GATE IT 2007 | Question: 51

Question

The following table shows the time between failures for a software system.

Error Number	1	2	3	4	5
Time since last failure(hours)	6	4	8	5	6

The reliability of the system for one hour of operation assuming an exponential model is :

• A. 0.45
• B. 0.63
• C. 0.84
• D. 0.95

Answer 1

MTBF is the mean (average) of a distribution of product life time or life between successive failures.

MTBF=(6+4+8+5+6)/5=29/5

the probability or reliability that the product will work for a defined period of time without failure is given by the following equation: R(T)=exp(-T/MTBF)

here T= 1hour

R(1)=e^(-5/29)=e^(-0.1724)=0.84

Reference:

http://www.profaceamerica.com/sites/default/files/cms/cms/resource_library/files/6fef09c498f66461/mtbf_communique.pdf

https://en.wikipedia.org/wiki/Mean_time_between_failures

Comments

if T is 1 then calculation should be  e^(-1/29)