STATISTICAL TOPICS AND ANALYSIS IN RISK ASSESSMENT - Risk Management Applications in Pharmaceutical and Biopharmaceutical Manufacturing - page 76

and

47

P = 1 − ( 1 − 0.05 )

So

P = 0.91

In this case, the probability that at least one or more t -tests will fail by random
chance alone is 91%.

4.7 RISK

Every manufacturing process and product has some risk and probability of failure.
Zero risk 100% of the time will cost an infinite amount of time and money and
is effectively unattainable as some risk (called residual risk ), although small, is
always present even after mitigation efforts are completed.
As explained elsewhere in this topic, risk can be the estimated probability
(also known as occurrence or likelihood) of an event times a severity estimate.

Risk (R) = P( or O) × S

In either case, probability is a root concept for risk. Risk cannot be understood
or estimated without an understanding of probability.

4.7.1 Venn Diagram

A good way to visualize the dimensions of probability described earlier is to look
at the entire population for a given process or product as shown in Figure 4.1.
Within that product population space, there are three subsets. Using the language
of Section E of ISO 14971, [4] two of the subsets, events, are of interest. One is
the area within the process or product space where Hazards have occurred, the
gray area or H. The second is the space defined by where Failure and thus harm
to the patient can occur, the blue area or F. The third is the intersection of gray
andblueorF&H.
So, when looking at assessing the occurrence or likelihood of an event, we
have to look at how often a given hazardous, H, situation happens (it may be
quite common) as well as how often these “happenings” lead to failure, F, and
thus harm to the patient. A basic discussion on conditional and joint probabilities
is important in understanding the topic.

4.7.1.1 General Rule for Addition For the two events in Figure 4.1, the prob-
ability of a hazard OR the probability of a failure is the sum of the two minus
the intersection of the two as in the formula.

P (Hazard or Failure) = P (Hazard) + P (Failure) − P (Hazard and Failure)