RJS Relibility PPT-1
RJS Relibility PPT-1
RJS Relibility PPT-1
These two measures are the mirror image of each other (Refer Figure
below). The reliability will start at 1 and decay to approach 0 over time.
The cumulative distribution of failure will start at 0 (no failures) and
approach 1 as all the items fail over time. The slope of the reliability
curve at any time t is the failure rate at that point in time. These measures
give the overall reliability or failure at time t.
Probability density function
We wish to have an idea of the probability of an item failing in a
given unit time period. This is termed the “probability density
function” and is given by
The failure or hazard rate gives the failure density over a period of
time as with the “probability density function”, but is based on the
current population. This gives a much better indication of the
changing reliability of a system over time.
BATH TUB CURVE
Most products go through three distinct phases from product
inception to wear out. Figure below shows a typical life cycle curve
for which the failure rate is plotted as function of time.
Infancy/ Green / Debugging / Burn-in-period: Many components
fail very soon after they are put into service. Failures within this
period are caused by defects and poor design that cause an item to
be legitimately bad. These are called infant mortality failures and
the failure rate in this period is relatively high. Good system
vendors will perform an operation called "burn in" where they put
together and test a system for several days to try to weed out these
types of problems so the customer doesn't see them.
Chance failure/ Normal Operating Life: If a component does not
fail within its infancy, it will generally tend to remain trouble-free
over its operating lifetime. The failure rate during this period is
typically quite low. This phase, in which the failure rate is constant,
typically represents the useful life of the product.
Wear out/ Ageing: After a component reaches a certain age, it
enters the period where it begins to wear out, and failures start to
increase. The period where failures start to increase is called the
wear out phase of component life.
Reliability Determination
In the adult or mature phase the failure rate of a component or system
is constant. Under such conditions the time to failure follows an
exponential law, and the probability density function of exponential
distribution is as given below:
Where ? denotes the failure rate. The Mean time to failure MTTF for
the exponential distribution is:
MTTF = 1 / ?
If the failure rate is constant, the MTTF is the reciprocal of the failure
rate. For repairable system it is also equal to MTBF. The reliability at
time t, R(t), is the probability of the product lasting up to at least time
t. It is given by
SYSTEM RELIABILITY
Series System: When components are in series and each component
has a reliability R i . If one component fails, the system fails.
R AB = R1 x R2 x R3
If R1 = R2 = R3 = 0.95
Overall reliability is R AB =1 - (1 - R 1 ) (1 - R 2)
For items which are repaired when they fail, reliability is the
probability that failure will not occur in the period of interest,
when more than one failure can occur. It can also be expressed as
the failure rate or the rate of occurrence of failures (ROCOF).
However, the failure rate expresses the instantaneous probability
of failure per unit time, when several failures can occur in a time
continuum. It is unfortunate that the expression failure rate has
been applied loosely in the past to non-repairable items. What is
really meant is that, in a repairable system which contains a part
type, the part will contribute by that amount to the system failure
rate. The part, being non-repairable, cannot have a failure rate.
This distinction does not always have practical significance, but it
can, as will be shown later. The expression ROCOF is sometimes
used to stress this point.
Cont.
1. Define (a) failure rate, and (b) hazard rate. Explain their
application to the reliability of components and repairable systems.
Discuss the plausibility of the ‘bathtub curve’ in both contexts.
2. (a) Explain the theory of component Failures derived from the
interaction of stress (or load) and strength distributions. Explain
how this theory relates to the behavior of the component hazard
function.
(b) Discuss the validity of the ‘bathtub curve’ when used to
describe the failure characteristics of non-repairable components.
3. What are the main objectives of a reliability engineering team
working on an engineering development project? Describe the
important skills and experience that should be available within the
team.
4.Briefy list the most common basic causes of
Failures of engineering products.