## What is the 'Hazard Rate'?

The hazard rate refers to the rate of death for an item of a given age (x), and it is also known as the failure rate. It is part of a larger equation called the hazard function (denoted by {\displaystyle \lambda }), which analyzes the likelihood that an item will survive to a certain point in time based on its survival to an earlier time (t). In other words, it is the likelihood that if something survives to one moment, it will also survive to the next. The hazard rate only applies to items that cannot be repaired.

The hazard rate for any time can be determined using the following equation:

h(t) = f(t) / R(t)

f(t) is the probability density function, or the probability that the value (failure or death) will fall in a specified interval (for example, a specific year).

R(t) is the survival function, or the probability that something will survive past a certain time (t).

The hazard rate cannot be negative, and it is necessary to have a set "lifetime" on which to model the equation.

Next Up

## BREAKING DOWN 'Hazard Rate'

The probability density calculates the probability of failure at any given time. For example, a person has a certainty of dying eventually, which is the probability density. As you age, you have a greater chance of dying at a specific age, since the average failure rate is calculated as a fraction of the number of units that exist in a specific interval divided by the number of total units at the beginning of the interval.

If we were to calculate a person's chances of dying at a certain age, we would divide one year by the number of years that person potentially has left to live. This number would grow larger each year. A person aged 60 would have a higher probability of dying at age 65 than a person aged 30 because the person aged 30 still has many more units of time (years) left their life, and the probability is less that the person will die during one specific unit of time.

## When is the Hazard Rate Used?

The hazard rate is part of a wider branch of statistics called survival analysis, which predicts the amount of time until a certain event occurs, such as death or failure (as in failure of a mechanical structure). The concept is applied to other branches of research under slightly different names including reliability analysis (engineering), duration analysis (economics), and event history analysis (sociology).

RELATED TERMS
1. ### Yearly Probability Of Dying

Yearly Probability Of Dying is a numerical figure that depicts ...
2. ### Moral Hazard

Moral hazard is the risk that a party to a transaction has not ...
3. ### Survival Analysis

Survival analysis is a branch of statistics that studies the ...
4. ### Consumer Product Safety Commission ...

Consumer Product Safety Commission is a U.S. agency that protects ...
5. ### Valuation Mortality Table

Valuation Mortality Table is a statistical chart used by insurers ...
6. ### Normal Retirement Age (NRA)

The normal retirement age (NRA) is the age at which people can ...
Related Articles

### Moral Hazards: A Bump In The Contract Road

Learn how this phenomenon can cause a party in an agreement to behave differently than expected.
2. Investing

### Financial Forecasting: The Bayesian Method

This method can help refine probability estimates using an intuitive process.

### Estate Plans Should Include Instruction Manuals

Death is not something that we wish to dwell on, but estate planning—and figuring out even more basic issues—is something we definitely should not avoid.
4. Retirement

### Estate Planning for Beginners, Part Two

If you die without a will, what happens to your assets? Here's how the state you live in can determine who will inherit your money and belongings.
5. Investing

### Scenario Analysis Provides Glimpse Of Portfolio Potential

This statistical method estimates how far a stock might fall in a worst-case scenario.

### Will Raising the Retirement Age Save Social Security?

Social Security is the federal government’s biggest expenditure. Here's why raising the age of retirement may not be a bad idea to keep it afloat.
7. Retirement

### The Case for Collecting Social Security Early

While it may seem counterintuitive, sometimes it makes sense to claim Social Security early.

### Identifying and managing business risks

Running a business comes with a lot of associated risks, but there are an equal number of ways to prepare for and manage them to lessen their impact.
9. Investing

### Real Estate Flipping: 8 Disclosures You Must Make

If you don't tell potential buyers about these situations and possible hazards, you could find yourself in court. Here's how to profit – and stay out of trouble.
10. Retirement

### Why Early Retirement Is a Bad Idea

8 good reasons to put off your retirement date
RELATED FAQS

2. ### What is moral hazard?

Understand that moral hazard is the idea that a party protected in some way from risk will act differently than if they didn't ... Read Answer >>
3. ### What are the most effective ways to reduce moral hazard?

Discover when moral hazard occurs, what it means in different arenas, and effective tools for lenders, insurers, and employers ... Read Answer >>
4. ### How did moral hazard contribute to the 2008 financial crisis?

Learn about moral hazard, how it can affect outcomes and how it contributed to the conditions that led to the 2008 financial ... Read Answer >>
Hot Definitions
1. ### Economies of Scale

Economies of scale refer to reduced costs per unit that arise from increased total output of a product. For example, a larger ...
2. ### Quick Ratio

The quick ratio measures a company’s ability to meet its short-term obligations with its most liquid assets.
3. ### Leverage

Leverage results from using borrowed capital as a source of funding when investing to expand the firm's asset base and generate ...
4. ### Financial Risk

Financial risk is the possibility that shareholders will lose money when investing in a company if its cash flow fails to ...
5. ### Enterprise Value (EV)

Enterprise Value (EV) is a measure of a company's total value, often used as a more comprehensive alternative to equity market ...
6. ### Relative Strength Index - RSI

Relative Strength Indicator (RSI) is a technical momentum indicator that compares the magnitude of recent gains to recent ...