Reliability of a Machine A machine used in a manufacturing...

Name: Problem 28, Chapter 13: Algebra and Trigonometry
Uploaded: 2020-09-22T18:24:34-08:00
Duration: 2 min 38 s
Channel: Sam Sohn
Description: Reliability of a Machine A machine used in a manufacturing process has 4 separate components, each of which has a 0.01 probability of failing on any given day. If any component fails, the entire machine breaks down. Find the probability that on a given day the indicated event occurs. (a) The machine breaks down. (b) The machine does not break down. (c) Only one component does not fail.

Reliability of a Machine A machine used in a manufacturing process has 4 separate components, each of which has a 0.01 probability of failing on any given day. If any component fails, the entire machine breaks down. Find the probability that on a given day the indicated event occurs. (a) The machine breaks down. (b) The machine does not break down. (c) Only one component does not fail.

Reliability of a Machine A machine used in a manufacturing process has 4 separate components, each of which has a 0.01 probability of failing on any given day. If any component fails, the entire machine breaks down. Find the probability that on a given day the indicated event occurs.
(a) The machine breaks down.
(b) The machine does not break down.
(c) Only one component does not fail.

Key Concepts

Independent Events

This concept refers to events whose outcomes do not affect each other. In probability theory, when components operate independently, the occurrence or non?occurrence of failure in one component does not change the probability of failure in any other component. This principle is essential when calculating the overall system reliability when multiple independent components are involved.

Series System Reliability

A series system is one in which the overall system fails if any one of the components fails. The reliability of such systems is determined by multiplying together the probabilities that each individual component functions properly. This concept is key in understanding how the failure of any component can affect the entire system’s performance.

Complement Rule in Probability

The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring. This rule is particularly useful in reliability analysis, where it may be easier to calculate the probability that no failures occur, and then use the complement to determine the probability that at least one failure happens.

Binomial Distribution

The binomial distribution applies to scenarios with a fixed number of independent trials, each with the same probability of a specific outcome. It is used to calculate the probability of a certain number of successes (or failures) occurring within those trials. This concept is relevant when determining events such as exactly a certain number of components failing or not failing in a system.

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