Page 556 - IRSEM_Main Book

3.5 Failure Rate and Mean Time Between Failures (MTBF)

Consider a batch of N items and that, at any time to, a number to have failed. The
cumulative time T is given by

Repairable Case: T = Nt, if it's assured that each failure is replaced when it occurs.

Non-Repairable Case T = [ t +t +t …...+t +(N-k) t ]
Where, t is the occurrence of first failure, etc. Failed items are not replaced.

The observed failure rate is given by
Gama = k/T

The observed MTBF of the N items

MTBF = T/k ______(for repairable items)

MTTF = T/k ______(for non-repairable items)
The only difference between MTBF & MTTF is that the value of T will be calculated
as indicated above.

Reliability equation is as under
R(t) = e-λt (for constant λ)

4.0 Safety Integrity Level (SIL)

4.1 Functional Safety: Functional Safety is part of the overall safety which depends on the
correct functioning of a safety related system.

4.2 Safety Related System: A system is safety related if its failure can cause harm to life and
property. A safety related system performs one or more safety functions.

4.3 Safety Function: Function which is intended to achieve or maintain a safe state of the
Equipment Under Control (EUC).

4.4 Equipment Under Control (EUC): Equipment, Machinery, Apparatus or Plant used for
manufacturing, process, transportation, medical or other activities, eg: Railway
station points & signals, train, etc.

4.5 Equipment Under Control Control System (EUCCS): System which responds to input
signals from the process and or from an operator and generates output signals causing the
EUC to operate in the designed manner, eg. Interlocking system, train driver.

4.6 Safety System Diagram:

Annexure:G1: Reliability, Availability, Maintainability & Safety (RAMS) Page 499 of 535