An Introduction to RAMSRC Sharma Consultant (O&M)Louis Berger Consulting Pvt. Ltd.Hyderabad

RAMS:

RAMS will provide Indicators as to how Sturdy and Reliable a System Design can potentially be.

It can help to identify which Parts of a System are likely to have the major impacts on System Level Failure, and also which Failure Modes to expect and which Risks they pose to the Users.

RAMS can assist in the Planning of Cost-effective Maintenance and Replacement Operations.

RAMS can provide Indicators for avoiding of the Hazards / Accidents. Risk Assessment would help to improve Safety Levels. RAMS Analysis has been increasingly used in the Assessment of Safety Integrity Levels (SIL).

Assessment of how good a Design Enhancement, like Implementation of a new Part or Redundancy shall work out in a Real Life Situation.

RAMS and the Life Cycle of a Product

Goals Achieved?Specify Reliability GoalsSystem Effectiveness & Life-cycle CostsSystem Safety Analysis (FTA)Allocate Reliability to ComponentsImplement Design MethodsFailure Analysis FMEA/FMECAReady for ProductionSafety Goals Achieved?NoYesYesNoDesign Process

Systems / Components experience a decreasing Failure Rate early in their Lifetime (Called Burn-in Period or Infant Mortality Period).

In the mid and most part of their Lifetime, the Useful Life, the Systems / Components experience a Constant Failure Rate.

Close to the end of the Lifetime, the Failures increase due to wear out of Parts and other ageing related problems.

The Bathtub Distribution may be seen as the sum or juxtaposition of three different Distributions.Early FailuresWear Out FailuresRandom FailuresFailure RateTimeUseful LifeBurn-in PeriodWear-out

Cost vs Reliability Curve

Availability:

Ability of a certain Entity to be in the State of providing a Certain Function under Certain Conditions, at a given Time Instant. It can be measured by the Probability of an entity E not being failed at a time instant t.

A(t) = Probability [Entity E not failed at time t]

It can be expressed as the Ratio of UP Time over Total Working Time:

MTR = MTTR + MDTM + MSDT,

Where,

MDTM is Mean Delay in Maintenance and MSDT is the Mean Delay in Supply of Resources (Spares, Tools & other Logistics.

Cost vs Availability Curve

Repair rate:

Limit of the Ratio of the Conditional Probability that the Corrective Maintenance Action ends in a Time Interval, [t, t + t], when t tends to zero, given that the Entity is Faulty at time t=0.

Repair Rate is represented by (t).

Maintainability:

Ability of an Entity to be restored into or be kept in a Condition or State that enables it to perform a Required Function, when Maintenance Operations are performed under Given Conditions and are carried using Stated Procedures and Resources. It is, thus, the Ability of an Entity to be repaired in a given time.

Maintainability is normally measured by the Probability that the Maintenance Procedure of a certain Entity E performed under Certain Conditions is finished at time t given that the Entity Failed at time t = 0.

M(t) = Prob [Maintenance of E is completed by time t, when E fails at time t = 0.

Maintainability Features

Safety Integrity Level SIL:

SIL is an Attribute of the Safety Functions. One of the 4 Levels SIL-1 to 4 can be assigned to a Function, depending on its Safety Requirements (Tolerable Hazard Rate THR).

THR provides the Failure Target for Random Failures (Examples: IC Chip Burnt, Hardware Damaged due to Lightning etc.).

THR Table in CENELEC 50129 provides SIL based on the THR. CENELEC Standard 50129 also provides for a Set of Design Techniques corresponding to the SIL to tackle the Systematic Failures (Examples: HW Design Faults, SW Coding Faults etc.).

THRSIL10-9 < THR < 10-8410-8 < THR < 10-7310-7 < THR < 10-6210-6 < THR < 10-51

If the Functional Requirements are to achieve a THR of less than 10-9, other means such as combination of several Systems to be used.

MTBF (Mean Time Between Failures):

It is the Expected Value for Operating Time between the Occurrences of Two Failures. For Constant Failure Rates, the Function (t) that returns the Time Elapsed between two Failures becomes a Constant Function as well and MTBF equals 1/.

MTTF (Mean Time to Failure):

MTBF of the First Failure.

MTTR (Mean Time to Repair):

Expected Value of all the Repair Times of a Component.

Reliability:

Ability of an Entity to perform a Required Function under Given Conditions for a given Time Interval. In other words, an Entity is Reliable if it hasnt Failed, i. e. stayed within the Specifications over a Time Interval.

R(t) = Prob [Entity E not failed over Time (0,t)], the Entity is assumed to be operating at time t = 0.

Feasible Design Region in terms of MTBF & MTTRAv.MTTR

Hazard:

Situation, which has the Potential to cause Damage to the System, Damage to its Surrounding Environment, Injuries or Loss of Human Lives.

Hazard Analysis:

An Analysis comprising Hazard Identification & Causal Analysis.

Hazard Log:

The Document in which Hazards Identified, Decisions Made, Solutions Adopted and their Implementation Status are recorded.

Safety:

Freedom from Unacceptable Risk of Harm.

Safety Case:

The Documented Demonstration that the Product, System or Process complies with the appropriate Safety Requirements.

Risk:

Result of the Crossing of two Criteria - Probable Frequency of Occurrence and Degree of Severity of the Impact of a Hazard.

Frequency of Occurrence of a Hazardous EventRisk LevelsSeverity Levels of Hazard ConsequencesInsignificantMarginalCriticalCatastrophicFrequentUndesirableIntolerableIntolerableIntolerableProbableTolerableUndesirableIntolerableIntolerableOccasionalTolerableUndesirableUndesirableIntolerableRemoteNegligibleTolerableUndesirableUndesirableImprobableNegligibleNegligibleTolerableTolerableIncredibleNegligibleNegligibleNegligibleNegligible

Risk EvaluationRisk Reduction / ControlIntolerableShall be eliminatedUndesirableShall only be Acceptable when Risk Reduction is Impracticable and with the Agreement of railway Authority.TolerableAcceptable with Adequate Control and the Agreement of Railway Authority.NegligibleAcceptable without any Agreement.

Derating: Operating the System below its Rated Stress LevelChoice of Technology (State-of-Art)Reducing the Complexity of the System (will reduce the )Decreasing Down Time through Good Maintainability Design -FLMD & SLMD + Attention to Environmental Conditions (Earthing & Surge Protection) Methods to improve Reliability & Availablity of a Product or SystemRedundancy or Duplicity for Critical Sub-systems

Reliability Function & MTTF:

Reliability is defined as the Probability that a System / Component will function over some Time Period t.

R(t) = Pr {T t }, whereFor a given value of t, R(t) is the Probability that the Time to Failure is t.

If T is the Time to Failure of the System then,

F(t) = 1 - R(t) = Pr {T < t }, where If f(t) is the Probability Density Function (PDF) (describing the Shape of Failure Distribution Function), R(t)tExponential Reliability FunctionF(t)tExponential Failure Function

For an Exponential Reliability Function, with as Failure Rate,MTTF is Inverse of the Failure Rate .

Probability Concepts:

If an Experiment can result in any one of N different equally likely outcomes, and if exactly n of these outcomes correspond to event A, then the Probability of event A is P(A) = n/N.

Probability of an Event A, the P(A), obeys following Postulates:Probability of A NOT occurring is: Joint Probability that both A & B occur is:

P(AB) = P(A).P(B)

Probability that A or B occur is:

P(AUB) = P(A) + P(B)

Probability Concepts:

Two Events are independent, if occurrence of A does NOT depend on the occurrence of B. Joint Probability of occurrence of two Independent Events A & B is:

P(AB) = P(A).P(B)

(The Joint Probability the Probability of Intersection is equal to the Product of their Probabilities)Two Events are Mutually Exclusive if Occurrence of one precludes the Occurrence of the other i.e. both cannot occur simultaneously.

If A & B are Mutually Exclusive:

P(AUB) = P(A) + P(B) = 1P(AB) = P() = 0 (Both can not occur simultaneously)Mutually ExclusiveIf two Events A & B are independent, P(A|B) = P(A) & P(B|A = P(B))

Bernoulli Distribution (for 2 Mutually Exclusive Outcomes):

Random Variable can take only two values 0 & 1.If P(x=0) = P(0) = p, then P(x=a) = P(1) = q = 1-p & p + q =1

f(x) = px.q1-x, for x = 0,1Mean = pVariance 2 = p.q Binomial Distribution (for 2 Mutually Exclusive Outcomes):

If Trials are repeated n times then the Probability for x number of Successes in n Trials:p(x) =px.(1 p)n-x, where=Mean = npVariance 2 = np.(1-p)

For p = 0.01 (A Component having 1 chance in 100 of failing),Mean Number of Failures = 5.(0.01) = 0.05Variance 2 = 0.05.(1-0.01) = 0.0495

Exponential Distribution:

Failures due to completely Random in nature follow this Distribution.

PDF (Probability Distribution Function) is:

f(t) = .e-t, for x 0, andf(t) = 0, for t = 0R(t) = e -t Also, R(MTTF) = e(MTTF/MTTF) = e-1 = 0.368

Above would mean that a Component, having Exponential Failure Distribution has a slightly better than Chance of surviving to its MTTF. Expressing the same in other way, following this Distribution, 63.2% of Components would have failed by MTTF.(variability of Failure Time increases as the Reliability increases)R(t)t123Exponential Reliability Function

Poisson Distribution:

Poisson Distribution is Discrete Distribution. It is applicable for Constant Failure Rate. If a Component having a Constant Failure Rate is immediately repaired or replaced, the number of Failures observed over a Time t has a Poisson Distribution.

If is the Failure Rate,An Example:

If x is a Discrete Random Variable representing number of Failures of a Restorable System over a one year period. If x has a Poisson Distribution with a Mean of = 2 Failures per year, the Probability of no more than one Failure a year shall be:

Parameters & 2 are the Mean and Variance of the Distribution. The Distribution is Symmetrical about its Mean with the spread of Distribution determined by the Standard Deviation .

Mode and Median are coincident with the Mean.

About 68% of Values drawn from anormal distributionare within one Standard Deviation away from the Mean, about 95% of the Values lie within two Standard Deviations, and about 99.7% are within three Standard Deviations. This fact is known as the 68-95-99.7 Rule, or the 3-sigma RuleNormal Distribution (Contd.):

Non Series Parallel System:Bridge NetworkPath / Tie Set Methods;

Tie Sets of above Bridge Network: {1,3} {2,4} {1,4,5}Above Tie Sets reveal that System will work if 1 & 3 work or 2 & 4 work or 1, 5 & 4 work.

Cut Set Method:

Cut Sets of above Bridge Network: {1,2} {3,4}System shall NOT function if Components of Cut Sets fail simultaneously.

For working out System Reliability, we need to work out the probabilities of either Tie Sets or Cut Sets.

K out of M System:

At least K of the Sub-systems or must function for System Success. M-K-1 or more Failures will result in System Failure.

A System comprising Components in a combined Series-Parallel Relationship

Failure Rate:

It is the Transition Function between a Working State and a Failed State of a Component, Sub-system or System. It can be analytically expressed as the Probability of a Failure to occur in a Time Interval given that the Component was working up until then. Being a Transition Function, it deals with Short Time Intervals. Transition States for a 2-Component System in a Redundant Configuration.

Rate Diagram for a 2-component SystemFor a 2-Component System in Redundant Configuration, only State 4 shall result in a Failure:

StateComponent 1Component 21OperatingOperating2FailedOperating3OperatingFailed4FailedFailed

Thanks for Kind Attention