# Reliability Glossary

## Reliability and Statistical Terms

**BX% life**

The time at which X% of the units in a population will have failed. For example,
if an item has a B10 life of 100 hours, then 10% of the population
will have failed by 100 hours of operation.

**Censored data**

Data in which not all of the data points represent exact failure times (e.g., there
may be operation times for units that have not failed). Censoring schemes include
right-censoring, left-censoring and interval censoring.

**Complete data**

Data that consists of only exact failure times.

**Conditional reliability**The probability that a product will successfully operate at a specific time interval given that it has operated successfully up to a specified time
(e.g., the probability that an item that has survived for 100 hours will
survive for an additional 100 hours).

**
Confidence bounds**

A measure of the precision of a statistical estimate. This is represented by a
range of values that the particular estimate should fall within a specified
percentage of the time. For example, if we perform ten different reliability
tests for our product and analyze the results, we will obtain slightly different
parameters for the distribution each time, and thus slightly different
reliability results. However, by employing confidence bounds, we obtain a range
within which these reliability values are likely to occur a certain percentage
of the time. This helps us gauge the utility of the data and the accuracy of the
resulting estimates.

**Cumulative distribution function ( cdf)**

A function obtained by integrating the failure distribution

*cdf*is equivalent to the unreliability function.

**Failure rate**

A function that describes the number of failures that can be expected to take
place over a given unit of time. The failure rate function has the units of
failures per unit time among surviving units (e.g., one failure per month).

**Fisher matrix**

A mathematical expression that is used to determine the variability of estimated
parameter values based on the variability of the data used to make the parameter
estimates. It is used to determine confidence bounds when using
maximum likelihood estimation (MLE) techniques.

**Hazard rate**

*
see Failure rate*

**Importance measure**

A measure of the relative contribution of a component’s contribution to the
overall system’s reliability. The importance measure of a component is
equivalent to the first partial derivative of the component reliability with
respect to the system reliability.

**Interval censored data**

Data that represents a range of time within which the unit is known to have
failed (e.g., it might be observed that a unit failed at some point
between 50 and 100 hours of operation).

**Kaplan-Meier estimator**

This is an estimator used as an alternative to the median ranks method for
calculating the estimates of the unreliability for probability plotting
purposes. It is also used to determine reliability estimates for nonparametric
data analysis.

**Left censored data**

A type of interval censored data where the
the failure is only known to have occurred before a specific time (e.g., it
might be observed that a unit failed at some point before 500 hours of operation).

**Life data analysis**

The statistical analysis of failure and usage data performed in order to be able
to mathematically model the reliability and failure characteristics of a
product.

**Likelihood function**

A function that represents the joint probability of all the points in a data
set. For complete data, the likelihood function consists of the product of the *
pdf* for each data point; for data sets that also include suspended or
censored data, the likelihood function is more complex. Maximum
likelihood estimation (MLE)
techniques maximize this function in order to determine the best parameter
estimates.

**Likelihood ratio**

The ratio of a likelihood function for an unknown parameter vector to the
likelihood function calculated at the estimated parameter vector. The
relationship of this ratio to the chi-squared distribution can then be used to
calculate confidence bounds and confidence regions.

**Maximum likelihood estimation (MLE)**

A method of parameter estimation involving the maximization of the likelihood
equation. The best parameter estimates are obtained by determining the parameter
values that maximize the value of the likelihood equation for a particular data
set.

**Mean Life**

A reliability measure that represents the expected value of the failure times
for a failure distribution, also known as the average or central life value.
While this represents a useful representative value of a distribution of failure
times, it is often over-used as the sole reliability metric.

**Median ranks**

Measures used to obtain estimates of the unreliability. Median ranks are the
values that the true probability of failure should have at the jth failure out
of a sample of N units, at a 50% confidence level, or the best estimate for the
unreliability. This estimate is based on a solution of the binomial equation.

**MTBF**

In the case of repairable systems, "MTBF" stands for "__m__ean __t__ime
__b__etween __f__ailures." This average time excludes the time spent
waiting for repair, being repaired, being re-qualified, and other downing events
such as inspections and preventive maintenances and so on; it is intended to
measure only the time a system is available and operating. Whereas, in the case
of non-repairable systems, MTBF stands for __m__ean __t__ime __b__efore __
f__ailure and is represented by the
mean life
value for a failure distribution of non-repairable units.

**MTTF**

"MTTF" stands for "__m__ean __t__ime __t__o __f__ailure" and is
represented by the
mean life
value for a failure distribution of non-repairable units.

**Probability
**
A quantitative description of the possible likelihood of a particular event.
Probability is conventionally expressed on a scale from 0 to 1, or 0% to 100%,
with an unlikely event having a probability close to 0 and a very common event
having a probability close to 1.

**Probability density function ( pdf)**

A mathematical model that describes the probability of events occurring over time. This function is integrated to obtain the probability that the event time takes a value in a given time interval. In life data analysis, the event in question is a failure and the

**Quality**

A common buzzword referring to the non-quantifiable point-level excellence of a
product or process. While sometimes used interchangeably with the term
reliability, quality refers to the characteristics of a product at one point in
time, while reliability refers to the
characteristics of a product over its entire lifetime.

**Reliability**

The probability of an item operating for a given amount of time without failure.
More generally, reliability is the capability of parts, components, equipment,
products and systems to perform their required functions for desired periods of
time without failure, in specified environments, and with a desired confidence.

**Reliable life**

*see Warranty time*

**Reliability analysis**

*
see Life data analysis*

**Reliability importance**

*
see Importance measure*

**Reliability life data analysis**

*
see Life data analysis*

**Right censored data**

Data that represents the length of time during which a unit has operated without
failure (e.g., it might be observed that a unit did not fail during a 100-hour
test); also called *suspended data*.

**Statistics**

The branch of mathematics that deals with the collection, organization, analysis
and interpretation of data.

**Suspended data**

*see Right censored data*

**Warranty time**

The time at which a specified reliability value will be reached (e.g., a goal of
90% reliability with a reliable life of 4 years means that if 100 identical
units are fielded, then 90 of them will be still be operating at the end of 4
years).