IEC 60605-6:2007

INTERNATIONAL IEC
STANDARD
CEI
60605-6
NORME
Third edition
INTERNATIONALE
Troisième édition
2007-05
Equipment reliability testing –
Part 6:
Tests for the validity and estimation
of the constant failure rate
and constant failure intensity

Essais de fiabilité des équipements –
Partie 6:
Tests pour la validité et l’estimation du taux
de défaillance constant et de l’intensité
de défaillance constante
Reference number
Numéro de référence
IEC/CEI 60605-6:2007
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INTERNATIONAL IEC
STANDARD
CEI
60605-6
NORME
Third edition
INTERNATIONALE
Troisième édition
2007-05
Equipment reliability testing –
Part 6:
Tests for the validity and estimation
of the constant failure rate
and constant failure intensity

Essais de fiabilité des équipements –
Partie 6:
Tests pour la validité et l’estimation du taux
de défaillance constant et de l’intensité
de défaillance constante
PRICE CODE
X
CODE PRIX
Commission Electrotechnique Internationale
International Electrotechnical Commission
МеждународнаяЭлектротехническаяКомиссия
For price, see current catalogue
Pour prix, voir catalogue en vigueur

– 2 – 60605-6 © IEC:2007
CONTENTS
FOREWORD.4
INTRODUCTION.6

1 Scope.7
2 Normative references.7
3 Terms and definitions .7
4 Symbols .8
5 Requirements .9
6 Test for constant failure rate .9
6.1 General remark concerning Clause 6 .9
6.2 Statistical test for constant failure rate .10
6.3 Probability plot.12
6.4 Total time on test plot .12
6.5 Hazard plot.13
6.6 Action to be taken if constant failure rate assumption is rejected .14
7 Test for constant failure intensity .15
7.1 General remark concerning Clause 7 .15
7.2 Test for constant failure intensity for a single repaired item .15
7.3 Test for constant failure intensity for multiple repaired items .16
7.4 M t plot .18
()
7.5 Action to be taken if the constant failure intensity assumption is rejected.19

Annex A (informative) Examples of the procedures given in this standard .20
Annex B (informative) Example of M(t) analysis for field data.34
Annex C (informative) Preparation of field data for M(t) analysis .39

Bibliography .43

Figure 1 – Tests for constant failure rate – Chart showing structure of Clause 6.10
Figure 2 – Tests for constant failure intensity – Chart showing structure of Clause 7 .15
Figure A.1 – Probability plot to check constancy of failure rate.26
Figure A.2 – Hazard plot to examine constancy of failure rate .28
Figure A.3 – M(t) plot for three repaired items .30
Figure A.4 – M(t) plot with 95 % confidence intervals .31
Figure A.5 – TTT plot to examine constancy of failure rate.33
Figure B.1 – Population of systems in use as function of operational time .35
Figure B.2 – Repair per month as percentage of population in use.36
Figure B.3 – M(t) plot .37
Figure B.4 – M(t) curve with 99 % confidence limits .38
Figure B.5 – Number of repairs per phone .38

60605-6 © IEC:2007 – 3 –
Table 1 – Critical value U as a function of α.11
α
Table 2 – Computation of times to failure for multiple repaired items.17
Table 3 – Quantiles for standardized normal distribution .19
Table A.1 – Twenty ordered times to failure out of 40 tested items.20
Table A.2 – Accumulated times to failure.20
Table A.3 – Time ordered sequence of failure times .21
Table A.4 – Accumulated times to failure.21
Table A.5 – Eight times at which item failures occurred .22
Table A.6 – Accumulated times to failure.23
Table A.7 – Failure data for multiple copy of repaired item.23
Table A.8 – Worksheet for computations .24
Table A.9 – Times to failure from test of non-repaired item .25
Table A.10 – Worksheet with calculations.25
Table A.11 – Ten ordered times with multiple modes .27
Table A.12 – Worksheet and calculations .28
Table A.13 – Failure times for three identical items of repaired item.29
Table A.14 – Worksheet with computations for M(t) .29
Table A.15 – Worksheet with computations for confidence intervals for M(t) .30
Table A.16 – Confidence intervals for M(t) .31
Table A.17 – Times to failure.32
Table A.18 – Worksheet and calculations .33

– 4 – 60605-6 © IEC:2007
INTERNATIONAL ELECTROTECHNICAL COMMISSION
___________
EQUIPMENT RELIABILITY TESTING –

Part 6: Tests for the validity and estimation
of the constant failure rate and constant failure intensity

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60605-6 has been prepared by IEC technical committee 56:
Dependability.
This third edition cancels and replaces the second edition, published in 1997, and constitutes a
technical revision.
The major technical changes with respect to the previous edition concern the inclusion of
corrected formulae for tests previously included in a corrigendum, and the addition of new
methods for the analysis of multiple items.

60605-6 © IEC:2007 – 5 –
The text of this standard is based on the following documents:
FDIS Report on voting
56/1181/FDIS 56/1191/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
A list of all the parts in the IEC 60605 series, under the general title Equipment reliability
testing, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until the
maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.
– 6 – 60605-6 © IEC:2007
INTRODUCTION
The techniques given in this part of IEC 60605 for testing constant failure rate or constant
failure intensity assumptions are numerical and graphical procedures. The graphical methods
allow patterns, such as early failures and non-constant failure rates and intensities, to be
identified and estimated. The techniques are appropriate for analysing test or field data.

60605-6 © IEC:2007 – 7 –
EQUIPMENT RELIABILITY TESTING –

Part 6: Tests for the validity and estimation
of the constant failure rate and constant failure intensity

1 Scope
This standard specifies procedures to verify the assumption of a constant failure rate or
constant failure intensity, as defined in IEC 60050(191), and to identify patterns in the failure
rate or intensity. These procedures are applicable whenever it is necessary to verify such
assumptions. This may be due to a requirement or for the purpose of assessing any variation
with time of the failure rate or failure intensity.
The objectives of the methods specified in this standard are as follows:
– to test whether the times to failure of non-repaired items are exponentially distributed, i.e.
the failure rate is constant;
– to test whether the times between failures of repaired item(s) have any time trend, i.e. the
failure intensity does not exhibit an increasing or decreasing trend;
– to construct graphs that allow the patterns in the failure rate or failure intensity to be
displayed, with a view to verifying whether they can be assumed constant, to estimate their
values or to identify the nature of any departure from constancy.
2 Normative references
The following referenced documents are indispensable for the application of this document. For
dated references, only the edition cited applies. For undated references, the latest edition of
the referenced document (including any amendments) applies.
IEC 60050(191), International Electrotechnical Vocabulary (IEV) – Chapter 191: Dependability
and quality of service
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050(191) apply.
However, the following clarifications should be noted:
a) the term "time" can refer to length, cycles or other quantities;
b) the term "failure" can also refer to other specified events such as repair completion or any
other particular event;
c) the term “failure rate” is used to mean the instantaneous failure rate, also known as the
hazard function;
d) the procedures are applicable for time-to-failure data collected from both test as well as
from in the field. In this standard, the term “test” is used in Clauses 6 and 7 and can refer to
time data collected from both test as well as from in the field.

– 8 – 60605-6 © IEC:2007
4 Symbols
indicator variables
ij,,k,l
cumulative hazard function at i -th time to failure
H
i
mean accumulated number of failures at time T
M T
() j
j
M t
()
mean accumulated number of failures per 100 systems
m
number of unique times to failure accumulated over all repaired items
total number of items on test or in use at time T
N T
()
l
l
indicator variable, set to 1 if failure of i -th item is observed at time T , set to 0 if
N T
j
()
ij
failure of i -th item is not observed at time T
j
n
sample size, the total number of non-repaired items tested for constant failure
rate
estimate of the reliability at the i-th ordered time to failure t used by the
R in,
()
i
graphical procedure when testing n items for constant failure rate
reliability function computed for i -th ordered failure
R
i
r number of relevant failures during test
total number of failures for multiple repaired items at time T
rT
()
l
l
number of failures for item i at accumulated time T
rT
() j
ij
number of relevant failures during test for k -th item
r
k
total time on test value for i -th time to failure
S
i
S initialization value for total time on test value, where S = 0
0 0
accumulated time to the i -th relevant failure
T
i
total time accumulated to the r -th failure
T
r
accumulated time to j -th failure of i -th item
T
ij
T ordered accumulated time to j -th failure TT<< . j 12 m
*
total time accumulated on test time
T
*
total time accumulated on test for k -th repaired item
T
k
time corresponding to the i-th ordered failure, used when testing n items for
t
i
constant failure rate
*
termination time of test for constant failure rate
t
value of the statistic calculated from observed values, used when testing for
U
constant failure intensity or constant failure rate
α quantile of the standardized normal distribution
U
α
60605-6 © IEC:2007 – 9 –
Var()T
variance of M T used in the calculation of the confidence interval
j ()
j
normalized total time on test value for i -th failure
Z
i
α
risk of wrongly rejecting the assumption that the (instantaneous) failure rate or
the (instantaneous) failure intensity are constant, when they really are constant,
often known as the significance level.
5 Requirements
In order for the procedures specified in this standard to be valid, the following requirements
shall be satisfied.
When testing n non-repaired items, for the constant failure rate assumption,
– for the numerical procedures, at least six times to failure are required;
– for the graphical procedure, at least four times to failure are required.
When testing one or more repaired items, for the constant failure intensity assumption,
– for the numerical procedures, at least six times between failures are required;
– for the graphical procedure, at least four times between failures are required.
NOTE 1 For repaired items, the repair time is assumed to be negligible.
NOTE 2 Numerical procedures are given in the statistical tests for constant failure rate and constant failure
intensity (see 6.2, 7.2 and 7.3) and the confidence intervals (see 7.4). Graphical procedures are outlined in the
plotting methods given in Clauses 6 and 7.
NOTE 3 The justification of the minimum number of failures can be found in the references given in the
Bibliography.
6 Test for constant failure rate
6.1 General remark concerning Clause 6
This clause deals with tests for constant failure rate for non-repaired items. The test procedure
is shown in the form of a chart (see Figure 1).

– 10 – 60605-6 © IEC:2007
Statistical test 6.2
for constant
failure rate
Non-repaired item
Probability plot
6.3
Graphical
methods
TTT plot 6.4
Hazard plot 6.5
IEC  529/07
Figure 1 – Tests for constant failure rate –
Chart showing structure of Clause 6
A formal statistical test for constant failure rate is given for tests terminated at a
predetermined time or failure.
Three graphical procedures are given as follows:
a) the probability plot is based on a linear transformation of the exponential distribution
function and is suitable when the set of times to failure are known for every non-repaired
item tested or when the test of all items is terminated at a predetermined time or failure;
b) the total time on test plot (TTT plot) is an empirical and scale-independent plot suitable for
data where the times to failure are known for all non-repaired items;
c) the hazard plot is a linear transformation of the cumulative hazard function for the
exponential distribution and is appropriate when the set of times to failure are known for
every non-repaired item tested, when the test of all items is terminated at a predetermined
time or failure, or when the times to failure of a non-repaired item are mixed with the
running times for items that have been removed from test at arbitrary points.
6.2 Statistical test for constant failure rate
This subclause applies when a sample of n items is put on test that is terminated at the time
*
of a pre-specified number of failures, r (failure terminated), or at a pre-specified time, t (time
terminated).
The operating environment shall be the same for all the items tested. At the end of the testing
period, not all of the items will have necessarily failed. There will be a total of r recorded
relevant times to failure.
Step 1
Order the times to failure in increasing order of magnitude and denote the ordered sample
tt, ,.,t .
12 r
For ir= 1 to , compute the accumulated time to the i-th failure as

60605-6 © IEC:2007 – 11 –
i
Tt=+()n−it
∑
ik i
k =1
For failure terminated tests, the total time accumulated on test at the r -th failure is given by
r
Tt=+n−rt
()
rk∑ r
k =1
*
and for time terminated tests, the total time accumulated on test at t is given by
r
**
Tt=+n−rt
()
∑ k
k =1
Step 2
For each relevant accumulated test time T compute the appropriate quantityU .

i
r−1
T
r
Tr−−1
()
∑
i
i=1
If failure terminated then U =
r−1
T
r
r *
T
Tr−
∑
i
i=1
If time terminated then: U =
*
r
T
Step 3
Specify the significance level α to reject wrongly the assumption of constant failure rate, given
that it really is constant. Recommended values of α are given in Table 1.
Table 1 – Critical value U as a function of α
α
α
Critical value of U
α
0,025 2,24
0,050 1,96
0,100 1,64
Step 4
Reject the assumption of constant failure rate if the absolute value of U is greater than the
critical value given in Table 1. Otherwise, the assumption is not rejected.

– 12 – 60605-6 © IEC:2007
Large positive values of U occur whenever there is an increasing failure rate. Conversely,
large negative values of U occur whenever the failures occur at a decreasing rate.
6.3 Probability plot
This method is appropriate when the set of times to failure are known for every non-repaired
item tested or when the test of all items is terminated at a predetermined time or failure.
Step 1
Order the times to failure eventstt, ,.,t from smallest to largest.

12 r
Step 2
Calculate the auxiliary function R(,in) where i is the index of the corresponding time to failure
t , and n is the sample size corresponding to the number of non-repaired items tested:

i
ni−+ 0,7
Ri(,n) =
+ 0,4
n
NOTE It should be noted that R(,in) is an estimate of the reliability at the i-th ordered time to failure t when
i
testing n items for constant failure rate. Strictly the auxiliary function is an estimator of the reliability function and
ˆ
conventionally would be represented by . However the ‘hats’ have been omitted within this standard as there
R(,in)
is no need to distinguish between the estimate and the true value.
Step 3
Plot the logarithm of R(,in)against the corresponding time to failure or plot the auxiliary
function R(,in) on the logarithmic scale of a semi-log paper.
NOTE Special probability paper can be used to construct the exponential probability plot.
Step 4
If the plot of this function looks linear, then there is no evidence to reject the assumption that
the failure rate is constant and the failure rate may be estimated as the absolute value of the
slope of the line. If the plot does not look linear then the assumption of constant failure rate
should be rejected.
6.4 Total time on test plot
The method is appropriate when the set of times to failure are known for every non-repaired
item tested.
Step 1
Order the times to failure events tt, ,.,t from smallest to largest, where tt≤≤ .≤t .

12 n 12 n
60605-6 © IEC:2007 – 13 –
Step 2
Calculate the total time on test (TTT) values,Si, =12, ,.,n , corresponding to each time to
i
failure, setting S = 0 :
Sn=+t n−11t−t+.+n−i+ t−t
()( ) ( )( )
ii121 i−1
Step 3
Normalize the TTT-values by calculating
S
i
Z =
i
S
n
Step 4
Plot the normalized TTT-values Z against the proportion of items that have failed by this time,
i
i
, for in=12, ,., , on linear scale paper and join the plotted points by line segments.
n
Step 5
If the TTT plot looks linear, then there is no evidence to reject the assumption that the failure
rate is constant and the failure rate may be estimated as the absolute value of the slope of the
line. If the plot does not look linear, then the assumption of constant failure rate should be
rejected.
6.5 Hazard plot
This method is appropriate when the set of times to failure are known for every non-repaired
item tested or when the test of all items is terminated at a predetermined time or failure. This
method is also appropriate when the times to failure of non-repaired items are mixed with the
running times for items that have been removed from test at arbitrary points.
Step 1
Order the event times, both failure and running, from smallest to largest and denote the i -th

ordered time by t (i.e. tt≤≤ .≤t≤ .≤t ).
i 12 in
Step 2
Compute the reverse ranks of all the times, nn,−−12,n ,.,2,1, where n represents the
number of events. The reverse rank of the i -th event is given by ni−+1.
Step 3
Calculate the hazard function at each failure time only as the ratio of 100 to the corresponding
i -th time, corresponding to a failure, is given by
reverse rank. Hence the hazard function at the
ni−+1
– 14 – 60605-6 © IEC:2007
Step 4
Calculate the cumulative hazard ( H ) at each failure time as the sum of the hazard function at
i
that time plus the preceding cumulative hazard.
Step 5
Plot the cumulative hazard against the corresponding time to failure on linear scale paper.
NOTE 1 Only the times to failure should be plotted and not the running times. The running times are used to
estimate the position of the hazard only.
NOTE 2 It is possible to express the cumulative hazard function as the reliability function using the
relationship R=−exp H and hence construct a probability plot as in 6.3.
()
ii
NOTE 3 Special hazard plotting paper may be used to construct the exponential hazard plot.
Step 6
If the plot of this function looks linear, then there is no evidence to reject the assumption that
the failure rate is constant and the failure rate may be estimated as the absolute value of the
slope of the line. If the plot does not look linear, then the assumption of constant failure rate
should be rejected.
NOTE In testing for constant failure rate, only the slope of the line is important and not the value of the intercept.
6.6 Action to be taken if constant failure rate assumption is rejected
If the constant failure rate assumption is rejected, it is recommended that the data be further
analysed in order to determine the possible cause. Numerical analysis should, wherever
possible, be supported by physical investigations and engineering considerations.
The items may be subject to wear-out in the time interval considered, or a mechanism inducing
early failures may be present. There is also the possibility that the items do not come from a
homogeneous population, in which case there may be a mixture of several failure rates related
to different failure modes, for example from weak and strong populations. All these situations
deserve further investigation.
If wear-out or early failures are suspected, the procedures of IEC 61649 should be used for
non-repaired items and IEC 61710 should be used for repaired items. If, on the other hand, a
mixture of populations is suspected, efforts should be made to identify and separate the
different populations, and to analyse these separately.
Whatever the cause for the rejection of the constant failure rate assumption, compliance
methods that require this assumption should not be applied.
NOTE If the constant failure rate assumption is not rejected, the conclusion is that the times to failure have not
been proven to deviate from the exponential assumption. This may often occur when a small number of failures are
observed.
60605-6 © IEC:2007 – 15 –
7 Test for constant failure intensity
7.1 General remark concerning Clause 7
This clause applies to repaired item(s) where the sequence of times between failures is
recorded. Testing for constant failure intensity implies that the sequence of times between
successive relevant failures exhibits neither an increasing nor a decreasing trend. If no such
trend exists, then the item can be considered as being renewed after each repair. The test
procedure is shown in the form of a chart (see Figure 2).

Single item 7.2
Statistical test for
constant failure
intensity
Multiple items 7.3
Repaired item(s)
Graphical M(t) plot 7.4
procedure
IEC  530/07
Figure 2 – Tests for constant failure intensity –
Chart showing structure of Clause 7
Two formal statistical tests for constant failure intensity are given:
a) single repaired items corresponding to a single system or multiple copies of the same
system operating in nominally identical environments;
b) multiple repaired items corresponding to multiple systems of the same type but operating
in different environments.
One graphical procedure is given, and it is appropriate when data are available for one or more
repaired items, even when they have been observed for different lengths of time.
NOTE The failure intensity of large complex systems can be constant even if the component parts do not have
constant failure rates. For example, approximately constant failure intensity can be observed for a repairable item
even though the components in the item are wearing out.
7.2 Test for constant failure intensity for a single repaired item
This numerical procedure requires that there are at least six relevant successive failures
*
recorded during the testing time T .
Step 1
For a repaired item, the accumulated time to the i-th failure is T . This procedure can be applied
i
*
either at the time of the last failure T or at any other later time T during which the item

r
continues to perform its function.
NOTE The time between successive failures is given by .
tT=−T
ii i−1
– 16 – 60605-6 © IEC:2007
Step 2
For each relevant accumulated failure time, T , compute the statistic U .

i
r
*
T
Tr−
∑
i
* i=1
If TT> then  U =
r
*
r
T
r−1
T
r
Tr−−(1)
∑
i
=1
* i
If TT= then  U =
r
r−1
T
r
Step 3
Specify the significance level α of wrongly rejecting the assumption of constant failure intensity,
given that it really is constant. Recommended values of α are given in Table 1.
Step 4
Reject the assumption of constant failure intensity if the absolute value of U is greater than the
critical value given in Table 1. Otherwise, the assumption is not rejected.
Under the no-trend assumption, i.e. assuming the failure intensity is constant over time, the
statistic U follows the standardized normal distribution. Large absolute values of U constitute
evidence to reject this assumption.
Large positive values of U occur whenever there is a decreasing trend in times between
successive failures. Conversely, large negative values of U occur whenever these times have
an increasing trend, i.e. they become longer since the failure intensity becomes smaller.
NOTE Not rejecting the constant failure intensity assumption should not be interpreted as implying that the times
between successive failures of a repaired item follow an exponential distribution. The only conclusion that can be
drawn is that these times have not been proven to exhibit a trend. Although this is consistent with exponentially
distributed times between failures, other distributions are also consistent with a trendless intensity.
7.3 Test for constant failure intensity for multiple repaired items
This procedure is an extension of the method given in 7.2. It is appropriate when data are
available for multiple repaired items and the constancy of the failure intensity of each is to be
examined.
Step 1
For each item, note the accumulated time until the end of the observation, the total number of
failures observed and the times of their occurrence as shown in Table 2.

60605-6 © IEC:2007 – 17 –
Table 2 – Computation of times to failure for multiple repaired items
Item Accumulated time until end Total number of failures
Times of j -th failure
of observation period within observation period
occurrence,
*
r j =12, ,.,r
T
i i
i i
1 *
r T
T
1 1j
2 *
r T
T
2 2j
3 *
r T
T
3 3j
k *
r T
T
k kj
k
*
NOTE If some items are observed only to the r-th failure, then set TT= for that item and set rr= - 1 in the
r
subsequent calculations for that item only.

Step 2
Compute the statistic U :
r
k
i
** *
Tr−+05,TrT+.+rT
()
∑∑ ij 11 2 2 k k
ij==11
U =
**22 *2
rT++r T + r T
...
()
11 2 2 kk
Step 3
Specify the significance level α to reject wrongly the assumption of constant failure intensity,
given that it really is constant. Recommended values of α are given in Table 1.
Step 4
Reject the assumption of constant failure intensity for all identical items if the absolute value of
U is greater than the critical value given in Table 1. Otherwise, the assumption is not rejected.
Under the no-trend assumption, i.e. assuming the failure intensity is constant over time, the U
statistic follows the standardized normal distribution. Large absolute values of U constitute
evidence to reject this assumption.
Large positive values of U occur whenever there is a decreasing trend in times between
successive failures in any of the identical items. Conversely, large negative values of U occur
whenever these times have an increasing trend, i.e. they become longer since the failure
intensity becomes smaller, in any of the identical items.
NOTE Not rejecting the constant failure intensity implies only that there is insufficient evidence to reject the claim
that the failure intensities of all the identical items are constant.

– 18 – 60605-6 © IEC:2007
7.4 M()t plot
This plotting method is appropriate when data are available for one or more repaired items,
even when they have been observed for different lengths of time. The M(t) plot allows patterns
in the failure intensity to be identified. This can help to establish whether the failure intensity is
constant and complements the numerical methods given in 7.2 and 7.3. The M(t) plot also
allows other patterns in the failure intensity to be identified, such as decreasing failure intensity
(early life failures).
NOTE The M(t) approach provides an empirical analysis of the observed failures for repaired items. It need not
make any assumptions about the form of the underlying process from which the data have been generated. M(t)
analysis provides a simple means of identifying patterns in the failure intensity applicable to the general case for
multiple repaired items and can be useful to detect departures from constancy.
Step 1
Order accumulated time to the j -th failure of the i -th item T from shortest to longest where
ij
ik=12, ,., .
Step 2
Identify m , the number of unique accumulated failure times over all items.
Step 3
Denote the ordered accumulated time to j-th failure over all items by Tj, =01, ,.,m ,
j
TT<< . 12 m
Step 4
Compute rT number of failures for item i at accumulated time T .
()
ij j
Step 5
Define N T to be an indicator variable, set to 1 if i -th item is observed at time T , set to 0
()
ij j
if i -th item is not observed at time T .
j
Step 6
Compute the mean accumulated number of failures at time T to be:
j
j
⎡ ⎤
rT
()
l
MT =
() ⎢ ⎥
j ∑
N T
()
l=1
l
⎣ ⎦
k
where rT = r T
() ()
ji∑ j
i=1
60605-6 © IEC:2007 – 19 –
k
NTN= T
() ()
∑
jij
i=1
Step 7
Plot M T against Tj, =01, ,.,m .
()
j j
Step 8
A constant failure intensity corresponds to a linear pattern in this plot. Any departure from
linearity implies the failure intensity is not constant.
Step 9
A two sided confidence interval can be constructed for M T as follows:
()
j
MTU± VarT
() ()
jjα /2
where U is the α/2 quantile of a standardized normal distribution corresponding to a
α /2
100 1−α % confidence interval, where selected values are shown in Table 3, and
()
j
k
⎧ ⎫
NT ⎡ rT ⎤
() ()
⎪ ⎪
il l
VarTr=−T
() ()
⎨ ⎢ ⎥⎬
ji∑∑ l
NT N T
() ()
il==11
ll
⎪ ⎣ ⎦⎪
⎩⎭
Table 3 – Quantiles for standardized normal distribution
100()1−α%
U
α /2
99 % 2,58
95 % 1,96
90 % 1,64
7.5 Action to be taken if the constant failure intensity assumption is rejected
If the test for constant failure intensity allows for rejection of this assumption, the interpretation
is that the failure intensity is either increasing or decreasing. This may be due either to
degradation of the overall system reliability or to reliability growth, after each repair. IEC 61710
gives numerical methods for modelling this degradation or growth.

– 20 – 60605-6 © IEC:2007
Annex A
(informative)
Examples of the procedures given in this standard

A.1 Test for constant failure rate for non-repaired item
A total of 40 items are put on test at the same time. The test is halted after the 20th failure.
Table A.1 contains the ordered failure times of the 20 items that failed. The methods given in
6.2 should be used to test whether the failure rate is constant.
Table A.1 – Twenty ordered times to failure out of 40 tested items
i i i
t t t
i i i
1 5 8 36 15 64
2 10 9 54 16 65
17 65
3 17 10 55
4 32 11 55 18 66
5 32 12 58 19 67
6 33 13 58 20 68
7 34 14 61
Step 1
The times to failure are ordered by magnitude and the accumulated time to the i -th failure is
noted as shown in Table A.2.
Table A.2 – Accumulated times to failure

i i
t T t T
i i i i
1 5 200 11 55 1 958
2 10 395 12 58 2 045
3 17 661 13 58 2 045
4 32 1 216 14 61 2 126
5 32 1 216 15 64 2 204
6 33 1 251 16 65 2 229
7 34 1 285 17 65 2 229
8 36 1 351 18 66 2 252
9 54 1 927 19 67 2 274
10 55 1 958 20 68 2 295
The test is failure terminated and so T = 2 295 .
r
60605-6 © IEC:2007 – 21 –
Step 2
The value of the U statistic is given by
2 295
r−1 ⎛⎞
T
r
30 822 − 19
()
∑Tr−−1
() ⎜⎟
i
i=1 ⎝⎠
U== = 3,123
r −119
T 2 295
r
12 12
Steps 3 and 4
At α =10 % significance level, the U statistic exceeds the critical value of U =1,64 (see
α
Table 1), therefore conclude that the assumption of constant failure rate is rejected. The
positive value of the U statistic implies that there is a statistically significant increasing failure
rate.
A.2 Test for constant failure rate for non-repaired items
The times to failure of a type of component are recorded on test. Twelve components are
tested and observation of the components is stopped at the time of the 12-th failure. The
sequence of times to failure is given in Table A.3. The methods in 6.2 should be used to test
the constancy of the failure rate.
Table A.3 – Time ordered sequence of failure times
1 2 5 6 7 11 16 20 20 21 23 32

Step 1
The accumulated times to failure are computed as shown in Table A.4.
Table A.4 – Accumulated times to failure
i
t T
i i
1 1 1
2 2 3
3 5 8
4 6 14
5 7 21
6 11 32
7 16 48
8 20 68
9 20 88
10 21 109
11 23 132
12 32 164
– 22 – 60605-6 © IEC:2007
Step 2
The value of the U statistic is given by
r−1
T 164
⎛⎞
r
Tr−− (1) 524 − 11
()
∑ i ⎜⎟
−378
2 2
i=1 ⎝⎠
U = == =−2,407
157,018
r −111
T 164
r
12 12
Steps 3 and 4
At α = 5 % significance level, the absolute value of the statistic does exceed the critical value
of U = 1,96 (see Table 1), therefore conclude that the assumption of constant failure rate is
α
rej
...