<P> Rapid technological change, increasing scale of industrial complexes, increased system integration, market competition, and other factors have been shown to increase societal risk in the past few decades . As such, risk assessments become increasingly critical in mitigating accidents, improving safety, and improving outcomes . Risk assessment consists of an objective evaluation of risk in which assumptions and uncertainties are clearly considered and presented . This involves identification of risk (what can happen and why), the potential consequences, the probability of occurrence, the tolerability or acceptability of the risk, and ways to mitigate or reduce probability of the risk . Optimally, it also involves documentation of the risk assessment and its findings, implementation of mitigation methods, and review of the assessment (or risk management plan), coupled with updates when necessary . Sometimes risks can be deemed acceptable, meaning the risk "is understood and tolerated...usually because the cost or difficulty of implementing an effective countermeasure for the associated vulnerability exceeds the expectation of loss ." </P> <P> Part of the difficulty in managing risk is that both the quantities by which risk assessment is concerned--potential loss and probability of occurrence--can be very difficult to measure . The chance of error in measuring these two concepts is high . Risk with a large potential loss and a low probability of occurrence is often treated differently from one with a low potential loss and a high likelihood of occurrence . In theory, both are of near equal priority, but in practice it can be very difficult to manage when faced with the scarcity of resources--especially time--in which to conduct the risk management process . </P> <P> To see the risk management process expressed mathematically, one can define total risk as the sum over individual risks, R i (\ displaystyle R_ (i)), which can be computed as the product of potential losses, L i (\ displaystyle L_ (i)), and their probabilities, p (L i) (\ displaystyle p (L_ (i))): </P> <Dl> <Dd> R i = L i p (L i) (\ displaystyle R_ (i) = L_ (i) p (L_ (i)) \, \!) </Dd> <Dd> R t o t a l = ∑ i L i p (L i) (\ displaystyle R_ (total) = \ sum _ (i) L_ (i) p (L_ (i)) \, \!) </Dd> </Dl>

In order to evaluate risk management may also set qualitative risk classes