Question

(4 %) Q3. In a process facility, emergency equipment operates 8 hr per day, 7 days per week. It is ift. estimated that on an average the equipment is turned on about 20 minutes per 8 hr sl The equipment is assumed to have a constant failure rate of o.08 per hour while it is on and of 0.005 per hour when it is turned off but being carried. a. What is the MTTF? b. What is the probability of light failing during one S hr shift?

Answer 1

a. MTTF expands to Mean time to failure, ie, the mean time to the first failure of an equipment.

b. The probability of light failing during one 8 hour shift can be calculated as :

= probability of failing when turned off + probability of failing when turned on

where :

probability of failing when turned off is calculated as :

$=\lambda e^-\lambda x$

$=\lambda is 0.005 per hour$

so for 8 hours $=\lambda$ = 0.005*8 = 0.04

Probability of first failure when turned off

P(X=1) =0.0384315

Similarly, probability of failure when turned on

$=\lambda is 0.08 per hour$

so \lamba for 8 hours will be 0.08*8= 0.64

and P(X=1) = 0.337467

Hence, the total probability of light failing during 8 hr shift is 0.3758985.