Risk Reduction Cost vs. Frequency Case Study

A Hazard and Operability (HAZOP) study identified a major loss scenario which could result in a total cost of $100,000,000 including plant replacement, product loss, business interruption, litigation costs, and subsequent environmental cleanup. Georges Melhem, Ph.D., FAIChE, presents a risk reduction case study.

The major loss scenario occurs with a frequency of λ per year. The proposed risk reduction cost is $1,000,000. After the mitigation measure is implemented, the scenario frequency becomes βλ, where β (< 1) is the frequency reduction multiplier [1]. We assume that the remaining plant life, N, is 30 years and the cost of money, i, is 8%. If the benefit (annual expected loss reduction) outweighs the risk reduction cost, then the risk reduction measure is justified.

Figure 1: Optimal risk reduction

To determine if the risk reduction measure is justified, we need to compare the annualized expected benefit, L₀ − L_n to the annualized cost of risk reduction, A:

If we expect a risk reduction factor of 10, β = 0.1, then the scenario frequency λ must be greater then 9.869 × 10−4/yr in order for the risk reduction measure to be cost effective.

A more detailed cost-benefit analysis can be performed by considering the Net Present Value (NPV) of all costs associated with the major loss scenario. If the risk reduction measure is not implemented, the annual risk accrual and NPV will be for the jth year:

where Q is the plant replacement cost (property damage) following the major loss scenario or product loss cost, or business interruption cost, or environmental cleanup cost, or litigation cost, or all of the above, x is annual increase in replacement cost, say 5%, y is the annual increase in λ as the plant is aging, say 5%.

If we consider the NPV concept, the major loss scenario threshold frequency would get smaller:

If we expect a risk reduction factor of 10, β = 0.1, then the scenario frequency λ must be greater than 2.7388 × 10−4 /yr in order for the risk reduction measure to be cost effective.

If we wanted to obtain a confidence level over the previous estimates, we can use Monte Carlo simulation.

1. Assume the interest rate follows a normal distribution with a mean of 8% and a standard deviation of 4%
2. Generate a random number from 0 to 1 (probability), and obtain the corresponding interest rate from the probability distribution
3. Plug the interest rate in the previous NPV and calculate the value of scenario frequency
4. Repeat the process 1000 times and store the results for λ
5. Count the number of times out of 1000 where λ exceeds 0.0001
6. Divide by 1000 to get the probability that the risk reduction investment will make sense if the scenario frequency is greater than 0.0001

In this approach, we have avoided attempting to evaluate human life [2] in financial terms because:

• It implies an acceptance of human fatality,
• It leads to placing a value on human life with potential ethical issues arising if different values are assigned at different locations,
• It suggests that fatalities are regarded as part of the natural cost of doing business.

Projects/expenditures aimed toward process modifications that reduce the chance of injury or fatality will also significantly lessen the potential for financial loss. This cost/benefit methodology has been developed to identify such projects to emphasize the proposition that safe operation is good business.

Hazard Identification

A Process Hazard Analysis (PHA) is an organized and systematic effort to identify and analyze the significance of potential hazards associated with the processing or handling of highly hazardous materials. The HAZOP methodology combines creativity with a systematic approach for examining hazardous situations which helps improve the thoroughness of a study. Hazard scenarios are identified using deviation guidewords in combination with process parameters such as flow, pressure, temperature, etc.

Hazard identification activities are routinely led by a senior ioKinetic engineer experienced with the methodology to be used. Wherever possible, the lead engineer will also have prior experience with operations similar to those being studied. Our engineers have extensive expertise in performing Process Hazard Analysis (PHA) studies in nearly all sectors of the process and processing industries.

Chemical Reactivity Assessment

The ioKinetic team can perform chemical reactivity assessments to evaluate chemical reactivity hazards present in the processing of reactive materials. This data is often used to meet PSM regulatory requirements, process specifications, and complete pressure relief and flare system design. Safe design and operation of chemical processes requires a thorough understanding of chemical reactivity and thermokinetics.

Prior to beginning a HAZOP study, up-to-date and accurate information on the materials is needed, such as:

• Toxicity information
• Permissible exposure limits
• Physical, reactivity, and corrosivity data
• Thermal and chemical stability data
• Hazardous effects of inadvertent mixing

Hazard Analysis Tools

PSMPro™ software is a powerful suite of time-saving tools for conducting quality risk analysis. PSMPro™ simplifies the recording of findings and tracking follow-up from PHAs and DHAs. It also eliminates the need for any special application software when working with the results. The pre-populated templates are available in English, Spanish, and Portuguese. PSMPro™ delivers professional, branded reports, and make it easier to comply with codes and standards, such as OSHA PSM, EPA RMP, and NFPA.

We Can Help

ioKinetic has reduced process safety risk, maintained compliance and substantially increased peace of mind for our clients worldwide. To learn more about how we can help you manage risk, contact us today or call us at 1-844-ioKinetic.

References

[1] R. Goyal. Understand quantitative risk assessment - Part i. Hydrocarbon Processing, pages 105–108, December 1994.

[2] Statistical value of a human life [3] has been set by the US EPA at $6.3 million, US FDA at $6.5 million, and the US DOT at ~ $9.1 million.

[3] L. Nara. Spotlight on safety - What is safety worth? Chemical Engineering Progress, page 57, August 2017.