l(50000)
Ln(.98) = -50000l
l = -ln(.98)/50,000 = 4.04x10-7
MTTF = 1/l = 2,474,916
P(1 of 42+x pumps will fail within 10 hrs) = 1%
= 1 - P(pump 1 fail)P(pump 2 fail)P(pump 3 fail) . . . P(pump 42+x fail)
= 1 – P R(10) = 1 - P e-l10 = 1 - .99999642+x = .01
.99 = .99999642+x
Yields x = 1 will provide .9998 overall reliability
NOTE: there will not be a problem like this.
31. You are to decide between 3 potential suppliers for an assembly for a product you are designing. After performing life testing on several assemblies, you find the following:
Supplier MTBF MTTR SA
A 45 2 .958
B 100 6 .943
C 150 9 .943
Based on system availability, which supplier should you choose?
SA = MTBF/(MTBF+MTTR) yields SA above yields choose supplier A
Additional. An electronic missile guidance system consist of the following components: A, B, C, and D with reliabilities of 0.96, 0.98, 0.90, and 0.99 respectively. Given the system design below, what is the reliability of the entire system?
The reliability of the parallel Rcc shown in the diagram above the problem, is calculated as:
Rcc = 1 - (1 - 0.90)2 = 0.99
RaRbRccRd = (0.96)(0.98) (0.99)(0.99) = 0.922