# Washing Machine Hazard Rate Problem

• e(ho0n3
In summary, the hazard rate function, h(t), is used to calculate the probability of a washing machine failing after t years. The conditional probability of the washing machine failing within the next two years is the sum of h(6+t) as t varies from 0 to 2. However, since h(6+t) is greater than 1, the correct approach is to use the formula P{X < 8|X > 6}, where X represents the number of years the washing machine has survived.
e(ho0n3
Homework Statement
The number of years that a washing machine functions is a random variable whose hazard rate function, h(t), is given by

- 0.2 if 0 < t < 2
- 0.2 + 0.3(t - 2) if 2 <= t <= 5
- 1.1 if t > 5

If the washing machine is still working six years after being purchased, what is the conditional probability that it will fail within the succeeding two years?

The attempt at a solution
My interpretation of h(t) is that it is the probability that the washing machine will fail given that it has worked for t years.

The answer to the problem, I reckon, is the sum of h(6 + t) as t varies from 0 to 2. Since 6 + t > 5, then h(6 + t) = 1.1 by the def. of h. Integrating, I get 2.2. This must be wrong since probabilities are <= 1. Where did I go wrong?

The solution in the book states that the answer is P{X < 8|X > 6}. What is X here? I guess it represents the number of years the washing machine has survived. This makes sense.

Why didn't my original idea work? It seems perfectly legit. to me.

## What is the "Washing Machine Hazard Rate Problem"?

The "Washing Machine Hazard Rate Problem" is a statistical problem that examines the failure rate of a washing machine over time. It looks at how likely a washing machine is to break down or fail after a certain amount of usage.

## Why is the "Washing Machine Hazard Rate Problem" important?

The "Washing Machine Hazard Rate Problem" is important because it helps manufacturers and consumers understand the reliability and durability of washing machines. It can also be used to inform maintenance schedules and warranty policies.

## How is the "Washing Machine Hazard Rate Problem" calculated?

The "Washing Machine Hazard Rate Problem" is typically calculated using a mathematical model called the Hazard Function, which takes into account the number of failures, the time period in which they occur, and the total number of units being tested.

## What factors can affect the "Washing Machine Hazard Rate Problem"?

There are several factors that can affect the "Washing Machine Hazard Rate Problem", including the quality of the washing machine's components, the frequency of use, and the maintenance and care of the machine.

## How can the "Washing Machine Hazard Rate Problem" be used in real-world applications?

The "Washing Machine Hazard Rate Problem" can be used by manufacturers to improve the design and quality of their products, and by consumers to make informed decisions about which washing machines to purchase. It can also be used by insurance companies to determine rates for appliance coverage.

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