Calculations
About the Required Probability of Failure
The required probability of failure is a number representing the probability that an instrumented function will fail in a dangerous scenario. This value is represented as a probability value (e.g., .001), and is an indicator of whether the instrumented function is meeting its requirements to mitigate risk. The required probability of failure value is based on the following values stored in the Instrumented Function:
- The SIL value, which is stored in the Selected SIL Level field. The higher the SIL value for an instrumented function, the lower the probability that the instrumented function will fail.
- The method used to determine the SIL value, which is stored in the SIL Assessment Method field (e.g., Risk Matrix).
- The demand rate, which is stored in the SIL Mode field and represents the estimated probability that a dangerous condition will exist where the instrumented function is required to take the process to its safe state. For instance, if the demand rate is more than once a year, the hazard rate must not be higher than the failure rate. In this case, the SIL mode is high demand or continuous.
The following sections describe how the required probability of failure is calculated based on the SIL value, assessment method, and demand rate.
SIL Mode: Low Demand
In an Instrumented Function, when the value in the SIL Mode field is Low Demand, the APM system assumes that the demand rate of the instrumented function is less frequent than once per year. In these cases, the failure rate is measured by the average probability of failure on demand (PFD Avg).
| SIL Value | Required Probability of Failure (PFD Avg) |
|---|---|
| 4 | ≥ 10-5 to < 10-4 |
| 3 | ≥ 10-4 to < 10-3 |
| 2 | ≥ 10-3 to < 10-2 |
| 1 | ≥ 10-2 to < 10-1 |
SIL Mode: High Demand or Continuous
In an Instrumented Function, when the value in the SIL Mode field is High Demand or Continuous, the APM system assumes that the demand rate of the instrumented function is more frequent than once per year. In this case, the failure rate is measured by the average probability of dangerous failures per hour (PFH). The required probability of failure is defined by an industry standard that is associated with the SIL.
The required probability of failure is defined by the industry standard that is associated with each SIL. The following table contains the standard PFD Avg values for each SIL. The following table contains the standard PFH values for each SIL.
| SIL Value | Required Probability of Failure (PFH) |
|---|---|
| 4 | ≥ 10-9 to < 10-8 |
| 3 | ≥ 10-8 to < 10-7 |
| 2 | ≥ 10-7 to < 10-6 |
| 1 | ≥ 10-6 to < 10-5 |
SIL Assessment Method: Internal
If you use a Risk Matrix (internal) in SIL assessment, the value in the Required Probability of Failure field is disabled and populated with the lowest (i.e., the most conservative) value as the targeted probability. For example, if the SIL value is 2, the Required Probability of Failure field will be populated automatically with 1E-07 (i.e., 10-7) in case of a Low Demand SIL mode.
If you use an Layer of Protection Analysis (internal) in SIL assessment, the value in the Required Probability of Failure field is disabled and populated with the difference between the values in the Mitigated Consequence Frequency field and the Required Mitigated Consequence Frequency field in the LOPA.
SIL Assessment Method: External
If you use any external SIL Assessment method, the Required Probability of Failure field will be enabled, and you can enter the probability value manually. In this case:
- If you modify the value in the Selected SIL Level field, the value in the Required Probability of Failure field will be updated automatically to fall within the correct range of values for that level.
- If you type a value that does not fall within the range defined in the table, an error message will appear.
- If you type a value in the Required Probability of Failure field without first typing a value in the Selected SIL Level field, an error message will appear.
Risk Reduction Factor
Risk reduction factor can also be used to indicate the probability of failure for an instrumented function when the SIL mode is low demand. The risk reduction factor is the inverse of the required probability of failure, which is represented in years. For example, a required probability of failure value of .001 would equal a risk reduction factor of 1,000, meaning that the instrumented function would fail during a dangerous scenario about once every 1,000 years.
Calculating Risk Reduction Factor
The required probability of failure is defined by the industry standard that is associated with each SIL. The following table contains the standard PFD Avg values for each SIL.
| SIL Value | Required Probability of Failure (PFD Avg) | Target Risk Reduction Factor |
|---|---|---|
| 4 | ≥ 10-5 to < 10-4 | > 10,000 to ≤ 100,000 |
| 3 | ≥ 10-4 to < 10-3 | > 1,000 to ≤ 10,000 |
| 2 | ≥ 10-3 to < 10-2 | > 100 to ≤ 1,000 |
| 1 | ≥ 10-2 to < 10-1 | > 10 to ≤ 100 |
If you use an internal SIL Assessment method, the Risk Reduction Factor field is disabled, and populated with the inverse of the value in the Required Probability of Failure field.
If you use an external SIL Assessment method, the Risk Reduction Factor field is enabled and populated with the inverse of the value in the Required Probability of Failure field. If you modify the value in the Risk Reduction Factor field, the Required Probability of Failure field is populated with the inverse of the value in the Risk Reduction Factor field.