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Chapter 2: Problem 171

In circuit testing of printed circuit boards, each board either fails or does not fail the test. A board that fails the test is then checked further to determine which one of five defect types is the primary failure mode. Represent the sample space for this experiment.

Short Answer

Expert verified
Sample Space: \( S = \{ \text{Not Fail}, \text{Fail with Defect 1, 2, 3, 4, 5} \} \)

Step by step solution

01

Identify Possible Outcomes

Start by understanding the possible outcomes of the circuit test for each board. The board can either "fail" the test or "not fail" the test. These are two principal outcomes.
02

Consider Subsequent Outcomes for Failures

For a board that fails, there are additional factors to consider. After failure, the board is checked for one of five defect types. These types are Defect 1, Defect 2, Defect 3, Defect 4, and Defect 5.
03

Define Outcomes in the Sample Space

The sample space includes all combinations of the initial outcomes plus any subsequent outcomes. The outcomes are: a board "does not fail," or a board "fails" with Defect 1, Defect 2, Defect 3, Defect 4, or Defect 5 as the defect type.
04

Represent the Sample Space

List the complete sample space using set notation. The sample space is: \[S = \{ \text{Not Fail}, \text{Fail with Defect 1}, \text{Fail with Defect 2}, \text{Fail with Defect 3}, \text{Fail with Defect 4}, \text{Fail with Defect 5} \}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Circuit Testing
In the world of electronics, circuit testing is a crucial step to ensure devices operate correctly. It involves examining a printed circuit board (PCB) to determine if it meets performance standards. Circuit testing typically boils down to two outcomes: pass or fail. However, upon failure, further analysis is conducted to pinpoint the exact issue. This is crucial because knowing what went wrong helps in fixing the defect and improving future designs. The initial testing is a broad check, while successive checks after failure are more detailed, focusing on specific issues.
Printed Circuit Boards
Printed Circuit Boards (PCBs) are the backbone of nearly every electronic device. They provide the mechanical support to assemble electronic components using conductive pathways. PCBs are made up of conductive layers and non-conductive substrates. As the central hub for electronic components, any fault in a PCB can disrupt the entire function of the device.
Creating a reliable PCB involves several stages, from design to manufacturing. Each stage must be completed meticulously to prevent defects, making the detection of flaws through testing essential before a final product is shipped.
Defect Types
In circuit testing, defects are specific inconsistencies or errors found in the electronic components or board itself. Each defect type represents a different kind of failure, such as connection issues or incorrect component placement. This exercise identifies five types of defects, each indicating a specific error that requires unique corrective actions.
  • Defect 1: Conductive paths not connected.
  • Defect 2: Components are incorrectly placed.
  • Defect 3: Short circuits between nodes.
  • Defect 4: Open circuits within traces.
  • Defect 5: Component failure due to manufacturing defects.
Each defect type provides critical information to engineers, guiding necessary adjustments and improvements.
Outcome Analysis
Outcome analysis is pivotal in assessing the quality and functionality of circuit boards. This involves evaluating the testing results in the context of the sample space, understanding every possible outcome. In this exercise, outcomes include:
  • A board that does not fail
  • Failures identified with Defect 1 to Defect 5
Such comprehensive outcome analysis helps in identifying patterns of failure, contributing to improved design processes. It guides manufacturers in addressing systematic issues and optimizing future production, ensuring higher reliability and quality of electronic products.

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Most popular questions from this chapter

An injection-molded part is equally likely to be obtained from any one of the eight cavities on a mold. (a) What is the sample space? (b) What is the probability a part is from cavity 1 or \(2 ?\) (c) What is the probability that a part is from neither cavity 3 nor \(4 ?\)

A byte is a sequence of eight bits and each bit is either 0 or 1 (a) How many different bytes are possible? (b) If the first bit of a byte is a parity check, that is, the first byte is determined from the other seven bits, how many different bytes are possible?

A message can follow different paths through servers on a network. The sender's message can go to one of five servers for the first step; each of them can send to five servers at the second step; each of those can send to four servers at the third step; and then the message goes to the recipient's server. (a) How many paths are possible? (b) If all paths are equally likely, what is the probability that a message passes through the first of four servers at the third step?

A bin of 50 parts contains five that are defective. A sample of two parts is selected at random, without replacement. Determine the probability that both parts in the sample are defective.

A player of a video game is confronted with a series of four opponents and an \(80 \%\) probability of defeating each opponent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends). (a) What is the probability that a player defeats all four opponents in a game? (b) What is the probability that a player defeats at least two opponents in a game? (c) If the game is played three times, what is the probability that the player defeats all four opponents at least once?
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