SystemLevel Diagnosis: A Review

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System-Level Diagnosis A Review
Computer Science Department, University of Pisa

• Seminars for the PhD in Computer Science
• Stefano Chessa

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Faults, Errors and Failures

• Fault Abnormal physical condition
• caused by temperature, cosmic rays, design
  errors, age,
• Classified by
• Duration
• Transient, Intermittent, Permanent
• Nature
• Logical,
• Extent
• Error caused by a fault affecting information
• Failure system component unable to work
• caused by an error

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Redundancy Management

• Fault-Detection / Masking
• Information redundancy
• Parity bit, codes,..
• Hardware redundancy
• Duplication, n-modular-redundancy,..
• Fault-Diagnosis
• Computation redundancy
• Tests
• Diagnosis algorithms
• Repair and Reconfiguration
• Replacement / Repair
• Graceful degradation
• Recovery
• Set the system in a consistent state
• Backward and Forward recovery

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System-Level Diagnosis The PMC Model

• Introduced in 1967 by Preparata, Metze and Chien
• Consider a set V of units
• The units are connected by an interconnection
  structure
• This defines the system graph G(V,L)
• Units may be Faulty or Fault-Free
• Permanent faults
• Units perform mutual tests exploiting the system
  interconnections
• Test have binary outcomes
• The Syndrome is the collection of all the test
  outcomes
• This defines the test assignment and the
  diagnostic graph DG(V, E)

A System Graph and a Diagnostic Graph
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System-Level Diagnosis The Tests

• The test of unit v performed by unit u consists
  of three steps
• u sends a test input sequence to v
• v performs a computation on the test sequence and
  returns the output to u
• Unit u compares the output of v with the expected
  results
• The output is binary (0 passes 1 fails)
• requires a bidirectional connection
• Outcome g of the test performed by unit u on unit
  v (denoted as u v) defined according to the
  PMC model
• u v Tests performed in both directions
  with outcomes respectively d,g.

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System-Level Diagnosis Some Definitions

• Centralized diagnosis
• An external, reliable diagnoser
• Collects and decodes the syndrome by a diagnosis
  algorithm
• Distributed diagnosis
• The syndrome is decoded by a distributed
  algorithm
• Centralized Diagnosis
• Given a syndrome s, a consistent fault set (CFS)
  Vf is such that
• For each u? Vf, v? V Vf v u
• For each u,v? V Vf v u
• The goal of the diagnosis is to identify a CFS
  of minimum cardinality
• However, in general there are many CFSs with
  that property

V1 1,2,3 V2 3,4,5
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System-Level Diagnosis Some Definitions

• The diagnosis algorithm outputs sets K, F and S
• K units declared fault-free
• F units declared faulty
• S units declared suspect
• The diagnosis is correct if K? V Vf and F ? Vf
• The diagnosis is complete if S ? (K ? F V)

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System-Level Diagnosis Some Definitions

• One-Step t-diagnosable systems
• Correct and complete diagnosis for any Vf, with
  Vf?t
• t is the one-step diagnosability of the system
• For any syndrome, either
• There exists a unique consistent fault set of
  cardinality at most t OR
• The minimum cardinality of the consistent fault
  set exceeds t
• Sequentially s-diagnosable systems
• Correct diagnosis for any Vf, with Vf?s
• s is the sequential diagnosability of the system
• For any syndrome, either
• The consistent fault sets of cardinality ?s have
  a non-empty intersection OR
• The minimum cardinality of the consistent fault
  set exceeds s

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System-Level Diagnosis Three Problems

• Characterization problem
• Finding necessary and sufficient conditions in
  order to achieve the desired diagnosability in a
  system
• Diagnosability problem
• Given a test assignment for a system, determine
  its one step and sequential diagnosability
• Diagnosis problem
• Given a system, a test assignment and a syndrome,
  determine a consistent fault set of minimum
  cardinality

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The Characterization Problem

• Let nV, and d be the diagnostic graph indegree
• Necessary conditions for the one-step
  diagnosability PMC67
• n ? 2t1
• d ? t
• These conditions are sufficient if no two units
  test each other HA74
• A general characterization for one-step
  t-diagnosable systems is also given HA74
• n ? 2t1
• d ? t
• For each X?V, Xn 2t p, 0?p?t, X is tested
  by p1 units in N X

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The Characterization Problem

• Sequential Diagnosable Systems
• n ? 2t1 is a necessary condition PMC67
• There exists a general characterization HX95

A sequentially 3-diagnosable system
A one-step 2-diagnosable system
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The Diagnosability Problem

• One-step Diagnosability
• Firstly solved by Sullivan Sul84
• The best algorithm determines the one-step
  diagnosability in O(nt 2.5) RT91a
• Sequential Diagnosability
• The problem is Co-NP Complete RT91b
• The sequential diagnosability can be determined
  for several classes of graphs

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The Diagnosis Problem

• One-Step Diagnosis
• (with no restrictions) the problem is NP-complete
  MH76
• The problem is O(n 2.5) for t-diagnosable systems
  DM84
• Step 1 Constructs the L-Graph
• Vf is a minimum cover set of the graph (finding
  Vf is NP for general graphs)

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The Diagnosis Problem

• Step 2 Finds a maximum matching in the L-Graph
• Matches a fault and a fault-free unit
• Step 3 Visits the L-Graph starting from a unit
  not included in the matching
• The unit is fault-free
• Sequential Diagnosis
• (with no restrictions) sequential diagnosis is
  co-NP complete FK78
• A general heuristic O(E) have been proposed in
  Man80
• Many algorithms for several classes of graphs

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The BGM model

• Permanent faults
• Faulty units never produce the same (faulty)
  outcomes
• Sequential Diagnosis
• Diagnosis is trivial
• Sequential diagnosability is Co-NP Complete
  RT91
• One-Step Diagnosis
• Necessary condition t ? n 2 BGM76
• Sufficient conditions are also given BGM76
• One-step diagnosability O(nt 2/log t ) RT91

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The Comparison Models

• Tests performed by comparison of the output of
  adjacent units
• The comparator can be either internal to units or
  external
• Models with reliable comparators
• Two faulty units never produce the same outcomes
  Mal80
• Two faulty units may produce the same outcomes
  CH81
• MM81 the comparator is an external unit
  subject to faults

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Distributed Diagnosis

• Releases the hypothesis of a centralized and
  reliable diagnoser
• Firstly introduced in KR80
• The diagnosis is performed by a distributed
  algorithm
• Units perform test on adjacent units
• Units exchange diagnostic information with the
  neighbors
• Fault-free units accept diagnostic information
  only from fault-free neighbors
• Same invalidation rule of the PMC model
• Faults do not occur during diagnosis
• This hypothesis was released in KR81 When a
  unit u receives new diagnostic information from
  v, it tests v and accept the information only if
  v is fault-free
• Optimal diagnosis algorithm in terms of number of
  tests, messages and diagnosis latency RDZ95
• Other models will be presented in the forthcoming
  seminars

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Probabilistic Diagnosis

• Introduced in MH76
• Will be presented in the next seminar by Paolo
  Santi

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Applications

• Diagnosis of massively parallel systems
• A very large number of processing elements
• Regular interconnection structures
• Generally used for huge computations
• MTTF can be very small even if the single
  components are reliable
• Wafer-Scale Self-Test
• A large number of ICs
• ICs arranged in a regular pattern on the wafer
• A large number of faulty ICs
• Up to 50
• With the current test technology testing costs
  are increasing rapidly
• In the near future testing costs will
  exceedmanufacturing costs!!!

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Wafer Test State of the Art

• ICs tested by a test tool
• A probe station and a controlling computer
• The pads of each IC are probed by the probe
  station
• The probe station supplies the IC with power,
  ground and a test sequence
• The IC output sequence is delivered to the
  controlling computer
• The controlling computer compares the output
  sequence with the expected output sequence
• In alternative compares the IC outcomes with the
  outcomes of a golden unit
• Drawbacks
• ICs generally cannot be tested at full speed
• The test computer generally does not match the
  actual speed of ICs
• The test is generally not accurate
• Limited fault coverage, tests mainly electrical
  properties
• Time required to test an entire wafer
• ICs tested sequentially
• After each test the probing station should
  position the probes on the next IC
• The time to test an IC increases with its
  complexity

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Wafer Test State of the Art
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Wafer-Scale Self-Test

• The ICs perform mutual tests
• The tests may proceed in parallel
• The tests produce binary outcomes
• The test tool collects the syndrome and executes
  the diagnosis algorithm
• Advantages
• The ICs undergo an intensive test before they are
  cut and packaged
• saves the cost of packaging faulty ICs
• ICs tests executed at the operating speed of ICs
  (or to a comparable speed)
• improves test accuracy
• ICs tested in parallel
• reduces the time needed to complete the test

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Wafer-Scale Self-Test
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Wafer-Scale Self-Test Implementation Issues

• Requirements
• ICs Interconnection
• Comparators to perform comparisons
• number, placement,...
• Test vectors, clock, power and ground supply to
  all ICs
• Syndrome collection and diagnosis algorithm
• The diagnosis algorithm should be able to
  diagnose a large fraction of ICs under realistic
  fault situations
• A Naive implementation
• Large number of bus interconnections across the
  entire wafer
• The links would cross the ICs boundary
• Wafer-level synchronization
• Very complex and expensive design
• Therefore, for a feasible implementation we need
  to
• reduce the design complexity by minimizing the
  interconnections
• and
• release the hypothesis of wafer synchronization

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Conclusions

• The classical results of system-Level Diagnosis
  are unsuitable to diagnose large, regularly
  interconnected systems
• The most promising applications require regular
  interconnection structures
• For this reason
• Research has recently focused on diagnosis of
  regular systems
• The forthcoming seminars will address these topics