# 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 pdf. In life data analysis, the 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 "mean time between failures." 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 mean time before failure and is represented by the mean life value for a failure distribution of non-repairable units.

MTTF
"MTTF" stands for "mean time to failure" 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 pdf is the basis for other important reliability functions, including the reliability function, the failure rate function and the mean life.

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).