RELIABILTY

Reliability Management

Why is it needed?

• Reliable operation of critical equipment• Planning of maintenance activities• Improved ‘quality’ of an item

Reliability Management

Reliability management is concerned with performance and conformance over the expected life of the product

“the probability that a product or a piece of equipment performs its intended function for a stated period of time under specified operation conditions’”

Definition of Reliability

The definition has four important elements:• Probability

• Time

• Performance

• Operating conditions

Definition of Reliability

Probability• A value between 0 and 1• Precise meaning

e.g. probability of 0.97 means that 97 of 100 items will still be working at stated time under stated conditions

Definition of Reliability

Performance• Some criterion to define when product

has failed

e.g. bearing clearances in an engine or amount

of emissions from a car

Definition of Reliability

Operating conditions• These describe the operating conditions

that correspond to the stated product life. e.g. for a car engine this might mean

→ Speed→ Loading→ Effects of an expected amount of misuse such as over-revving and

stalling.

Reliability Measurement

This is based on the Failure Rate

i.e. TimeOperatingTotalFailedItemsrateFailure

Some products are scrapped when they fail e.g. hairdryer

Others are repaired e.g. washing machine.

Failure rate over the life of a product

The failure rate is expected to vary over the life of a product – ‘Bathtub Curve’

Time

Failu

re R

ate

A

C

D

B

Bathtub Curve

A-B Early Failure• ‘Infant Mortality’ Caused by

design/material flaws

B-C Constant Failure• Lower than initial failure rate and more or

less constant until end of life

C-D End of life failure• Failure rate rises again due to

components reaching end of life

Simplifying Assumption• Exponential distribution of failure rate is

assumed. This means that the failure rate remains constant over life of product

• Bathtub curve becomes a straight line

Time

Failu

re R

ate

Calculating Failure Rate

Calculating Failure Rate

Failure rate

te

TimeOperatingTotalFailedItems

usually expressed by the Greek letter lambda ()

The probability of a product surviving until time (t) is given by the following function:

Reliability at time (t) =e is the exponential function

ProcedureTo establish reliability of an item:

• Conduct a series of tests until a number of them fail.

• Calculate failure rate (Lambda).

• Calculate reliability for a given time using

Reliability at time (t) = e-t

Example

Trial data shows that 105 items failed during a test with a total operating time of 1 million hours. (For all items i.e. both failed and passed).

The failure rate 41005.11000000105 x

ExampleFind the reliability of the product after 1000 hours i.e. (t) =1000

Reliability at 1000 hours:

R(1000) = 0.9

te

)10001005.1( 4 xxe

Therefore the item has a 90% chance of surviving for 1000 hours

• As products become more complex (have more components), the chance that they will not function increases.

• The method of arranging the components affects the reliability of the entire system.

• Components can be arranged in series, parallel, or a combination.

System Reliability

RS = R1 R2 ... Rn

1 2 n

•For a series systems, the reliability is the product of the individual components.

•As components are added to the series, the system reliability decreases.

Series System

Rs = 1 - (1 - R1) (1 - R2)... (1 - Rn)

1

2

n

• When a component does not function, the product continues to function, using another component, until all parallel components do not function.

Parallel System

• Convert to equivalent series system

A B

C

CD

RA RB RCRD

RC

A B C’ D

RA RB RD

RC’ = 1 – (1-RC)(1-RC)

Series-Parallel System

The most important aspect of reliability is the design.

• It should be as simple as possible.• The fewer the number of components,

the greater the reliability.• Another way of achieving reliability is to

have a backup or redundant component (parallel component

Design

• Reliability can be achieved by overdesign.• The use of large factors of safety can

increase the reliability of a product.• When an unreliable product can lead to a

fatality or substantial financial loss, a fail-safe type of device should be used.

• The maintenance of the system is an important factor in reliability.

Design

• The second most important aspect of reliability is the production process.

• Emphasis should be placed on those components which are least reliable.

• Production personnel.

Production

Distributions Applicable to Reliability:• Exponential distribution.• Normal distribution.• Weibull distribution.Reliability Curves:• The curves as a function of time.

Additional Statistical Aspects