GATE IT 2005 | Question: 64

Question

The availability of a complex software is 90%. Its Mean Time Between Failure (MTBF) is 200 days. Because of the critical nature of the usage, the organization deploying the software further enhanced it to obtain an availability of 95%. In the process, the Mean Time To Repair (MTTR) increased by 5 days. What is the MTBF of the enhanced software?

• A. 205 days
• B. 300 days
• C. 500 days
• D. 700 days

Answer 1

Availability = MTBF/(MTBF + MTTR)

Case 1 :

0.9 = 200/(200 + x)

x = 22.22

Case 2 :

0.95 = y/(y+22.22+5)

0.95 = y/(y+27.22)

y = 517.18 (It is near to option C)

Comments

Availability is given by $\frac{Mean Time To Failure}{MeanTimeToFailure+MeanTimeToRepair}$

And $Mean Time Between Failure = Mean Time To Failure + Mean Time To Repair$

Before Enhancement:

Given 90 = $\frac{MTTF}{200}$

MTTF  = 180 days

MTTR = MTBF – MTTF

MTTR = 20 days

After Enhancement :

MTTR increases by 5 days. So MTTR = 25 days

95 % = $\frac{MTTF}{MTTF+25}$

MTTF = 475

MTBF = 475 + 25

MTBF = 500 exactly

Option (c)

Answer 2

Given,

          Availability = 90%
          MTBF = 200 Days=200*24=4800 Hours.

As we know that,

        Availability = MTBF*100/MTBF+MTTR

         90 = 4800*100/4800+MTTR

      432000+90MTTR = 480000

     90MTTR = 480000-432000

      90MTTR = 48000

    MTTR = 48000/90

   MTTR = 533.33 Hours.

According to question, we have to find MTBF,

It is given that, MTTR is increased by 5 Days = 5*24=120 hours.

Availability = MTBF*100/MTBF+MTTR

95 = MTBF*100/MTBF+533.33+120

95 = 100MTBF/MTBF+653.33

95MTBF + 62066.35 = 100MTBF

62066.35 = 100MTBF – 95MTBF

62066.35 = 5MTBF

62066.35/5 = MTBF

MTBF = 12413.27 Hours

Convert it into Days,

MTBF = 12413.27/24

MTBF = 517.21 Days

So, Option C is the Correct Answer.

Answer 3

Availability = (1 – (MTTR/MTBF)) x 100%

Simplify above

Availability = (MTBF-MTTR) / MTBF             ------(equation 1)

 

Case1:

Availability=90%

MTBF=200

put values in equation 1

90/100=(200-MTTR)200

MTTR=20

 

Case 2:

increasing 5 days in MTTR

20+5==>25

and new availability need is 95%

put values in equation 1

95/100 = (MTBF-25) / MTBF

MTBF=500

 

 

Correct me if i m wrong.