2-1 calculations pfd ang 1.pptx

Reliability

1

Car “A” very rarely breaks down in 10 years. Car “B” breaks down unexpectedly many times a year.

2-1

CAR “A”

CAR “B”

Which would be preferred ?

Reliability

22-1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510

1 Car B

Number of week

At t

he G

arag

e

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510

1

Car A

Number of week

At t

he G

arag

e

Time to failure 1 (0-20)

Total time to failure(1,2..etc) =41 Number of failures=8


Mean Time To Failure (MTTF)

Time to failure 2 (22-47)

Reliability

32-1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510

1 Car B

Number of week

At t

he G

arag

e

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510

1

Car A

Number of week

At t

he G

arag

e



Mean Time To Failure (MTTF)

MTTF(A) = (49/2 ) = 24.5

MTTF(B) = (41/8 ) = 5.125

Reliability

42-1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510

1 Car B

Number of week

At t

he G

arag

e

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510

1

Car A

Number of week

At t

he G

arag

e

Total time out of service=11 Number of failures=8

Total time out of service time=3 Number of failures=2

Mean Time To Repair (MTTR)

MTTR(A) = (3/2 ) = 1.5

MTTR(B) = (11/8 ) = 1.375

Reliability

52-1

Observe that ( Total time = Time to failures + time to repair failures)

Mean Time Between Failures (MTBF)

Then it’s the number of faults that matter most ?

Mean Time Between Failures

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510

1

Car A

Number of week

At t

he G

arag

e

Reliability

62-1

MTBF = 52 / 2 = 26

MTBF = MTTF+MTTR

Mean Time Between Failures (MTBF)

In industry repair time is considered to be 8-24 hoursThen MTTF >> MTTR ( less than 1% ) Then MTBF = MTTF

Failure rate λ = 1/MTBF

Total Time

Number of fails=

Time to failure

Number of fails Number of fails+

Time being repaired

Reliability

72-1

Types of failureTotal failures that affect Safety, Functionality & Reliability can be categorized into:

1. Failure to danger that was not detected or failed when needed to function safely. ( Fault of sensor, actuator, valve when it was supposed to control or shutdown). λ dangerous undetected , λDU.

2. Failure to danger that was detected. ( Failure of sensor, actuator, valve that could have became “Fail to Danger” but was detected during inspection or testing. λ dangerous detected , λDD

3. Fail to safe detected by instrument before any triggering of shutdown was initiated. λ safe undetected , λSU

4. Fail to safe but was not detected and caused the system to halt for no high risk reason.( Falls Alarm). λ safe detected , λSD

Types of failure

82-1

Total Device Random Failure Rate

λTOT or λCRIT

Safe Undetected , λSU

Dangerous Detected , λDD

Danger Undetected , λDU

Safe Detected , λSD

Danger , λDU

Spurious, λSP

Probability of Failure at Demand Average PFDavr

92-1

•Lets buy some light bulbs.•Average life time 1 year.•Mean Time Before Failure 1 year.

•Some will burn within days.•Some may last for much longer than 1 year.

•For any bulb, what’s the probability of failure ?

•Probability of failure =


102-1

•Probability of lamp still working at time t (P on t)= e-λDt •Where λD = 1/ MTTF

•Probability of lamp failing at time t (P on t)= 1- e-λDt

The probability of failure

The probability of correct operation


112-1

•Same thing for any device or system.•The probability of failure keeps getting closer to 1 with time.

•If testing can be done every Tp period.•With assumption that the device is returned to original state.

Probability of failure with regular proof testing

The probability of failure


122-1

•To calculate Probability of Failure on Demand Average. PFD avg

•For Tp << MTBF, (Tp << 1/ λDU ), or λDU*Tp<< 1).

•PFDavg = ½ * λDU Tp.

PFDavg

λDU Tp

2PFDavg

=

Power Supply

13

LT1

LT2

Basic Process Control System

Shut Down Valve

Emergency Shutdown System

FT

InputsOutputsInputsOutputs

s


Solenoid valve

Level transmitter

Logic solver

ItemMTTF D

Years

MTTF SP

Years

Level Transmitter 150 75

Logic Solver 750 225

Solenoid Valve 60 25

Shutdown Valve 50 200

2-1

14

Shut Down Valve


Solenoid valveLevel transmitter Logic solver

ItemMTTF D

Years

MTTF SP

Years λDU λSP

Level Transmitter 150 75 6.67E-3 1.33E-2

Logic Solver 750 225 1.33E-3 4.44E-3

Solenoid Valve 60 25 1.67E-2 4.00E-2

Shutdown Valve 50 200 2.00E-2 5.00E-3

2-1


152-1

•What is the probability of complete failure of system and the occurrence of accident. ?

Assume on a random day the fluid was going high:•Level transmitter not functional.•OR Logic solver not functional.•OR Solenoid valve not responding.•OR Shutdown Valve not working.

So the probability of system failure of system , Dangerous Failure Rate

Item MTTF D MTTF SP λDU λSP

Level Transmitter 150 75 6.67E-3 1.33E-2

Logic Solver 750 225 1.33E-3 4.44E-3

Solenoid Valve 60 25 1.67E-2 4.00E-2

Shutdown Valve 50 200 2.00E-2 5.00E-3

Any Failure 22 16 ƩλDU =4.47E-2 Ʃ λSP=6.3E-2

2-1 calculations pfd ang 1.pptx

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