class 07- techniques to evaluate systems reliability

7/30/2019 Class 07- Techniques to Evaluate Systems Reliability

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Reliability

The growth in unit sizes of equipment in most industries with the

result that the consequence of failure has become either muchmore expensive, as in the case of low availability or potentiallycatastrophic makes the following more important:

Prediction of the expected life of plant and its major parts.

Prediction of the availability of plant

Prediction of the expected maintenance load

Prediction of the support system resources needed for effectiveoperation

These predictions can only result from careful consideration ofreliability and maintainability factors at the design stage.

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Reliability

In reliability analysis of engineering systems it is often assumed

that the hazard or time- dependent failure rate of items followsthe shape of a bathtub with three main phases.

The burn-in phase (known also as infant mortality, break-in ,debugging):

During this phase the hazard rate decrease and the failure occu

due to causes such as:

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Incomplete final testPoor test specificationsIncorrect use procedures

Wrong handling or

packaging

Over-stressed partsPoor quality control

Poor technical

representative training

Incorrect installation or

setup

Inadequate materials

Power surgesPoor manufacturing

processes or tooling

Marginal parts


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The useful life phase:

During this phase the hazard rate is constant and the failuresoccur randomly or unpredictably. Some of the causes of thefailure include:

A. Insufficient design margins

B. Incorrect use environmentsC. Undetectable defects

D. Human error and abuse

E. Unavoidable failures

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The wear-out phase (begins when the item passes its useful

life phase):

During this phase the hazard rate increases. Some of thecauses of the failure include:

A. Wear due to aging.

B. Inadequate or improper preventive maintenance C. Limited-life components

C. Wear-out due to friction, misalignments, corrosion and cree

D. Incorrect overhaul practices.

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Reliability

The whole-life of failure probability for the generality of

components is obtained by drawing the three possible (t)

However, the following will vary by orders magnitude from onesort of item to another:

I. The absolute levels of(t)

II. The time scale involved

III. The relative lengths of phases I, II, and III

Some times one or two of the phases could be effectivelyabsent.

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Reliability

Estimates of the parameters of the whole-life failure probability

profile of the constituent components are an essentialrequirement for the prediction of system reliability.

Additional information, such as repair-time distribution, thenleads to estimates of availability, maintainability, and the level

(and cost) of corrective and preventive maintenance.

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System Reliability

Reliability Prediction for Complex Systems (plants or equipment

To predict the reliability of complex plant the following should beperformed:

1. Regard the large and complex system (plant) as a hierarchyof units and items (equipment) ranked according to theirfunction and replaceability.

2. At each functional level, the way in which the units anditems (equipment) in this level is connected is determine

(The equipment in general could be connected in series, inparallel or in some combination of either)

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System Reliability

3. The appropriate measure of reliability is calculated for each

unit and item (in this analysis The appropriate measure ofreliability is the failure survival .

4. The analysis starts from the component level upwards andat the end of the analysis the survival probability of the

system is calculated.

5. All the component mean failure rates are calculated. Theyare either being known or susceptible to estimation.

6. At each level the survival probability calculation takes thefunctional configuration into account.


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7. The result of the system can be used in the

selection of design or redesign alternatives, in thecalculation of plant availability, or in the prediction ofmaintenance work load.


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System Reliability

A few important prerequisites are given for application of the

Boolean theory: The system must be non-repairable, that is, the first

system failure ends the systems lifetime. Thus, forrepairable systems it is only possible to calculate thereliability up to the first system failure.

The system elements must be either in a functional orfailed state of condition.

The system elements are independent, that is, thefailure behaviour of a component is not influenced by thefailure behaviour of another component.


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System ReliabilityIndustrial Engineering

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Series and Parallel System Reliability

Series-Connected Components

For a system of series-connected components (independentand non identical), survival probability of the system is:

And the system reliability is:

Since survival probabilities must always be less than 100%, itfollows that for the system must be less than that of anyindividual component.


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If the times-to-failure of the components behave according to th

exponential p.d.f, then the overall p.d.f of times-to-failure is alsoexponential:

In addition, for exponentially distributed times to failure of unit ,the unit reliability is:


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And the series system reliability at time t is:

The mean time to failure in this case is:

The hazard rate of the series system is :


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Parallel-Connected Components

A system with components connected in parallel, fails if all thecomponents in this system fail. (at least one of the units mustwork normally for system success)

If the failure behaviour of any component in the system is quiteuninfluenced by that of the others (failure probabilities arestatistically independent), the failure probability that allcomponents will fail before time has elapsed is given by theproduct of the separate failure probabilities,


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For a system with n parallel-connected components, the failure

probability of the system:

And the system survival probability is:


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This means that system reliability, in this case is:

Since survival probabilities cannot be grater than 100%, itfollows that the survival probability for the system mustbe grater than that of either of its components.

If the times-to-failure of the components behave according to thexponential p.d.f, then the overall p.d.f of times-to-failure is not asimple exponential. For example, if the system compose of twocomponent, then the system times-to-failure p.d.f :


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For exponentially distribution times to failure of unit , the paralle

system reliability is:

And for identical units ( ) the reliability of the parallel

system simplifies to:


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And the mean time to failure for the identical unit parallel system

is:

The mean time to failure in this case:


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The advantages of connecting equipment in parallel are:

1. To improve reliability of the system by making some of theequipment redundant to the other.

2. Extensive preventive maintenance can be pursued with noloss in plant availability since the separate parallel units canbe isolated.

3. In the event of failure corrective maintenance can bearranged under less pressure from production or fromcompeting maintenance tasks.

In the case of very high reliability units, there are only very

marginal increments in reliability to be gained by installingredundant capacity unless the safety factors become evident.


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Combination of serial and parallel structures:


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Convert to equivalent series system

A B

C

C

D

RA RB RCRD

RC

A B C D

RA RB RD

RC = 1 (1-RC)(1-RC)


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Example


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Example


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S i d P ll l S t R li bilit


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Example


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Example

A system composes of three components. These components have

constant failure rates of 0.0004, 0.0005, 0.0003 failures per hour. Thesystem will stop working, if any one of its components fails. Calculatethe following:

1. The reliability of the system at 2500 hour running time?

2. The system hazard rate?

3. Mean time to failure of the system?


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Example

Another system composes of four items and each one of these items

has constant failure rate of 0.0008 failures per hour. These items whenthey work the system will work. However, when any one of the system'sitems fails, the whole system will come to a complete halt. Calculate thfollowing:

1. The reliability of the system at 2000 hour running time?

2. The system hazard rate?

3. Mean time to failure of the system?


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Example

A machine has two independent cutting parts. Any one of these cutting

parts is sufficient to operate the machine. The hazard rates for the twoparts of this machine are constant and they are 0.001 and 0.0015failures per hour. Calculate:

1.The survival probability of the machine at 300 hour of running time?

2.The mean time to failure for this machine?


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class 07- techniques to evaluate systems reliability

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