**DATA ITEM DESCRIPTION**

**Title:** Reliability Block Diagrams and Mathematical Model Report

**Number:** DI-RELI-81496 **Approval Date:** 30 Oct. 1995

**AMSC Number:** N7166 **Limitation:** N/A

**DTIC Applicable:** No **GIDEP Applicable:** No

**Office of Primary Responsibility:**

**Applicable Forms:** N/A

**Use/relationship:**

This report documents data used to determine mission reliability and
support reliability allocations; predictions, assessments, design
analyses, and trade-offs associated with end items and units of the
hardware breakdown structure.

This data Item description contains the format and content preparation
instructions for the data product generated by the specific and discrete
task requirement as delineated in the contract.

This DID is applicable during the Mission Analysis, Investment Analysis
and Solution Implementation phases.

This DID suspends DID DI-R-7094

This DID is not applicable to the production phase unless warranted by
significant design changes associated with improvement programs.

Defense Technical Information Center (DTIC), Cameron Station, Attn:

DTIC-FDAC, Alexandria, VA 22304-6145.

**Requirements:**

[Content:]{.underline} This report shall include reliability block
diagrams, mathematical models, and supplementary information suitable
for allocation, prediction, assessment, and failure mode, effects, and
critically analysis task related to the end item and units of hardware
breakdown structure. The report shall contain sufficient detailed
information to preclude separate special effort, modification, or
adaptation of the diagrams or models for other reliability tasks.

The type of reliability model (mission reliability or logistics
reliability) and the modeling method shall be identified in the report.

[Reference designation list.]{.underline} The report shall include a
reference designation list when warranted by item complexity. The list
shall be provided when block diagrams include elements which require
correlation between block diagram reference numbers, hardware break down
structure identification, Work Unit Code (WUC) identification numbers,
or location of specific elements on a diagram set and or sheet. The list
shall be a composite cross-reference and item element locator (both by
name and designation).

[Excluded equipment list:]{.underline} An excluded equipment list which
describes item elements not shown on the block diagram shall be
included. Rationale for each item exclusion shall be provided.

[Conclusions and recommendations.]{.underline} The report shall contain
contractor conclusions and recommendations based upon the data
developed. Contractor interpretation and comments concerning diagrams,
models, and concerns of action to resolve reliability problems shall be
included. Consideration should be given to data deficiencies, Government
Furnished Equipment (GFE) problems, tradeoffs, assumptions, risks,
interpretations affecting reliability planning, qualitative or
quantitative information affecting the program, and other pertinent
factors related to the diagrams or models.

[Item Coverage.]{.underline} Reliability block diagrams shall represent
the item specification and be segmented to represent variables such as:
mission type, mission phase, functional mode(s) of operation, duty
cycle, stores mix, maintenance concept, or other factors. Block diagrams
developed for feasibility purpose shall include separate models
reflecting differing reliability requirements, hardware configurations,
and mission application. When complexity warrants, charts, tables or
other methods may be used to indicate which segments, diagrams, or sets
of diagrams apply to specific mission(s) or other variables.

[Government furnished equipment (GFE), Non-developmental Items (NDI),
and Commercial Off the Shelf equipments (COTS)]{.underline}. Reliability
block diagrams shall include and identify blocks representing GFE, NDI
and COTS items. Information shall be included to reflect the integration
of designated GFE, NDI, and COTS into the design.

[Alternative configurations.]{.underline} The report shall include block
diagrams prepared during feasibility estimation to compare alternative
configurations or design concepts.

[Diagram partitioning.]{.underline} Reliability block diagrams shall be
partitioned to agree with the hardware breakdown structure of the end
item. Partitioning shall provide diagrams for each end item subdivision
which reflect and emphasize interfaces with the next smaller units of
the breakdown structure. In this manner, the block diagram consists of a
series of models which are logically derived and capable of being
combined to any level of hardware complexity (see sample provides as
Figure 1).

[Diagram interfaces.]{.underline} Bloc diagrams included in the report
shall indicate interfaces both external to the physical boundary of the
item and internal to the item. An interface may be functionally
dependent on another item(s) and vice versa, or one which is
functionally independent of other items but is an element of a higher
level model. Particular attention should be paid to interfaces of
functional significance including GFE, NDI, and COTS. Interfaces shall
be consistent with end item specification, intended purpose, mission
use, or higher order functions when the item is used in conjunction with
other items.

[Assumptions.]{.underline} All assumptions relating to the reliability
block diagrams shall be documented in the report. The assumptions shall
included technical assumptions prepared as part of the diagram statement
of conditions and general assumptions for diagram interpretation, and
report completeness or reliability understanding. Assumptions shall be
consistent with the phase of item definition. Typical assumption
considerations include:

a.  Service use profile, mission profile, environmental profile

b.  Operational and maintenance concepts and requirements

c.  Item data deficiencies

d.  Redundancy, alternate modes of degraded operation

e.  Tradeoff considerations

f.  Human reliability

g.  Software reliability

[Functional level diagram option]{.underline}. When information is
limited in the early phase of item development, functional level black
diagrams shall be constructed. Diagrams constructed at this level shall
contain blocks representing the lower identifiable functions consistent
with item definition.

[Reliability block diagrams]{.underline}.

[Redundancy.]{.underline} The report shall include redundant
configurations identified during redundancy studies, allocations, or
tradeoff studies related to item reliability improvement. Reliability
problems leading to the inclusion of redundant elements shall be
identified. The degree, level, and other features related to redundant
elements included in block diagrams shall be identified. Additional
information describing redundancy features not obvious from the block
diagrams shall be included. Typical redundancy considerations include:

a.  Level (e.g., subsystem, part)

b.  Type (e.g., automatic, switch able, alternative mode)

c.  Element monitoring (e.g., continuous, interval monitored)

d.  Rational (e.g., repair without downtime, prolong operating life)

e.  Alternatives with/without redundancy

f.  Elements which can be checked

g.  Elements which can be inspected

h.  Elements whose failure stresses alternate path elements

i.  Elements whose failure degrades performance

[Automatic test equipment]{.underline}. Reliability block diagrams shall
include and identify Automatic Test Equipment (ATE) for online testing
peculiar to the item to permit reliability impact assessment. Built-in
test equipment (BITE) shall be diagrammed to show function(s) being
tested. When BITE is diagrammed separately, interface points shall be
included at blocks being tested to reflect sensor isolation or other
elements which degrade its reliability. BITE usage of item elements as
part of test equipment, features incorporated to detect or predict
impending failure and features which interrupt the normal operational
function shall be identified. ATE which is separate from the item shall
be diagrammed in a similar manner when it is included in the same
specification. Source of ATE reliability requirement, either as part of
item requirement or as a separate requirement shall be identified.

[Mathematical models.]{.underline} Reliability mathematical modes shall
reflect the level of detail incorporated into bloc diagrams and be
suitable for use in allocation, feasibility estimations, and prediction.
Each block in the diagram shall be flexible to accommodate substitution
of model parameter values of calculation of item subdivision reliability
and to permit changes in failure rate and repair time distributions or
any other factors consistent with assumptions and configuration
alternatives.

[Item coverage]{.underline}. Reliability mathematical models shall
represent the item specification and be organized consistent with the
reliability block diagram. Charts, tables, or other methods may be used
to indicate which equation, model, or sets of models apply to specific
mission(s) or other variables. The method used shall be the same used
for block diagrams, and may include provisions for both the diagram and
mathematical model.

[Mathematical symbols.]{.underline} Mathematical models shall use
symbols, terms, expressions, notations, or other elements of the
reliability equation consistent with the block diagram and reference
designation list (see 10.1.2 of this DID). The report shall identify and
define each separate constant, variable, or other element of the
mathematical equation(s) represented by mathematical shorthand,
alpha-numeric designators, or other methods.

[Assumptions.]{.underline} All assumptions relating to development and
preparation of mathematical models shall be documented in the report.
The assumption may be included with block diagram assumptions (see
10.1.8 of this DID). Assumptions shall include those necessary for model
interpretation, model completeness, and model clarity. The assumptions
shall be consistent with reliability block diagram assumptions and phase
of item development. Typical assumption considerations include:

a.  Frequency distributions (failure rate, time to repair)

b.  Mathematical approximations

c.  Statistical techniques

d.  Single mode/multimodal failure

e.  Wear out factors/characteristics

f.  Failure independency

g.  Operating time

[Numerical results]{.underline}. Reliability mathematical models based
upon approximations, truncations, or other factors which affect
numerical results of item reliability or maintainability shall be
identified.

[Computer programmed model.]{.underline} The report shall contain a
summary description of Computer Program Models including programming
approach, essential data required for operation, program verification,
operational details, etc.

[Alternative configurations.]{.underline} Mathematical models shall have
provisions for computation of alternative configurations when the block
diagram includes alternatives.

[Reliability mathematical model.]{.underline}

[Reliability mathematics]{.underline}. Reliability mathematical models,
depending upon the phase of development, configurations, or other
factors may utilize various techniques (e.g., classical reliability,
Boolean algebra, etc.) for use in the analysis, calculation, and
presentation of item reliability. The possibility of misinterpretation
of the reliability mathematical model and its mathematics shall be
minimized by the inclusion of supplementary information in the report.
Supplementary information necessary for proper understanding and use of
the model shall be included when specific method(s) of mathematics
employed extend beyond the basic rules, practices, and procedures of
reliability mathematics (e.g., rules of Boolean algebra, classical laws
of reliability, etc.). Truth tables, Boolean matrices, Karnaugh maps or
other reliability mathematical techniques used in the development or
presentation of item reliability as mathematical equation shall be
included in appendices of the report. Operations for series, parallel,
series-parallel, parallel-series redundancy or combinations thereof may
be included as part of higher order item equations or included
separately in appendix. Mathematical derivations for complex redundant
configurations (network, T-bridge, lattice, etc.) shall be included in
an appendix. The use of multimodal (e.g., open, short, tolerance) or
single mode redundancy analysis in the mathematical model shall be
consistent with the reliability block diagram.

[Format.]{.underline} Contractor format is acceptable.

**See Block Diagram Below**

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