Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

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45-2

REFERENCE DATA

FOR

ENGINEERS

DEFINITtONS

AND

TERMINOLOGY

Availability:

Probability of a system subject to repair

operating satisfactorily

demand.

Average Life:

The mean value for a normal distribu-

tion of lives. Generally applied to mechanical failures

resulting from “wear-out.”

Burn-In

(also

Initial Failure):

Initially high failure

rate encountered

first placing a component

test.

Burn-in failures are usually associated with manufactur-

ing defects and the debugging phase of early service.

Component:

(Normally used interchangeably with the

term “unit.”) A component is defined as an article

which is normally a combination

of parts, subassem-

blies, or assemblies, and is a self-contained element of a

complete operating equipment and performs a function

necessary to the operation of that equipment.

Examples:

indicator unit, power unit, receiver, transmitter, rotat-

ing antenna, modulator unit, amplifier unit.

Confidence Level (Coeficient):

The degree of desired

trust or assurance in a given result. A confidence level is

always associated with some assertion and measures the

probability that a given assertion is true. For example, it

could be the probability that a particular characteristic

will fall within specified limits, i.e., the chance that the

true value of

lies between

and

Configuration Management:

Management of and

knowledge of where all specifications, procedures, and

associated test results are located and assigned,

that it

is possible to produce these controlled items and all

reliability evaluations and predictions pertaining to the

system.

Cumulative Distribution Function:

is a random

variable, then the cumulative distribution function of

is defined to be the function

such that for every real

number

F(t)

is the probability that a given outcome of

will

not

exceed t; in symbols:

F(t)

Defect:

Any deviation of a unit of product from

specified requirements.

unit of product may contain

more than one defect.

Degradation Failure:

failure that results from a

gradual change

performance characteristics of an

equipment or part with time.

Design Reviews:

(A)

Preliminary design review: As

soon

as possible

after a contract has been signed, a breadboard model

should be built and its reliability estimated. Reliability

engineering shall re-evaluate all parts and components

and determine and recommend improvements in the

design.

(€5)

Intermediate design reviews: While developing

the system, conduct design reviews

a formal basis at

all suppliers as well as at the prime contractor. This

program should be coordinated with the reliability

growth program. Account must be taken of the contract

requirements for reliability goals at scheduled points in

the production schedule.

lieves the design is ready to be “frozen” and also when

a satisfactory prototype has met the qualification and

other reliability tests, a final design review shall be

scheduled. This formal review takes into account all

contract demands as modified by the most recent

changes in the contract. If the product is adjudged to be

satisfactory, the final design may be approved for

production. The block system should be used and

authorization should be given to production to make

units per the specifications and blueprints without any

change.

Downtime:

Time during which equipments are not

capable of doing useful work because of malfunction.

This does not include preventive-maintenance time.

other words, downtime is measured from the occur-

rence

a malfunction to the correction of that mal-

function.

Equipment:

Material or articles (such as sets) com-

prising an outfit. The term “equipment” sometimes is

used instead of “set,” i.e., one or more assemblies or a

combination of items capable of independently per-

forming a complete function.

Examples:

Radio receiv-

er, digital computer, automobile. An equipment may

contain several sets as components. An example would

be two radio receivers assembled for dual-diversity

reception. The combination would constitute the equip-

ment.

Failure:

A failure is a detected cessation of ability to

perform a specified function

functions within previ-

ously established limits

the area of interest. It is

beyond adjustment by the operator by means of controls

normally accessible to him during the routine operation

of the device. This requires that measurable limits be

established to define satisfactory performance

the

function.

Failure Mode Analysis:

Research, development, and

production engineers as well as the reliability engineers

analyze the basic design and determine by simulation

and logistics what possible failures might occur. Cor-

rective measures for eliminating and preventing failures

are built into the basic design. Standard forms for the

failure mode analysis are made available, and the results

must be given to the prime contractors and production

engineers for evaluation.

Failure Modes and Effects Analysis (FMEA):

Exten-

sion of failure mode analysis which also considers the

consequences of the failure mode, such

“revealed

fault

,”

“fail-safe,

”

etc.

Failure Rate and Hazard Rate:

Failure rate is general-

the rate at which failure occurs during an interval of

time (given that it has not occurred before the start of

RELIABILITY AND LIFE TESTING

45-3

that interval) as a function of the total interval length.

Hazard rate is an instantaneous failure rate and is

defined as the limit of the failure rate as the time

interval approaches

An example might be: A family

takes an automobile trip of

120

miles and completes the

trip in three hours. The average rate was

mph,

although they drove at various rates of speed. The rate

at any given instant could be determined by reading the

speedometer at that instant. Therefore, the

mph is

equivalent to the failure rate and the speed at any instant

of time equals the hazard rate.

Inherent Reliability:

The basic or generic failure rates

of components have often been compiled by several

companies as well as by some government agencies.

library covering failure rates should be part of a good

reliability program. Such a listing gives concretely the

reliability that can be guaranteed.

Lot Size:

specific quantity of similar material or

collection of similar units from a common source; in

inspection work, the quantity offered for inspection and

acceptance at any one time. It may be a collection of

raw material, parts, subassemblies inspected during

production, or a consignment of finished products to be

sent out for service.

Maintainability:

The maintainability of an equipment

in a specified maintenance environment is the probabil-

ity that a failure will be repaired within a specified time

after the failure occurs.

Mean Time Before Failure (MBF):

The total mea-

sured operating time of a population of equipments

divided by the total number of failures of a repairable

equipment is defined as the ratio of the total operating

time to the total number of failures. The measured

operating time of the equipments of the population that

did not fail must be included. This measurement is

normally made during that period of time between the

early life and wear-out failures. In the case of a constant

hazard rate, this ratio is the reciprocal of the failure rate.

The MTBF can be determined by dividing the

product of the number of equipments tested,

and the

test time,

by the number of failures,

which occur

during that time; i.e., MTBF, or often just

is equal

Ntlf.

The quantity

is the reciprocal of

Le.,

l/A,

and is related to the probability of survival by the

exponential law

e(-t/m).

The figure of merit

(sometimes expressed as

is convenient for use in

determining if the reliability of an equipment is likely to

be adequate for missions of specific lengths.

Mean Time to Failure (MTTF):

The measured opera-

ting time of a single piece of equipment divided by the

total number of failures of the equipment during the

measured period of time. This measurement is normal-

ly made during that period of time between the early life

and wear-out failures.

Mean Time

Repair (MTTR):

The measured repair

time divided by the total number of failures of the

equipment.

Mission Success Rate:

That percentage of the total

missions uninterrupted by failure of the equipment.

This figure of merit is more closely dependent on the

reliability of the parts included in the system and on the

design of the system than are either maintenance ratio or

in-commission rate. However, this measure of reliabili-

ty is valuable primarily to a using agency that has a

regular schedule of missions.

mission success rate

obtained by one agency is not typical of the equipment

in general and will not necessarily apply for other

agencies with different operating schedules.

Mode of Failure:

The physical description of the

manner in which a failure occurs and the operating

condition of the equipment or part at the time of the

failure.

Part Failure Rate:

The rate at which a part fails to

perform its intended function.

Probability:

The limiting relative frequency in an

infinite random series. If an event can occur in

ways

and its failure in

ways, and if these

ways are

equally likely, then the mathematical probability that

the event will occur in any one trial is the ratio

nl(n

In other words, the probability of an event is the

theoretical relative frequency with which it will occur,

such relative frequency being the ratio of the number of

times the event is observed under experimental condi-

tions to the total of a great number of observations made

under those conditions.

Common notation is:

Pr(X)

Probability of event X

Pr(X/Y)

Probability of event X

given

has occurred

Probability Density Function (PDF):

The relative

frequency of a continuous random variable, obtained

from the cumulative distribution function by differentia-

tion.

f(t)

dF(t)/dt

Probability of Survival:

numerical expression of

reliability with the accepted nomenclature of

and a

range from

indicating the extremes of “impos-

sibility” and “certainty.”

other words, the probability of a given equipment

performing its intended function or the given use cycle

R(t)

F(t)

Product Effectiveness:

The entire reliability program

must be tied in with the quality engineering programs

for securing the most effective operation possible.

Product effectiveness includes all the elements for

45-4

REFERENCE

DATA

FOR ENGINEERS

securing at minimum cost a product with maximum

effectiveness. Programs for quality assurance contain

schedules and procedures that encompass within them

reliability, preventive maintenance, value engineering,

human engineering, quality control, inspection, and

tests that result in systems and products that will prove

most effective when in operation.

Quality Assurance (QA):

All those activities, includ-

ing surveillance, inspection, control, and documenta-

tion, aimed at ensuring that the product will meet its

performance specifications, Quality assurance generally

has an independent role from production and reports

directly to senior management.

Reliability Allocations:

With an overall system relia-

bility goal and where the confidence level is known,

reliability values may be allocated to every component

in the system by the use of available failure rates and

weighting factors.

Reliability Demonstration:

Critical tests must be

programmed to provide sufficient valid data to deter-

mine the reliability

of the system and all critical

component parts. Provision should be made for proc-

essing all such data as expeditiously as possible

speed

up all phases of the program with truly reliable

materials and parts.

Reliability Goals:

Requests for bids, specifications,

and contracts requiring quality assurance and reliability

generally describe completely the reliability goals. The

reliability of the system with specified confidence levels

is the principal goal. Values to be secured at specified

points in time are listed

the growth curves. A

reliability demonstration program is detailed to show

that the reliability goals have been attained. How are

such reliability goals expressed? The simplest statement

covers only an expected value. The quality assurance

paragraph

the specification will state simply: “The

desired reliability is 99.7%.” This is too simple, as the

length of the mission or number of cycles of operation

has not been detailed. The statement should be, “For

100

hours of operation the specified reliability is

99.7%.”

Many contracts also introduce confidence levels. For

example, after the initial design review, the reliability of

the system must be 99% with a confidence level of

0.60.

After qualifying, the system must have a reliability of

99.7% for a mission time of

hours with a confidence

level of 0.99. Thus expressed, this goal has within it a

final goal plus some information concerning the desired

growth curve

for reliability.

many programs, pros+

sion for the reliability demonstration program has not

been made, or in making final arrangements for the

finalized contract it is cancelled because

lack of

funds. The reliability engineer should establish a very

modest program to check the achievement of the

reliability goals by means of an economic reliability

demonstration program. Thus, it must be emphasized

that the simplest possible reliability demonstration test

should be made a part of the final program covered by

contract and funds. This provides vital evidence that the

reliability goals have been achieved and that the custom-

er reliability requirements have been met.

Reliability Growth Curves:

Periodic reports, such as

monthly or quarterly, should be prepared containing

up-to-date predictions of the system’s reliability. These

should be presented graphically

the reliability

growth curves for this system and its various compo-

nents and parts.

Reliability Predictions:

Many agencies and compa-

nies have compiled failure rates for parts, components,

subassemblies, assemblies, and systems. These generic

failure rates are used as basic data to predict a value for

reliability.

Sample:

One or more sample units selected at ran-

dom from a quantity of product to represent that

quantity of product for inspection purposes.

Sequential Sampling:

Sampling inspection in which,

after each unit is inspected, the decision is made to

accept, to reject, or to inspect another unit.

Note:

Sequential sampling as defined here is sometimes called

“unit sequential sampling” or “multiple sampling.”

Multiple sampling is preferred, to differentiate from

sequential testing.

SigniJicance Level:

The level of confidence (i.e., the

probability of being correct) at which a hypothesis, such

as “goodness of fit,” is to be accepted or rejected.

SpeciJication Limits:

The specification limit(s) is the

requirement that a quality characteristic should meet.

This requirement may be expressed as an upper or a

lower specification limit (called a single specification

limit) or both upper and lower specification limits

(called a double specification limit).

System (General):

A combination of parts, assem-

blies, and sets joined together to perform a specific

operational function or functions.

Examples:

Piping

system, refrigeration system, air conditioning system.

Test

Failure:

Testing conducted

one or more

items until a predetermined number of failures have

been observed. Failures are induced by increasing

electrical, mechanical, and/or environmental stress lev-

els, usually in contrast to life tests in which failures

occur after extended exposure to predetermined stress

levels.

life test can be considered a test to failure using

age as the stress.

Value Engineering:

One feature of a good reliability

program is a concurrent value engineering program.

Many programs include incentive provisions. If an

operation is usually expensive, provisions should be

made for a series of improvements that fall

with the

value engineering and incentive programs. Provisions

for successive cost reduction programs as well as basic

value engineering improvements should be added to

each contract. It may be made a part of the incentive

programs that are now usually included in military and

government contracts for procurement.

RELIABILITY

AND

LIFE TESTING

45-5

Weapon System:

A missile and all the necessary

support equipment (either ground or airborne) neces-

sary to launch and properly operate a missile.

Wear-out Period:

The wear-out period of an equip-

ment is that period of equipment life, following the

normal operating period, during which the equipment

failure rate increases above the normal rate.

RELIABILITY DEFINITIONS

Reliability is the probability that a given product,

system, or action will achieve its designated goal

successfully under the specified environmental condi-

tions and for a prescribed period of time or for the

number of cycles of operation required for the mission

or task.

Reliability involves three distinct concepts:

Attaining a specified level of performance

The probability of achieving that level

Maintaining that level for a specified time

ORGANIZATION FOR

RELIABILITY

Reliability

one of the disciplines that form the

assurance sciences. These disciplines govern the quali-

ty, safety, and dependability of a product throughout its

life cycle. Whereas many of the aspects

assurance

science, such as quality control,

are

aimed at ensuring

that a product has been manufactured within acceptable

limits, reliability is also related to aspects of design and

development, in that its objective is to predict and

assure an acceptable level of performance in service.

For this reason, provision must be made in the structure

of any manufacturing organization to integrate reliabili-

ty activities with the product evolution process.

There is no single answer to the question of where the

reliability function should exist in any organization. To

some extent, the solution depends on the form of

product and the organization itself. Comprehensive

discussions of organization for product assurance and

reliability are contained in References

and

Guid-

ance is also available from professional bodies. For

instance, the Institute of Electrical and Electronics

Engineers and the American Society for Quality Con-

trol have defined a structure as shown in Fig.

Today, reliability seems to fit most naturally into the

product-assurance or product-effectiveness section of

major space equipment manufacturers.

The most important organizational aspect is the fact

that reliability and well-versed quality personnel use

one tool which, when shared jointly, adds to the

“experience-retention” capability; that tool is statis-

tics. If the intent of any organization is to get the most

out

of the “fall of data,” the organization of Fig.

effective. Because of the problem of decision making,

reliability is best placed at the staff level.

In a small organization, reliability

usually shared

by engineering and by quality assurance. Some firms,

to better satisfy the requirements of the Department of

Defense, put reliability in the quality organization

spectrum of operations, viz.,

Quality and reliability assurance tasks

Data reduction

Planning

Inspection, etc.

Test plan

Vendor survey

Quality-control engineering

Reliability planning, to be effective, must fit into the

total program. One of the best ways to gain acceptance

of the reliability or maintainability effort is to establish

PRESIDENT

DIRECTOR LEVEL

Fig.

Typical organization chart showing

reliability chain

responsibility.

++lfl+l

ENGINEERING PRODUCTION

MANAGER

RELIABILITY ENGINEERINC

45-6

REFERENCE DATA FOR ENGINEERS

a proper sequence for its insertion into a master

operating plan. For companies without a particular

project, this plan usually is discussed with the engineer-

ing head and the production head. For corporations

working on a program that requires reliability by

specified intent, the customer invariably requires a

reliability plan. The major items (or task delineators) in

a reliability plan are noted in Chart

In the plan itself, the time relationships of the tasks to

reliability and overall project tasks are noted as mile-

stones. Some of these milestones are then placed

more sophisticated PERT* or CPM? charts for manage-

ment review of major effort.

The recognition of reliability as an integral part of

product performance is more than simply a matter of

early prediction of in-service behavior. It also identifies

a number of major economic and safety implications.

The realization that failures are inevitable adds an extra

dimension to conventional design, consideration being

given to the consequences of failures and actions which

must be taken to mitigate them. One possible action, for

instance, is

provide redundant or standby systems.

Others are to give early attention to availability (the

percentage of time a system is in a working state) and

maintainability (the average time required to repair a

system after failure).

Alternatively, potentially catastrophic failures can be

prevented by designing in deliberate weak links, such as

fuses or breakers that cause the system to fail prema-

turely in a safe manner (“fail-safe” design).

None of the above actions can be implemented unless

product development and the reliability assessment

program are closely coordinated. In the case of complex

systems, for which high reliability must be achieved, the

required performance in service may be impossible to

obtain without conscious design for reliability.

ELEMENTS OF RELIABILITY

ASSESSMENT

Reliability assessment, rather than occupying one

place in product development, is involved in a more or

Program Evaluation and Review Technique.

‘f

Critical Path Method.

less continuous basis from the early conceptual stages

through to the monitoring of service performance. As a

result, reliability analysts may be called on to take part

in the following activities:

Design reviews

Failure mode analysis

Quantitative reliability assessment

Failure data collection and assessment

Design Reviews

Several reviews

a system design are performed,

usually by an interdisciplinary team of designers, pro-

duction engineers, safety and reliability analysts, and

others. The objectives are generally to ensure that the

product is capable of meeting performance require-

ments, conforms with necessary standards, optimizes

production facilities, and contains no unanticipated

flaws. Guidelines for performing a design review have

been set

out

in Reference

These emphasize careful

documentation and the use of check lists prepared from

past experience to ensure coverage of all relevant

factors. The list of reliability terms at the beginning of

this chapter gives a brief description of three common

design reviews.

Failure Mode Analysis

An essential step in controlling reliability is a full

investigation of all potential failure mechanisms and

their causes, effects, and possible consequences. This is

largely a qualitative exercise aimed at finding out what

may happen, rather than how often, but it forms an

essential foundation for all subsequent quantitative

analysis. In fact, there are many instances where

more important

have all the failure modes identified

than to make accurate analyses of some while neglect-

ing others altogether. This task is known by a variety of

titles, one alternative being cause and effects analysis,

but the most frequently used name is failure modes and

effects analysis (FMEA). As

the case of design

reviews, FMEA is helped considerably by a systematic

approach using check lists and analysis sheets (See

Reference

for examples.) In addition, the sequential

structure of many forms of failure can be used to

identify the failure itself, using logic diagrams or

CHART

TASK

DELINEATION

Program plan update

Education and manuals

Apportionment

Models and prediction

Cost-effectiveness analysis

Human factors

Stressistrength analysis

Design review

Design

specified reliability and maintainability

Failure modes and effects analysis

Change and configuration control

Reports and project review

Corrective action control

Supplier control

Manufacturing reliability and maintainability control

Failure diagnosis

Data acquisition and reduction

Verification

Summary

References

45-7

MITIGATING SYSTEMS

SUCCESS

HAZARD

CONSEQUENCES

Fig. 2.

A simple

event

tree.

FAILURE

decision trees. Two of the many variants available are

shown in Figs.

and

Fig.

illustrates an event tree.

This type of diagram is commonly used to map the end

results of a sequence of safety device operations. Each

branch point represents two possibilities, e.g., “device

operates” or “device fails to operate.” The event tree

starts from an initiating event and progresses forward

through subsequent events

a final state which may or

may not be a significant failure state for the system. It is

capable of pointing to undesirable event sequences

which might not be identified by a less systematic

approach. Unfortunately, event trees tend to generate

many spurious branches and rapidly reach unmanagea-

ble proportions. Their main use is in mapping sequenc-

es where there is a clear chain of events, for instance, as

in certain human operations (see Reference

3).

The most common form of diagram is the fault tree

(Fig.

3).

This diagram employs a top-down logic,

expanding out from a known end result to identify

events, or combinations of events, that lead to failure.

Fault trees use the same conventions for logic gates that

EVENT

AND

D OR

Fig.

simple

fault

tree.

ABC

AB?

ABC

--’

are used in logic-circuit theory. They are not confined

to only two branches at each branch point as is normally

the case in event-tree construction.

theory, there is a

problem with fault-tree analysis, in that the top event

must first be identified by some other means. In

practice, it is usually possible

identify failure events

at a sufficiently high level to ensure exhaustive coverage

of all possibilities. For instance, the top events for

reliability analysis of a radio receiver would include:

Fail to operate at all

Fail to receive any signal

Fading or hunting reception

Drift

Excessive interference and noise levels

More detailed failure mechanisms can then be identi-

fied within each category, on the next lower level of

detail. Fig.

is a partially developed fault tree for the

top event, “fail to operate.” To illustrate the technique

more fully, it has been assumed that the receiver is

powered from a mains (power-line) supply with an

automatic switching backup battery. This diagram is by

no means complete.

Fault trees can grow rapidly beyond easy manipula-

tion by hand, and, for formal analysis, it is advisable to

resort to computer codes, of which several are currently

available for fault tree analysis. (See Reference

for an

extensive summary of currently available software.)

a less formal level, the fault tree is an extremely useful

aid in that it imposes a disciplined approach to the

problem of failure-mode identification and it provides a

structure whereby details of potential failures can be

recorded in a sequential manner, without getting lost in

the process.

addition to identifying individual events that lead

to failure, a fault tree also contains the logic governing

the necessary sequences of events that lead to failure.

These sequences are known as “cut sets.”

Fig.

any one of the combinations

and

G, or

and

is a cut set.

more complicated

problems, the cut sets may be very complex themselves,

and not necessarily independent of one another. It can

be shown that cut sets can be reduced to an equivalent

set of minimal independent requirements for failure

called “minimum cut sets.” Two simple examples are

shown in Fig.

Fig.

5A,

four events,

and

45-8

REFERENCE

OPERATE

011’

POWER

FAILURE

FAIL

OPERATE

WIRING FAULT

OPEN

CIRCUIT

F=Q+R+S

L*M+N+P+H+J.B

=(A+B+C)(D+ETG)+J*B+N+P+H

=A-[D+E-

B.(D+E+

+J)

ID +E+

(N+P+

Fig.

Fault tree for radio-receiver failure mode “fail to operate

demand.”

contribute to some failure event

Combining these

events by the rules of Boolean logic algebra,

occurs if

and

occur. These

sequences are cut sets and, in this case, minimum cut

sets.

In Fig. 5B, a similar fault tree contains a common

element

in both branches. In this case, the top event,

Y, is only dependent on the occurrence

and

Here,

represents an important class of failures called

“common mode” or “common cause” failures. It can

be easily seen that if

and

all have similar

probabilities of occurrence,

has a much higher

probability of occurrence that

because it only re-

quires a single event instead of two simultaneous events.

Failure

identify common modes or dependencies

between different failure mechanisms is a frequent

cause of excessively optimistic reliability predictions. It

can be seen from the above simple example how fault

tree analysis can be used to avoid this problem.

Quantitative Reliability

Assessment

Quantitative reliability assessment

one of the most

important tasks of the reliability analyst. Reliability

quantification covers two dimensions-probability of

occurrence and magnitude of the consequence of fail-

ure. Assessment of failure consequence is probably

more the task of design. Nevertheless, it cannot be

neglected in reliability assessment, particularly when

assigning reliability targets, or allocating reliability to

subsystems. Intuitively, it seems sensible to assign a

higher reliability target to a subsystem with potentially

catastrophic failure consequences than to one that

involves only a degradation in performance.

Consequences of failure can be extremely difficult to

estimate.

the preliminary stages

development, a

useful technique is called worst-case analysis. It takes

the most pessimistic values of all parameters, regardless

of the likelihood of this occurring. In electronic cir-

cuits, for instance, all components are assumed to be at

the extreme limits of their tolerance bands, including

any drift due to environmental factors. By this proce-

dure, it is possible to identify undesirable modes of

operation that might not be considered possible other-

wise. The detection of potentially catastrophic modes

of failure is probably the most useful outcome of this

type of analysis. Regardless

their likelihood, failures

of this type may require designing out of the system

completely. It is only in those cases where the cost of

failure can be reasonably balanced against the cost of

RELIABILITY AND LIFE TESTING

45-9

EVENT

AND

Pr(A)=A-C+A.D

+B.C+

B.D

PrlA) =Pr(B) =PIC =Pr(DI

PrIXl +Pr(AI*Pr(C)

+Pr(AI.Pr(D)+Pr(B).PrlC)

+PrlB)*Pr(D)

=4~10-~

(A)

Independent euents.

Y=A-B+A.C+B.C-B

=A*C-B

PriM=2xlO-4+10-

2-10-2

Pr!W

PrlX)

(E)

Dependent events.

Fig.

Calculation of

event

probability.

improved design that the question of probability of

occurrence becomes important.

The area of quantification most closely identified

with the reliability analyst

the assessment of failure

probability. This is a natural result of defining reliabili-

ty in probabilistic terms.

wide range of mathematical

techniques have been developed in the general fields of

probability and statistics, supplemented with methods

specifically directed toward reliability modeling. These

metho$ will be reviewed in a special section later in

this chapter.

Failure Data Collection and

Assessment

The collection of failure data is part of a continuous

feedback loop that is essential to reliability growth. The

process begins in the early stages of product develop-

ment, where failures are likely to be common due to

design faults and as yet uncontrolled production proc-

esses, and extends through to collection of data under

normal service conditions. The reliability analyst

should be closely involved in this process.

addition to

receiving basic failure-rate data from this source, the

reliability analyst also has an active role in evaluating

failure reports, assessing whether the failures are ran-

dom or represent a significant deviation from expected

conditions, providing backup to quality control, and

offering recommendations for remedial action.

For failure analysis to be successful, the data collec-

tion system must be carefully designed and controlled.

Considerable thought has been given to this problem in

recent years, and a mmber of reporting systems have

been developed.

comprehensive review of data banks

and their methods of operation is contained in Refer-

ence

Some of these are appropriate models for

in-house reporting systems. This subject will be dis-

cussed further in a later section of this chapter on

sources of data. One reporting system of particular

relevance to integrated circuit reliability was developed

by Lockheed Corporation on behalf of

NASA

(Refer-

ence

5).

This report is both an excellent source of

information and a model for setting up an in-house

reporting and analysis system.

COMPONENT RELIABILITY

population of components

test or

service

under nominally similar conditions will decrease in

time as a result of failures as shown in Fig.

The

numbers failed and surviving after time

are

Nkt)

and

N,(t),

respectively. For a sufficiently large population

number

the relative frequencies represent the cumu-

lative probability of failure and the probability

survival (Le., the reliability), respectively:

$(t)

Nht)/N

B(t)

N,(t)/N

TEST TIME TO FAILURE.

Fig.

Cumulative

failure distribution

and

reliability

plots

for

test

with

samples-experimental

and

theoretical

curves

shown.

REFERENCE

DATA

FOR ENGINEERS

010

002

008

006

004

TEST TIME

FAILURE,

Fig.

Failure probability density derived from Fig.

tends to infinity, estimates

and

tend to

the true failure and reliability functions,

F(t)

and

R(t).

Here, and subsequently in this chapter, a “hat”

(*)

will

be used to represent an estimate of a random variable.

These functions are shown also in Fig.

By differenti-

ating

Fa),

the probability density function of failures,

f(t),

is obtained (Fig.

7).

This represents the relative

frequency of failures with respect to the original popula-

tion. Three zones can be identified in this figure. They

are an initial period of high failure density, correspond-

ing to initial manufacturing defects, an intermediate

period of relatively low failure rate, where the only

cause is external and random, and a final peak of high

density corresponding to wearout or material deteriora-

tion. These zones can be more readily distinguished by

calculating the instantaneous failure rate, or hazard

rate,

h(t),

which is the failure rate expressed as a

proportion of the population surviving at time

f(t)/[l

FMl

The hazard rate has a characteristic shape, illustrated

in Fig.

known as the “bathtub curve.” Here, initial,

or burn-in, failures; random failures; and wearout

failures are clearly identified by having decreasing,

constant, and increasing hazard rates, respectively. This

characteristic of the hazard rate is an important diag-

nostic tool, as will be demonstrated later in this chapter.

It can be shown (see Reference

for details) that

Knowing the hazard rate, e.g., from life tests, permits

the reliability function,

R(t),

to be calculated.

0 10

0 08

006

004

0 02

TEST TIME

FAILURE,

Fig.

Hazard rate for

data

given

Fig.

In electronic components, it is common practice to

require a burn-in test period that, as far as service

performance is concerned, effectively removes the ini-

tial stage of the hazard rate. It is also generally assumed

that stress levels have been

chosen in design that there

is little likelihood of the occurrence of wearout failures.

Under these conditions, it is reasonable to use a

restricted version of reliability theory that assumes a

constant hazard rate and is relatively easy to manipulate

mathematically. In fact, the majority of formal reliabili-

ty theory is based on the constant-hazard-rate model

(sometimes referred to loosely and erroneously in much

of the literature as a “constant-failure-rate” theory). In

this model,

h(t)

constant

R(t)

F(t)

exp(

-At)

This is the so-called exponential distribution, a special

case of the Poisson distribution.

In many cases, one is interested only in high compo-

nent reliabilities, in which case there is a simple

approximation. That is,

1, 1

F(t)

R(t)

Where the simple models discussed above are not

valid, other more complex distributions must be used.

Table

summarizes some of the more commonly used

distributions. In choosing a particular distribution,

there is sometimes a degree of rationale, based on the

physics of the problem. More often, however, the

choice is empirical

as to best fit the availabk data.

One distribution of predominant interest in reliability

studies is the Weibull distribution (see Table

1).

This

distribution has some justification in that it is one of a

class of extreme distributions, Le., distributions of

extreme values of groups of components. Its main

RELIABILITY AND

LIFE

TESTING

45-1

TABLE

1. LIST

COMMON FREQUENCY DISTRIBUTIONS

Name

Binomial

Poisson

Normal

Lognormal

Student-t

Gamma

Exponential

Weibull

Chi-square

MasdDensity Function

Mean

exp(p

22/21

attribute is its ability

represent any one of the three

zones in the bathtub curve (Fig.

by choosing the

shape parameter,

be less than, equal to, or greater

than unity (see Fig. 9). This property of the Weibull

distribution will be shown later to be a useful method of

evaluating service data.

SYSTEM RELIABILITY

System reliability can be dealt with in two different

ways, depending on the advancement of the project.

In the early stages of making a bid, the evzntual

configuration will not be known precisely, but a relia-

bility estimate is required for the purpose of making the

proposal. This estimate is inevitably crude and must

draw on previous experience and generic data for its

quantitative basis. The simplest approach, once the

number and types of components are known approxi-

mately, is to assume the individual failure rates to be

additive:

The system reliability,

R,(t),

is obtained as

R,(t)

exp(-A$)

This

simple approach can also be used

reverse to

assign component reliabilities

as to achieve a target

system reliability that may have been set as a design

requirement.

Illustrating this simple method, if an

assembly is made up of two components of equal weight

and is to have an end reliability of 0.99, then each

component should have a reliability of at least 0.995.

The product 0.995

0.995

0.990025. If the

assembly

made up of three units of equal weight, then

each should have a reliability of 0.997, since (0.997)3

0.991026973, The same procedure is used even if the

parts have widely different importance and hence ex-

tremely different reliability values.

Formalized variants of this approach are given in the

AGREE report (Reference

and in a more recent

version in Military Handbook MIL-HDBK-217B (Ref-

erence 7).

The AGREE report uses a more complex method,

detailed on pages 192-195 of Reference 18. The

AGREE report cautions against the use of its method for

items of low importance. Its basis is the complexity of

the units rather than their failure rates. Consideration is

given to the number of hours the jth unit will be

required to operate in

system hours and the total

number of modules in the system. The importance

factor of each unit must also be considered. All units do

not operate the same length of time; hence, these times

of operation must be considered, and many of these

values will be less than

hours. The AGREE report

gives the allocated rate of the jth unit as

nj[-logR*(T)]/EjtjN

This is used in many instances

allocate reliabilities

among the components.

MIL-HDBK-2 17B describes two methods of failure-

rate prediction, "part stress analysis" and "parts

count." The latter is the simpler of the two, and more

appropriate to early design and bidding.

For

full

expla-

nations, reference is made to the handbook itself and to

an expanded explanation in Reference 1. A parts count

failure rate prediction lumps components into generic

part types and assigns part quality levels to each type.

The inputs are therefore

Generic part types

Quantities of parts in each type

Part quality levels

Equipment environment