Title Maintanability,Maintenance, And Reliability for Engineering Reliability Engineering Probability Distribution Technology Mathematics 5.7 MB 221
##### Document Text Contents
Page 110

C012xEq_0015.eps

Maintainability Tools and Specific Maintainability Design Considerations

99

C:

Repair facilities or tools are unavailable.

D:

There are no spare parts.

Furthermore, either of the following two factors can result in the unavailability
of spare parts:

E:

Parts are no longer available in the market.

F:

Parts are out of stock.

In addition, the unavailability of skilled manpower can be caused by either of
the following two factors:

G:

Poor planning.

H:

Labor shortage.

Develop a fault tree for this undesired event: the equipment will not be repaired
by a given point in time. Calculate the probability of the occurrence of the undesired
event if the probabilities of occurrence of factors B, C, E, F, G, and H are 0.03,
0.02, 0.04, 0.05, 0.06, and 0.07, respectively.

For this example, the fault tree shown in Figure 8.2 was developed using the symbols
from Figure 8.1 . Single capital letters in the figure diagram donate corresponding fault

FIGURE 8.2

Fault tree for Example 8.1.

T

D

F
E

HG

A

C
B

Equipment will not be repaired
by a given point in time

No spare
parts

No skilled
manpower

Parts out of
stock

Poor
planning

Labor
shortage

Parts no
longer
available in
market

Equipment
too
damaged
to repair

Required
repair
facilities/
tools
unavailable

7243_C008.fm Page 99 Friday, January 1, 1904 12:48 AM

© 2006 by Taylor & Francis Group, LLC

Page 111

C016xEq_0038.eps

100

Maintainability, Maintenance, and Reliability for Engineers

events. By substituting the given data values into Equation 5.1, the probability of
occurrence of event A (i.e., skilled manpower is unavailable) is given by

Similarly, by substituting the specified data values into Equation 5.1, the prob-
ability of occurrence of fault event

D

(i.e., no spare parts) is given by

With the above two calculated values and the data in Equation 5.1, the probability
of occurrence of the undesired event (i.e., equipment will not be repaired by a given
point in time) is given by

where

P

(

T

) is the probability that the equipment will not be repaired by a given
point in time.

Figure 8.3 presents the Figure 8.2 fault tree with given and calculated fault event
occurrence probability values. As per Figure 8.3, the probability that equipment will
not be repaired by a given point in time is 0.2421.

FIGURE 8.3

A fault tree for Example 8.1 with given and calculated fault event occurrence
probability values.

P A( ) ( . ) ( . )

.

= − − −
=

1 1 0 06 1 0 07

0 1258

P D( ) ( . ) ( . )

.

= − − −
=

1 1 0 04 1 0 05

0 088

P T( ) ( . ) ( . ) ( . )( . )= − − − − −
=

1 1 0 088 1 0 02 1 0 03 1 0 1258

00 2421.

T

D

FEHG

A

C B

0.2421

0.0880.1258

0.050.06 0.07
0.04

0.030.02

7243_C008.fm Page 100 Friday, January 1, 1904 12:48 AM

© 2006 by Taylor & Francis Group, LLC