Safety Instrumented Systems Verification: Practical Probabilistic Calculations

There are a number of common metrics used within the field of reliability engineering. Primary ones include reliability, unreliability, availability, unavailability, and MTTF. But, when different failure modes are considered as they are when doing SIF verification then new metrics are needed. These include PFS, PFD, PFDavg, MTTFS, and MTTFD.
In developing the applicable metrics concepts in this chapter, a single failure mode is assumed throughout. Multiple failure mode metrics are presented in a subsequent chapter.
Probability of Success This is often defined as the probability that a system will perform its intended function when needed and operated within its specified limits. The phrase at the end tells the user of the equipment that the published failure rates apply only when the system is not abused or otherwise operated outside its specified limits.
Using the rules of reliability engineering, one can calculate probability of successful operation for a particular set of circumstances. Depending on the circumstances, that probability is called "reliability" or "availability" (or on occasion, some other name).
Reliability A measure of successful operation for a specified interval of time. Reliability, R(t), is defined as "the probability that a system will perform its intended function when required to do so if operated within its specified limits for a specified operating time interval." The definition includes five important aspects.
The system's "intended function" must be known.
"When the system is required to function" must be judged.
"Satisfactory performance" must be determined.
The "specified design limits"...