Technical note

MTBF calculations MTBF figures for diesel UPS systems

Input data The MTBF of the diesel UPS system can be determined on the basis of the reliability figures of its components. The following table lists the main components and the corresponding MTBF-value.

The utility supply is assumed to show an average failure rate of 1 interruption per 100 hours (i.e. 88 interruptions or disturbances per year). The mean time to repair (MTTR) of the diesel UPS system is 8 hours on average.

Reliability of the diesel UPS system The MTBF of the diesel UPS system can be determined depending on the system configuration. Following table shows the results for single and multiple UPS configurations. Note that these figures refer to the proper functioning of the UPS system rather than the presence of output voltage.

Reliability of the diesel UPS power supply The MTBF of the diesel UPS system can also be expressed in terms of availability of UPS output voltage. This includes the bypass operating mode. Hence the reliability of the utility supply and the average UPS repair time must be considered. Following table shows the results for single and multiple UPS configurations.

Glossary of terms and definitions Failure: Any interruption or

degradation of the UPS output

power which results in a

complete loss of power on load side or a switch to bypass

mode.

Reliability (Rt): The probability that an item operating under specified

conditions shall perform

satisfactorily for a given period

of time.

Failure rate (λ): The probability that an item

becomes defective over a unit

of time

MTBF: Mean Time Between Failure,

The average time between two

consecutive failures, which equals the average time

between the moment that the

UPS system is commissioned

and the first occasion on which the system fails.

Component MTBFinput circuit breaker 1,000,000 hoursoutput circuit breaker 1,000,000 hoursbypass circuitry 500,000 hourschoke coil 2,000,000 hoursdiesel engine 1,000,000 hoursfreewheel clutch 500,000 hoursinduction coupling 1,000,000 hoursgenerator 1,000,000 hourscontrol system 500,000 hours

Number of units none oneparallel redundant redundant

1 12.0 years n.a.2 5.7 years 57.0 years3 3.9 years 38.0 years4 2.9 years 28.5 years5 2.4 years 22.8 years6 2.0 years 19.0 years

Number of units none oneparallel redundant redundant

1 42.2 years n.a.2 32.7 years 53.1 years3 27.2 years 51.3 years4 23.3 years 49.7 years5 20.4 years 48.1 years6 18.1 years 46.6 years

MTBF calculations

Hitec Power Protection bv

P.O. Box 4

7550 GA Hengelo

The Netherlands

Phone: +31 74 246 20 00

Fax: +31 74 246 22 00

E-mail: info@hitecups.com

www.hitecups.com

MTTR (µ): The average time needed to

perform repair work

Availability: The time fraction during which a system is performing

satisfactorily for the required

time.

Reliability (Rt): R ett= −λ

Failure rate (λ): λ =1

MTBF

The failure rate (λtot) of an assembly of n

components:

λ λ λ λtot n= + + +1 2 ...

The failure rate (λsystem) of a UPS system,

including bypass and mains failure rate:

λλ λ

λ λ µλsystem

UPS mains

UPS mainsbypass=

+ ++

.

The failure rate (λred) of n units parallel, of

which 1 unit is redundant (Q3 is the output

circuit breaker):

λλ

λ µλred

UPS

UPSQ

n nn

n=−

− ++

( )( )

12 1

2

3

Availability (As): AMTBF

MTBF MTTRs =+