qm zg528-l2.ppt

7/25/2019 QM ZG528-L2.ppt

1/27

BITSPilaniPilani Campus

QM ZG528 L-2

Reliability EngineeringGajanand Gupta

Department of Mechanical Engineering

1

7/25/2019 QM ZG528-L2.ppt

2/27

BITSPilaniPilani Campus

The Failure distributin

7/25/2019 QM ZG528-L2.ppt

3/27

BITS Pilani, Pilani Campus

The Reliability function

Mean time to failure

Hazard rate function

Bathtub curve Conditional reliability

Objective

3

7/25/2019 QM ZG528-L2.ppt

4/27


Reliabilit is the

!1" conditional probability, at a gi#en

!$" Confidence le#el that the e%uipment &ill

!3"perform its intended functions satisfactoril or withoutfailure, i'e', &ithin specified performance limits, at a gi#en

!(" age, for a specified length of time, function period, or

!)" mission time, &hen used in the manner and for the

purpose intended &hile operating under the specifiedapplication and operation en#ironments &ith their

associated

!*" stress levels

!"M#RE$E%SI&E 'EFI%ITI"% "F RELI(BILIT)

(

7/25/2019 QM ZG528-L2.ppt

5/27


Reliabilit is defined as the probabilit that a sstem

!Component" &ill function o#er some time period t'

+o epress this relationship mathematicall &e define the

continuous random #ariable + to be the time to failure of

the sstem !component" - + . /

+hen Reliabilit Can be epressed as

R!t" 0 Pr + . t 2

hereR!t" . /, R!/" 01 and limt45 R!t" 0/

6or a gi#en #alue of t, R!t" is the probabilit that the time to

failure is greater than or e%ual to t'

The Reliability Fun*tin

)

7/25/2019 QM ZG528-L2.ppt

6/27


*

7/25/2019 QM ZG528-L2.ppt

7/27BITS Pilani, Pilani Campus

7

7/25/2019 QM ZG528-L2.ppt


8

7/25/2019 QM ZG528-L2.ppt


9f &e define

6!t" 0 14 R!t" 0 Pr + : t 2

here 6!/" 0 / and ;im t 4 5 6!t" 0 1

+hen 6!t" is the probabilit that a failure occurs before time t'

let R!t" 0 Reliabilit function

6!t" 0 cumulati#e distribution function

+hen Probabilit densit function is gi#en b

qm zg528-l2.ppt

Documents