Frequency Analysis

Purchase

Frequency Analysis

This material in this ebook describes risk quantification. It shows how to estimate how often incidents may occur. Topics covered include risk ranking, fault tree and event tree analysis, Monte Carlo simulations, Markov models, safeguards and Layer of Protection Analysis (LOPA). Also discussed are the sources and management of failure rate data.

The quotations, “What gets measured gets done” and “You become what you measure” are well known. This means that, if risk is to be properly understood and reduced to an acceptable level then quantification is needed.

The basic risk equation is:

RiskHazard  =  Consequence  *  Predicted Frequency............. (17.1)

This ebook discusses how a value for the Predicted Frequency term can be obtained (the distinctions between frequency, predicted frequency, probability and likelihood are explained in Chapter 1 of Process Risk and Reliability Management. Concepts covered include:

• The Pareto Principle: identifying the important few and ignoring the unimportant many;
• Fault trees;
• Event trees;
• Monte Carlo simulation;
• Markov models; and
• Layers of Protection Analysis.

The Pareto Principle

In the late nineteenth century the Italian economist and misanthrope Vilfredo Pareto (1848 – 1923) famously noted that most of the wealth in a community was held by a small proportion of the population. From this insight he developed the 80/20 rule, or the Pareto Principle, which, in the case of community wealth, meant that about 20% of any population owns about 80% of the wealth.

His principle, which has no theoretical underpinning, is widely observed to be true in many fields of human activity (Juran 1951). It is applied here to the topic of risk analysis in the process industries.

The Pareto Principle can be expressed mathematically.

log n  =  c  +  (m * log x).................................................... (2)

where n is the number of items whose value is greater than x; c and m are constants.

Examples of the principle’s applications in an industrial context include:

• 80% of a company’s sales come from 20% of its customers.
• 80% of a company’s sales are made by 20% of the sales force.
• 20% of the workers are involved in 80% of the accidents.
• 20% of the equipment items cause 80% of the facility shutdowns.
• 20% of a company’s products will account for 80% of the total product defects.
• 80% of weight loss during a diet is achieved with the first 20% of the effort.

In each of the above examples, an ‘important few’ or the ‘vital few’ have a great impact on the business, whereas the ‘unimportant many’ are much less significant. Therefore a safety manager should direct his or her program toward that minority of incident-creating workers. Spending time on the ‘unimportant many’ is not likely to have much benefit.

One commonly-held misconception to do with the Pareto Principle is that 80% of the problems can be resolved with 20% of the resources. In fact the Principle makes no statement at all as to how much effort is needed to address the contributing factors.

Table of Contents

Introduction
The Pareto Principle 
Importance Ranking 
Fault Tree Analysis 
   Gates 
      OR Gate 
      AND Gate 
      VOTING Gate
   Events 
      Top Event 
      Intermediate Events
      Base Events 
      House Event 
   Top-Down Development of a Fault Tree 
      1.  Define the Top Event 
      2. Build the Tree 
      3. Identify the Cut Sets 
      4. Eliminate Repeat Sets 
      5. Eliminate Repeat Events in a Set
      6. Eliminate Redundant Events 
      7.  Quantify the Risk 
         Mathematics of an OR Gate 
         Mathematics of an AND Gate
         Mathematics of a Voting Gate
         Cut Set Quantification 
      8.  Risk Rank 
      Event Contribution
      Important Few 
      Unimportant Many 
      Power of the AND Gate
      Importance Equalization
      Cost-Benefit Analysis
   Importance Ranking Using Cut Sets
      Birnbaum Factor Method 
      Fussell-Vesely Method 
      Perturbation Method 
   Common Cause Events 
   Fukushima-Daiichi 
   Generic Fault Trees 
      Generic Safety Fault Tree 
      Generic Reliability Fault Tree
   Discussion of the Fault Tree Method
   Qualitative Fault Tree Analysis 
Event Tree Analysis
   Quantification of an Event Tree
   Scope of Event 
   Combining Event Trees and Fault Trees
   Short Sequence of Events 
   Many Events 
   Partial Success 
Discrete Event Analysis 
   Non-Linearities and Complexities
   Conveying Statistical Uncertainty
Monte Carlo Simulation 
   Random Number Generators 
   Seed Numbers 
   Speeding the Simulation 
Markov Models 
   Top-Down / Bottom-Up Approach 
   Top-Down 
   Bottom-Up 
   Qualitative Insights 
Limitations to Quantification 
   Mathematical Understanding 
   Value-Laden Assumptions 
   Lack of Exhaustivity 
   Human Behavior 
   Data Quality 
Safeguards 
   Safeguard Level 1:  Normal Operations 
   Safeguard Level 2:  Procedural Safeguards
   Safeguard Level 3:  Safety Instrumented Systems
   Safeguard Level 4:  Mechanical Safeguards 
   Safeguard Level 5:  Passive Safeguards 
   Safeguard Level 6:  Emergency Response 
Layer of Protection Analysis 
   The LOPA Process
   Single Scenarios
   IPLs 
      Specific 
      Independent
      Dependable
      Auditable 
   Human Response
   Implementing LOPA
      Team Makeup
      Timing 
      Tools 
      Procedures and Inspections
      Risk Criteria 
Failure Rate Data 
Conditional Probability / Bayes’ Theorem
   Evaluation of Tests 
   Sequential Observations
   Combining Data Sources