Process engineers are often asked to evaluate the reliability of a piece of equipment or a process. The evaluation may be for quality reasons, reliability, preventative maintenance, or, more often, to evaluate process safety. Quantitative reliability methods are proven tools for predicting system reliability and quantifying potential outcomes. These methods help us to make better decisions regarding the use of public and private resources. Such methods are applied daily in government and public welfare, as well as in industries such as insurance, finance, and the chemical process industries (CPI).

Decision trees can be combined with utility functions (1) to make an overall determination of the risks and value of different alternatives in a system. In this article, we will look at applying fault and event trees as tools to predict process safety. As an example, we will look at a hypothetical heat-treating chamber where any oxygen present could produce an explosive atmosphere. The probabilities are expressed as the probability of an event during any one-hour period. The probability P of an event is a number from 0 to 1. Individual events in a sequence have a probability of E and a reliability of (I - E) = E.

The tree elements are computed using Bayes' theorem, which was proposed by Thomas Bayes in about 1760. This theorem allows us to compute conditional probabilities for sequences of events. The branches of the tree are treated as reliabilities

Each branch of the tree connects at a logic point describing the physical system with a logical AND or a logical OR gate. With a logical AND, the combined probability

Combining a fault and event tree can be useful in quantifying and visualizing potential hazards. Various root causes can be traced through the tree to the branch bearing the outcome. Figure 3, as noted before, illustrates the combined system for the explosion hazard due to the loss of purge gas. The results are summarized in Table 1.

Table 1. Predicted outcomes for the explosion hazards in the heat-treating chamber. |

Event |
Probability |
Odds |

Normal Operation |
9.999E-01 | 1 in 1.000135 |

Oxygen High (alone) |
1.345E-04 | 1 in 7,435 |

Oxygen High with no explosion |
1.345E-04 | 1 in 7,434 |

Oxygen High with explosion |
6.726E-09 | 1 in 148,685,875 |

A major challenge in quantitative risk analysis is in finding representative data. AIChE's Center for Chemical Process Safety (CCPS) has published several references (see "Further Reading") which are an excellent starting point for obtaining probabilities for various types of events.

Finally, the combined fault and event tree can be extended beyond process safety analysis to aid in decision making for various business decisions, marketing plans, and public policy decisions, where one or more varied conditions might lead to many different outcomes through one or two main channels.

CEP |

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