Testing Fault Matrix

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Testing Fault Matrix
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Testing Boolean Differences (from Design and
Analysis of Fault Tolerant Digital Systems by
Johnson)

• Algebraic method for developing test patterns for
  combinations circuits
• Limited use
• A switching function needs to be developed
• Computationally intensive
• A method to determine the primary inputs required
  to force a function to be sensitive to a
  particular input variable

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Testing Boolean Differences

• The Boolean difference of a function
• If , the function is completely
  independent of the input xi
• If , the function depends directly on
  the value of xi.
• Appropriate specification of
  can force to be 1.

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Testing Boolean Differences

• Example

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Testing Boolean Differences

• If x1 1 or x2 0, the value of f will depend
  on x3

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Testing Boolean Differences

• The use of Boolean difference to determine test
  patterns for faults that occur on primary inputs
  consists of two steps
• Primary input xi s-a-1, select xi 0. If the
  primary input xi s-a-0, select xi 1
• Select the remaining primary inputs such that the
  output is sensitive to the value of xi. Use
  Boolean difference
• for s-a-1 faults
• for s-a-0 faults

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Testing Boolean Differences

• Example
• Determine test patterns for s-a-0 and s-a-1
  faults on the primary input

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Testing Boolean Differences

• For s-a-0,
• Test patterns (x1, x2, x3, x4) (1100, 1101,
  and 1110)

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Testing Boolean Differences

• For s-a-1
• Test patterns (x1, x2, x3, x4) (0100, 0101, and
  0110)

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Testing Boolean Differences Internal to a
circuit

• Example

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Testing Boolean Differences Internal to a
circuit

• For s-a-1
• Test patterns 1000, 1100, 0100

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Testing Boolean Differences Internal to a
circuit

• For s-a-0
• Test pattern 0000

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Testing Boolean Differences Chain Rule

• If line k within a circuit depends on line m, and
  line m depends on line n, then the Boolean
  difference of k w.r.t. n can be written as
• In general,

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Testing Boolean Differences Chain Rule

• Example

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Testing Boolean Differences Chain Rule