This document discusses Safety Instrumented Systems (SIS) and methods for determining risk reduction requirements. An SIS monitors industrial processes for dangerous conditions and executes actions to prevent or mitigate hazardous events. The document describes various methods to determine the necessary level of risk reduction for a given process, including risk graphs and Layer of Protection Analysis, both of which consider the consequences, frequency, possibility of avoidance, and probability of occurrence of an event. The determined risk reduction requirement is characterized by a Safety Integrity Level (SIL) on a scale of 1 to 4. An SIS provides risk reduction by successfully performing its safety functions, with its effectiveness measured by its probability of failure on demand (PFD).

1. 359
15
Safety
Instrumented
Systems
As defined by ANSI/ISA-84.00.01-2004 (IEC 61511 Mod) [Ref. 4] a Safety
Instrumented System (SIS) is a control system consisting of sensors, one or
more controllers (frequently called logic solvers), and final elements. The
purpose of an SIS is to monitor an industrial process for potentially danger-
ous conditions and to alarm or execute preprogrammed action to either pre-
vent a hazardous event from occurring or to mitigate the consequences of a
hazardous event should it occur. An SIS:
• Does not improve the yield of a process and
• Does not increase process efficiency but
• Does save money by loss reduction and
• Does reduce risk cost.
Risk Cost
Risk is usually defined as the probability of a failure event multiplied by
the consequences of the failure event. The consequences of a failure event
are measured in terms of risk cost. The concept of risk cost is a statistical
concept. An actual cost is not incurred each year. Actual cost is incurred
only when there is a failure event (an accident). The individual event cost
can be quite high. If event costs are averaged over many sites for many
years, an average risk cost per year can be established. If actions are taken
to reduce the chance of a failure event or the consequences of a failure
event, risk costs are lowered.

2. 360 Control Systems Safety Evaluation and Reliability
Risk Reduction
There are risks in every activity of life. Admittedly some activities involve
more risk than others. According to Reference 1, the chance of dying dur-
ing a 100 mile automobile trip in the midwestern United States is 1 in
588,000. The average chance each year of dying from an earthquake or vol-
cano is 1 in 11,000,000.
There is risk inherent in the operation of an industrial process. Sometimes
that risk is unacceptably high. A lower level of risk may be required by
corporate rules, regulatory environment, law, the insurance company,
public opinion, or other interested parties. This requirement leads to the
concept of “acceptable risk.” When inherent risk (perceived or actual) is
higher than “acceptable risk,” then risk reduction is required (Figure 15-1).
While “inherent risk” and even “acceptable risk” are very hard to quan-
tify, risk reduction is a little easier. Several methods have been proposed
to determine the amount of risk reduction to at least to an order-of-magni-
tude level (Ref. 2).
EXAMPLE 15-1
Problem: Records maintained over many sites for many years
indicate that on average once every 15 years an industrial boiler has
an accident if no protection equipment like an SIS is used. The
average cost of each event is $1 million. What is the yearly risk cost
with no protection equipment?
Solution: The average yearly risk cost is $1,000,000/15 = $66,667.
Figure 15-1. Risk Reduction

3. Safety Instrumented Systems 361
Risk Reduction Factor
The risk reduction factor (RRF) may be defined as:
RRF = Inherent Risk / Acceptable Risk
An SIS provides risk reduction when it monitors a process looking for a
dangerous condition (a process demand) and successfully performs its
preprogrammed function to prevent an event. Assuming that the SIS has
been properly programmed, it reduces risk whenever it operates success-
fully in response to a process demand. It will not reduce risk if it fails to
operate when there is a process demand. Therefore, an important measure
of the risk reduction capability of an SIS is PFD, probability of failure on
demand. In the case of a de-energize-to-trip system, this is the probability
that the system will fail with its outputs energized. For low demand sys-
tems, a dangerous condition occurs infrequently therefore PFDavg (Chap-
ter 4) is the relevant measure of probability of dangerous failure. In such
cases the risk reduction factor (RRF) achieved is defined as:
RRF = 1 / PFDavg (15-1)
How Much RRF is Needed?
Some find it hard to numerically estimate the necessary RRF in an indus-
trial process. That is one reason why functional safety standards provide
an order-of-magnitude framework with which to work. This order of mag-
nitude risk reduction framework is called “safety integrity level (SIL).”
Figure 15-2 shows the safety integrity levels (SIL) established by IEC 61508
(Ref. 3) with some examples of various industrial processes. It should be
noted that any particular industrial process can be assigned different SILs
depending on the actual or perceived effect of events that are known (or
likely) to occur in connection with that process.
Several methods to determine SIL are published in Part 3 of ISA’s 84.01
standard (Ref. 4). One qualitative method from 84.01, Part 3 was devel-
oped to deal with personnel death and injury is shown in Figure 15-3. This
method is called a risk graph. The developer of a risk graph must deter-
mine four things: the consequence (C), the frequency of exposure (F), the
possibility of avoidance (P), and the probability of occurrence (W).
The probability of occurrence of an event is characterized by three of the
factors: F, P, and W. The fourth factor, C, completes the estimate of risk. A
description of each factor is shown in Table 15-1.

4. 362 Control Systems Safety Evaluation and Reliability
Figure 15-2. Risk Reduction Categories
Figure 15-3. Risk Graph SIL Determination Method
Safety Integrity
Level
Average Probability of
Failure on Demand
(PFDavg) Low Demand
4
3
2
1 0.1 - 0.01 10 - 100
0.01 - 0.001 100 - 1,000
0.001 - 0.0001 1,000 - 10,000
< 0.0001 > 10,000
Risk Reduction Factor
(RRF)
Typical Applications
Rail Transportation
Utility Boilers
Industrial Boilers
Chemical
Processes
C1
C2
C3
C4
F1
F2
F1
F2
P1
P2
P1
P1
P1
P2
P2
P2
SIL1
SIL2
SIL3
SIL4
SIL1
SIL1SIL2
SIL2SIL3
SIL3SIL4
F2
F1
W3 W2 W1
NSS
NSS
NSS
NS NS
NS
NS - No Safety Requirements
NSS - No Special Safety Requirements
NPES - Single SIS Insufficient
NPES

5. Safety Instrumented Systems 363
The consequences refer specifically to personnel injury or death. The fre-
quency of exposure is a measure of the chances that personnel will be in
the danger area when an event occurs. If a process is only operated once a
week and no operators are normally at the site, this constitutes a relatively
low risk compared to continuous operation with personnel always on
duty—given that both processes present similar inherent risks.
The possibility of avoidance considers such things as warning signs, the
speed at which an event will develop, and other avoidance measures such
as protective barriers. The probability of unwanted occurrence parameter
includes consideration of other risk reduction devices.
The danger area is also an important consideration. If there is only risk of
injury near the process unit then perhaps only the operators and other
plant personnel need be considered in the analysis. But if a hazardous
event could harm people in the neighborhood or over a wide geographic
area, then that must be considered in the analysis.
Table 15-1. Description of Risk Graph Factors
Consequence
C1 Minor Injury
C2 Serious injury or single death
C3 Death to multiple persons
C4 Very many people killed
Frequency of Exposure and Time
F1 Rare to frequent
F2 Frequent to continuous exposure
Possibility of Avoidance
P1 Avoidance possible
P2 Avoidance not likely, almost impossible
Probability of Unwanted Occurrence
W1 Very slight probability
W2 Slight probability, few unwanted occurrences
W3 High probability
EXAMPLE 15-2
Problem: An industrial process may need an SIS to reduce risk to an
acceptable level. Use the risk graph of Figure 15-3 to determine this
need.

6. 364 Control Systems Safety Evaluation and Reliability
Many corporations have versions of risk graphs in corporate procedures.
Frequently, these documents provide detailed descriptions of how to clas-
sify the various parameters. In addition to personnel risk, risk graphs are
needed for equipment damage and environmental damage (Ref. 5). When
all three graphs are completed for a process the largest risk reduction need
is the one specified for the SIL (Figure 15-4).
EXAMPLE 15-2 continued
Solution: Experts estimate that an event may result in serious injury
or a single death, C2. The process operates continuously and
personnel are usually present; therefore, exposure is rated as
frequent to continuous, F2. Since there is little or no warning of a
dangerous condition the probability of avoidance is rated avoidance
not likely, P2. Finally, it is judged that there is only a slight probability
of occurrence, W2, because pressure relief valves are installed to
provide another layer of protection. Using the risk graph, this process
needs a SIL2 level of risk reduction.
Figure 15-4. Screen Shot—Risk Graph for Personnel, Equipment, and Environmental
(Ref. 5)

7. Safety Instrumented Systems 365
Another risk reduction determination method published in ISA-84.01 is
called Layer of Protection Analysis (LOPA). This method considers all the
valid, independent layers of protection and credits those layers for the risk
reduction provided. LOPA can be used qualitatively or semi-quantita-
tively with most practitioners using a semi-quantitative approach as
shown in Figure 15-5.
Quantitative Risk Reduction
In some cases corporations and insurance companies determine risk
reduction factors based on quantitative risk analysis. Statistics are com-
piled on the frequency and severity of events. These statistics are used to
determine risk reduction factors based on risk cost goals or event probabil-
ity goals. While these methods may seem easy, it must be understood that
the uncertainty of the statistical data and the variability of the factors con-
tributing to an event must be taken into account. This is typically done by
increasing the required risk reduction factor by a certain safety margin.
Figure 15-5. Screen Shot—Frequency Based LOPA Results Example (Ref. 5)

8. 366 Control Systems Safety Evaluation and Reliability
SIS Architectures
An SIS consists of three categories of subsystems: sensors/transmitters,
controllers, and final elements, that work together to detect and prevent,
or mitigate the effects of a hazardous event. It is important to design a sys-
tem that meets RRF requirements. It is also important to maximize the
production uptime (minimize false trips). In order to achieve these goals,
system designers often use redundant equipment in various architectures
(Chapter 14). These fault tolerant architectural configurations apply to
field instruments (sensors/transmitters and final elements) as well as to
controllers.
Sensor Architectures
An SIS must include devices capable of sensing potentially dangerous
conditions. There are many types of sensors used including flame detec-
tors (infrared or ultraviolet), gas detectors, pressure sensors, thermocou-
ples, RTDs (resistance temperature detectors), and many types of discrete
switches. These sensors can fail, typically in more than one failure mode.
Some sensor failures can be detected by on-line diagnostics in the sensor
itself or in the controller to which it is connected. In general, all of the reli-
ability and safety modeling techniques can be used.
EXAMPLE 15-3
Problem: The risk cost of operating an industrial boiler is estimated
to be $66,667 per year. The insurance company that insures the
operation of the boiler needs a risk cost of less than $1,000 per year
in order to remain profitable without a significant increase in
premiums. What is the needed risk reduction factor?
Solution: The ratio of risk costs is 66667/1000 which equals 66.7. In
order to account for the uncertainly of the data, the insurance
company chooses a higher number and mandates that a safety
instrumented function (SIF) with an RRF of 100 be installed in the
SIS. (Note: this is a SIL2 category SIF).
EXAMPLE 15-4
Problem: A two-wire pressure sensor transmits 4–20 mA to the
analog input of a trip amplifier that is configured to de-energize a
relay contact when the mA input current from the sensor goes higher
than the trip point. The sensor manufacturer supplies the following
failure rate data (Ref. 6):
Fail Danger Detected High = 59 FITS
Fail Danger Detected Low = 33 FITS

9. Safety Instrumented Systems 367
EXAMPLE 15-4 continued
Fail Danger Detected Diagnostics = 264 FITS
Fail Danger Undetected = 37 FITS
Fail Annunciation Undetected = 5 FITS
The pressure transmitter is configured to send its output to 20.8 mA
(over-range) if a failure is detected by the internal diagnostics. The
transmitter is fully tested and calibrated every five years. In this
application, what is the PFDavg for a single transmitter in a 1oo1
architecture for a five year mission time? What is the Spurious Trip
Rate (STR)?
Solution: The trip amplifier will falsely trip if the transmitter fails with
its output signal high. The system will fail dangerous if the transmitter
fails with its output signal low or if it has a dangerous undetected
failure. The failure rates are therefore:
λS
= (59 + 264) × 10-9
= 3.23 × 10-7
failures per hour
λD
= (33 + 37) × 10-9
= 7.0 × 10-8
failures per hour
No automatic diagnostics are given credit in the PFD calculation
since there is no diagnostic annunciation mechanism configured in
the controller. Therefore, using equation 14-2, PFDavg = DU × 5 ×
8760 / 2 = 0.0015.
The term Spurious Trip Rate refers to the average rate at which a
subsystem will cause a shutdown when no dangerous condition
occurs. The STR is equal to the safe failure rate of 3.23 × 10-7
trips
per hour.
EXAMPLE 15-5
Problem: A two-wire pressure sensor transmits 4–20 mA to the
analog input of a safety certified logic solver. The sensor
manufacturer supplies a safety certificate with the term “Systematic
Capability = SIL 3.” The sensor manufacturer also supplies the
following failure rate data (Ref. 6):
Fail Danger Detected High = 59 FITS
Fail Danger Detected Low = 33 FITS
Fail Danger Detected Diagnostics = 264 FITS
Fail Danger Undetected = 37 FITS
Fail Annunciation Undetected = 5 FITS
The logic solver is programmed to recognize an out-of-band current
signal as a diagnostic fault and will hold the last pressure value while
the failure is annunciated and repaired. Average repair time at the
facility is 168 hours (one week). The transmitter is fully tested and
calibrated every five years. What is the PFDavg for a single

10. 368 Control Systems Safety Evaluation and Reliability
Figure 15-6 shows two discrete sensors measuring the same process vari-
able. These two sensors can be configured in a 1oo2 architecture by simply
adding logic to initiate a shutdown if either of the two sensors signals a
dangerous condition. Like the 1oo2 controller architecture (Chapter 14),
this configuration will substantially reduce the chance of a dangerous fail-
ure but will almost double the chance of a safe failure. Note that common
cause failures apply when redundant configurations are used. The com-
mon cause defense rules (Chapter 10; Common-Cause Avoidance) apply.
Avoid close physical installation, use high strength sensors, use diverse
design sensors, or some combination of all three techniques.
EXAMPLE 15-5 continued
transmitter in a 1oo1 architecture for a five year mission time? What
is the Spurious Trip Rate (STR)? What does the term “Systematic
Capability” mean?
Solution: The logic solver will detect out-of-range current signals and
hold the last pressure value. Therefore, these failures are dangerous
detected (DD). The total DD failure rate is 356 FITS (One FIT = 1 ×
10-9
failures per hour). Using Equation 14-2,
PFDavg = 3.56×10-7
× 168 + 3.7×10-8
× 8760 × 5 / 2 = 0.00087
Spurious Trip Rate: Because the logic solver is configured to hold the
last pressure reading on failure of the sensor, no false trips will occur.
The STR is zero.
The term Systematic Capability in an IEC 61508 certification means
that the design, test, and manufacturing processes used to create
and build the product have a level of integrity needed for SIL 3 to
reduce design and manufacturing faults inside the product. This
allows the designer of a Safety Instrumented System to use that
component at up to and including the rated SIL level. A product with a
systematic capability rating of SIL 3 can be used in SIL 1, SIL 2, or
SIL 3 without safety integrity justification but cannot be used in a SIL
4 application without further justification based on extensive prior use.
EXAMPLE 15-6
Problem: Two pressure switches measure the same process
variable. They are connected to a safety certified logic solver with
logic to perform a 1oo2 vote. The manufacturer supplies a certificate
with the term “Systematic Capability = SIL 3.” The manufacturer also
supplies the following failure rate data (Ref. 7):
Fail Safe = 83.8 FITS
Fail Danger Undetected = 61.3 FITS

11. Safety Instrumented Systems 369
The 1oo2 sensor concept can be applied to analog sensors as well. Figure
15-7 shows two analog sensors measuring the same process variable. A
“high select” or “low select” function block (depending on the fail-safe
direction) is used to select which analog signal will be used in the
calculation.
EXAMPLE 15-6 continued
What is the PFDavg for a 1oo2 sensor subsystem for a five year
mission time? What is the Spurious Trip Rate for the sensor
subsystem?
Solution: With a common-cause beta factor of 10% (0.10), the failure
rates are:
λSUC = 0.1 × 83.8E-9 = 8.4E-9 failures per hour
λSUN = (1-0.1) × 83.8E-9 = 7.54E-08 failures per hour
λDUC = 0.1 × 61.3E-9 = 6.1E-9 failures per hour
λDUN = (1-0.1) × 61.3E-9 = 5.52E-08 failures per hour
Since a common cause safe failure or a safe failure in either switch
will cause a false trip, the STR equals 8.4E-9 + 7.54E-8 + 7.54E-8,
which totals 1.59E-7 trips per hour.
PFDavg can be calculated using Equation 14-5. Note that there are
no detected failures, therefore RT (average repair time) = 0. PFDavg
is 0.00014.
Figure 15-6. 1oo2 Discrete Sensors
Discrete Sensor
Pressure
Sensor
Discrete Input
Discrete Input
Logic Solver
1oo2 logic
trip if either
sensor
indicates a trip is
needed
+
-
+
-
Discrete Sensor
Pressure
Sensor

12. 370 Control Systems Safety Evaluation and Reliability
Figure 15-7. 1oo2 Analog Sensors
EXAMPLE 15-7
Problem: A two wire pressure sensor transmits 4 –20 mA to the
analog input of a safety certified logic solver. Two of these sensors
measure the same process variable and are configured to trip if either
sensor indicates a trip (1oo2 logic). The sensor manufacturer
supplies a safety certificate with the term “Systematic Capability =
SIL 3.” The manufacturer also supplies the following failure rate data
(Ref. 6):
Fail Danger Detected High = 59 FITS
Fail Danger Detected Low = 33 FITS
Fail Danger Detected Diagnostics = 264 FITS
Fail Danger Undetected = 37 FITS
Fail Annunciation Undetected = 5 FITS
The logic solver is programmed to recognize an out of range current
signal as a diagnostic fault and will hold last pressure value while the
failure is annunciated and repaired. Average repair time at the facility
is 168 hours (one week). The transmitter is fully tested and calibrated
every five years. What is PFDavg for a 1oo2 sensor subsystem
architecture for a five year mission time? Assume a common cause
beta factor of 10%. What is the Spurious Trip Rate (STR) of the
sensor subsystem?
Solution: The logic solver will detect out-of-range signals and hold
the last pressure value. Therefore, these out-of-range failure rates
are classified as dangerous detected (DD). The total DD failure rate
for each sensor is 356 FITS. Considering common cause, the failure
rates are:
λDDC = 0.1 × 3.56E-7 = 3.56E-8 failures per hour
λDDN
= (1-0.1) × 3.56E-7 = 3.2E-7 failures per hour
Analog Transmitter
4 to 20 mA
Pressure
Transmitter
Analog Input
Analog Transmitter
4 to 20 mA
Analog Input
Logic Solver
+
-
+
-
1oo2 Logic -
high or low
select
depending on
trip functionPressure
Transmitter

13. Safety Instrumented Systems 371
The previous examples show different approaches to the design of sensor
subsystems. The PFDavg and STR of these designs are shown in Table
15-2.
The results show the significant advantage of using an analog sensor,
especially if a logic solver configured to detect out of range current signals
is used. This approach yields good safety as long as the repair time is short
(less than one week per this example) and there is exceptional process
availability.
Many other sensor architectures are possible. A common approach in the
days of relay logic was to use three transmitters in a 2oo3 architecture.
This worked well to achieve good process availability and safety when
automatic diagnostics were not available, and this approach is still being
used. Other possible architectures are 2oo5 or the general MooN, used
most often in fire and flammable gas applications. Note that some sensor
architectures are not what they seem. In one installation, two toxic gas
detectors are installed in each “zone.” Ten zones exist. At first look this
might be described as a 2oo20 vote. The vote-to-trip logic in the logic
solver requires a 2oo2 signal to trip from the sensor pair within each zone.
But if any pair in any zone indicates a trip signal, the logic will initiate a
trip. That portion of the logic appears to be 1oo10. However, the probabil-
ity model is NOT 1oo10. A question might be asked, “Why 10 sets of sen-
sors?” The answer is that one set could not be certain of detecting the
hazard caused by the toxic gas. Given that answer, there are 10 safety
functions, each of which has a 2oo2 sensor. There is no safety redundancy
benefit from the 10 sets of sensors if each set is not able to independently
detect the toxic gas hazard.
EXAMPLE 15-7 continued
λDUC
= 0.1 × 3.7E-8 = 3.7E-9 failures per hour
λDUN
= (1-0.1) × 3.7E-8 = 3.33E-8 failures per hour
Using Equation 14-5,
PFDavg = 0.000088
STR = 0.
Table 15-2. Sensor Subsystem Results
Architecture PFDavg STR
1oo1 Analog Sensor/Trip Amp 0.0016 3.23-7
1oo1 Analog Sensor/Logic Solver 0.00087 0
1oo2 Switch 0.00014 1.67-7
1oo2 Analog Sensor/Logic Solver 0.000088 0

14. 372 Control Systems Safety Evaluation and Reliability
Final Element Architectures
Final elements are the third major category of subsystems in an SIS. Final
elements in the process industries are typically a remote-actuated valve
consisting of an interface component (a solenoid-operated pneumatic
valve), an actuator, and a process valve. Final elements have failure
modes, failure rates, and (in some devices) on-line diagnostics. The reli-
ability and safety modeling techniques developed for other SIS devices are
appropriate.
The simplest final element configuration is the 1oo1 as shown in Figure
15-8. The controller normally energizes a solenoid valve that supplies air
under pressure to the actuator. The actuator keeps the valve open (or
closed, if that is the desired position). When an unsafe condition is
detected, the controller de-energizes the solenoid valve. The valve stops
the compressed air delivery and vents air from the actuator. The spring
return actuator then moves the valve to its safe position. In such final ele-
ment systems, failure rates must be obtained for the solenoid valve and
the actuator/ valve assembly.
Figure 15-8. 1oo1 Final Element Assembly
Controller
Solenoid Valve
Air Supply
Actuator
Valve
VentDiscrete Output

15. Safety Instrumented Systems 373
Figure 15-9 shows a common implementation of a 1oo2 configuration for
final elements. The valves close when a dangerous condition is detected.
The system is considered successful if either valve successfully closes. This
configuration is intended to provide higher safety than a single-valve sys-
tem and can be effective especially if common cause is applied.
EXAMPLE 15-8
Problem: Solenoid valve failure rates provided by the manufacturer
from a third party FMEDA are λS
= 71 FITS and λD
= 100 FITS (Ref.
8). Actuator failure rates from a third party FMEDA are λS = 172 FITS
and λD
= 343 FITS (Ref. 9). Valve failure rates from a third party
FMEDA are λS
= 0 FITS and λD
= 604 FITS (Ref. 10, full stroke). No
automatic diagnostics are available. What is the total safe and
dangerous failure rate of the final assembly? What is the STR? What
is the PFDavg if the final element assembly is removed from service
and tested/rebuilt every five years?
Solution: The solenoid valve, actuator, and valve comprise a series
system so the failure rates are added. The total is λS = 243 FITS and
λD
= 1047 FITS. The STR equals the safe failure rate: STR = 2.43-7
trips per hour. Equation 14-2 can be used to approximate the
PFDavg.
Substituting the failure rates,
PFDavg = 0.000001047 × 5 × 8760/2 = 0.023
Figure 15-9. 1oo2 Final Element Subsystem
Discrete OutputController
Discrete Output
Air Supply
Valve
Air Supply
Valve

16. 374 Control Systems Safety Evaluation and Reliability
Safety Instrumented Function (SIF) Components
An SIF consists of a process connection, sensor, power supplies, controller,
and final element. The “process to process” approach must be used to
ensure that the safety and reliability analysis includes all components,
which may include a sensor impulse line (for pressure or vacuum) and
possibly a manifold. When modeling entire SIFs (Ref. 11), all components
needed for the protection function must be modeled.
EXAMPLE 15-9
Problem: Using the failure rates of Example 15-8, what are the STR
and PFDavg of a 1oo2 final element assembly? Assume a common-
cause beta factor of 10%. No diagnostics are available. The final
element assembly is removed from service and tested/rebuilt every
five years.
Solution: The failure rates are:
λSUC = 24 FITS
λSUN
= 219 FITS
λDUC
= 105 FITS
λDUN = 942 FITS
Using a first order approximation, Equation 14-5, the PFDavg of this
system is:
PFDavg = ((0.000000942)2
× (5 × 8760) 2
)/3 + 0.000000105 × 5 ×
8760/2 = 0.0029. This is considerably better than the PFDavg of
Example 15-8.
STR = (24+219+219) ×10-9 = 0.000000462 trips per hour.
EXAMPLE 15-10
Problem: A pressure sensor is connected to a process via an
impulse line. Records indicate that the impulse line clogs up, on
average, once every twenty years. This condition is dangerous as the
protection system may not respond to a demand. An algorithm based
on high speed statistical analysis of the pressure signal (Ref. 12) can
detect 80% of the clogs. When a clog is detected it is repaired in 168
hours on average. If the impulse line is inspected and cleaned out
every five years, how will the diagnostic algorithm affect the PFDavg?
Solution: Assuming a constant failure rate for the impulse line, the
failure rate is calculated using Equation 4-18. λ = 1/(20 × 8760) =
0.0000057 failures per hour. Equation 14-2 can be used to
approximate the PFDavg. Without the diagnostic algorithm the entire
failure rate must be classified as dangerous undetected.

17. Safety Instrumented Systems 375
Exercises
15.1 A process is manned continuously and has no risk reduction mech-
anism. An accident could cause death to multiple persons. Danger-
ous conditions do build slowly and alarm mechanisms should
warn of dangerous conditions before an accident. Using a risk
graph, determine how much risk reduction is needed.
15.2 A quantitative risk assessment indicates an inherent risk cost of
$250,000 per year for an industrial process. Plant management
would like to reduce the risk cost to less than $25,000 per year.
What risk reduction factor is required? What SIL classification is
this?
15.3 What components must be considered in the analysis of an SIF?
15.4 A process connection clogs every year on average. This is a danger-
ous condition. No diagnostics can detect this failure. Assuming a
constant failure rate, what is the dangerous undetected failure
rate?
15.5 Using the failure rate of Exercise 15.4, what is the approximate
PFDavg for a three-month inspection interval in a 1oo1
architecture?
EXAMPLE 15-10 continued
Therefore, the PFDavg impulse = 0.0000057 × 5 × 8760 / 2 = 0.125.
With the diagnostic algorithm, the failure rate is divided into
dangerous detected (0.0000046 failures per hour) and dangerous
undetected (0.0000011 failures per hour). Using Equation 14-2, the
PFDavg impulse = 0.00000046 × 168 + 0.0000011 × 5 × 8760 /2 =
0.026. The diagnostics provide a considerable improvement.

18. 376 Control Systems Safety Evaluation and Reliability
Answers to Exercises
15.1 Death to multiple persons is classified as a C3 consequence. The
frequency of exposure is continuous, F2. Alarms give a possibility
of avoidance, P1. Since no protection equipment is installed the
probability of unwanted occurrence is high, W3. The risk graph
indicates SIL3. The risk reduction factor needed for an SIF would
be in the range of 1,000 to 10,000.
15.2 The necessary risk reduction factor is 250,000/25,000 = 10. This is
classified as SIL1.
15.3 SIF reliability and safety analysis should consider all components
from sensor process connection to valve process connection. Typi-
cally this includes impulse lines, manifolds, sensors, controllers,
power supplies, solenoids, air supplies, valve actuators, and valve
elements. If communications lines are required for safe shutdown
by an SIS then they must be included in the analysis.
15.4 All failures are dangerous undetected. The dangerous undetected
failure rate is 1/8760 = 0.000114155 failures per hour.
15.5 Using Equation 14-2, the approximate PFDavg is calculated as
0.125. At this high failure rate the approximation method is
expected to have some error. Use of the full equation or a Markov
based tool would eliminate the error.
References
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