STATISTICAL TOPICS AND ANALYSIS IN RISK ASSESSMENT - Risk Management Applications in Pharmaceutical and Biopharmaceutical Manufacturing - page 79

H F

Subset iii- Failure, F

Subset : ii Joint Probability:
Intersection of Hazard
and the Failure, F & H .

Subset i - Hazard, H

Set 1 -
Population

Figure 4.3 Joint probability. ( See insert for color representation of the figure .)
Joint probability refers to the occurrence of two (or more) events happening
and we use the multiplication rule shown to define it.

P ( ) = P ( | ) P ( )

Failure & Hazard Failure Hazard Hazard

It is just a restatement of the equation for conditional probability. Where
the joint probability, P (Failure and Hazard) , of the failure is equal to the pro-
portion of the number of times the failure has occurred within the hazard, P
(Failure | Hazard), multiplied by the proportion of the number of times the hazard,
P (Hazard), has occurred within the population.
Conceptually, it is simply the number of joint occurrences of the hazard and
the harm in reference to the entire population as shown in Figure 4.3.

4.8 STATISTICAL RISK

In statistical literature, risk is often discussed as a simple probability. Statisti-
cians differentiate between two types. A Type I (one) error or alpha level is the
probability of rejecting a hypothesis when it is true. This is the producer's risk.
A Type II (two) error or beta level is the probability of accepting a hypothesis
when it is false. This is the consumer's risk.
These probabilities can be used to calculate risk for defined models. For a
further introduction to probability, see a statistical textbook such as Introduction
to the Practice of Statistics , Moore and McCabe [5]. For a good (and humorous)
overview of basic probability, see The Cartoon Guide to Statistics , Gonick and
Smith [6].

4.9 RARE EVENTS

“If anything can go wrong, it will.”

—Murphy's Law