Question

Given the following failure time data in hours: {50, 65, 78, 92, 99, 107, 120, 190, 200, 205}. Assume that the system under study follows an exponential failure distribution. The system under study has a 50 hour warranty. What is the probability that a system in the field will fail during the warranty period?

Answer 1

Let X be the failure time and is exponentially distributed.

Probability that a system in the field will fail during the warranty period =P(X<50)

Mean failure time = =AVERAGE(C3:L3)=120.6

The decay parameter =m =1/ =1/120.6 =0.008292

In exponential distribution , we have

P(X<x) =1-e^-mx

P(X<50) =1-e^-0.008292*50

=1-0.660609

=0.339391

=0.3394