Reliability Glossary

Accelerated life testing
A testing strategy whereby units are tested at stress levels higher than use stress in order to facilitate failures in a timely manner. The results of these tests are then analyzed in such a manner so that a profile of the failure behavior of the products at the use stresses can be determined based on the behavior of the products at the accelerated stresses.

AMPM
AMPM stands for AMSAA maturity prediction model. This is an enhanced reliability growth model that allows the user to predict failure rates in future stages of development. This model allows the user to assess the effectiveness of proposed and implemented fixes in order to determine the future failure rate.

AMSAA model
AMSAA stands for Army Material Systems Analysis Activity. This is a reliability growth model that uses a relationship between cumulative test time and cumulative failures to develop a reliability growth model.

ANOVA
ANOVA stands for analysis of variance, a method by which the source of variability is identified. This method is widely used in industry to help identify the source of potential problems in the production process, and identify whether variation in measured output values is due to variability between various manufacturing processes, or within them. By varying the factors in a predetermined pattern and analyzing the output, one can use statistical techniques to make an accurate assessment as to the cause of variation in a manufacturing process.

Arrhenius model
A model used in accelerated life testing to establish a relationship between absolute temperature and reliability. It was originally developed by Swedish chemist Svante Arrhenius to define the relationship between temperature and the rates of chemical reaction.

Availability
Availability is the probability that an item will be able to function (i.e. not failed or undergoing repair) when called upon to do so. This measure takes into account an item’s reliability (how quickly it fails) and its maintainability (how quickly it can be repaired).

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, that means that 10% of the population will have failed by 100 hours of operation.

Block diagram
A diagram that represents how the components, represented by "blocks," are arranged and related reliability-wise in a larger system. This is often but not necessarily the same as the way that the components are physically related. This is also called a Reliability Block Diagram or RBD.

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

Competing failure modes
A model whereby items that fail due to more than one failure mode can be represented as a series reliability system with each block representing a failure mode. The failure modes are considered to be "competing" amongst each other to see which one will cause the item to fail.

Complete data
A data set consisting only of failure times.

Complex system
A block diagram that cannot be reduced to series and/or parallel systems.
 
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 between a specified percentage of the time. For example, if we perform ten different reliability tests for our items 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.

Contour plot
A graphical representation of the possible solutions to the likelihood ratio equation. This is employed to determine confidence bounds as well as comparisons between two different data sets.

Cumulative damage model
An accelerated life testing model used to model accelerated tests where the stress levels vary with time.

Cumulative density function (cdf)
A function obtained by integrating the failure distribution pdf. In life data analysis, the cdf is equivalent to the unreliability function.

Decomposition method
A method for determining the reliability of complex systems. The decomposition method is an application of the law of total probability, which involves choosing a "key" component and then calculating the reliability of the system twice: once as if the key component failed and once as if the key component succeeded. These two probabilities are then combined to obtain the reliability of the system, since at any given time the key component will be failed or operating.

Degradation analysis
Analysis involving the measurement and extrapolation of degradation or performance data that can be directly related to the presumed failure of the product in question. Degradation analysis allows the user to extrapolate to an assumed failure time based on the measurements of degradation or performance over time.

Down time
The amount of time a repairable unit is not operating. This can be due to being in a failed state, administrative delay, waiting for replacement parts to be shipped or undergoing active repair.

Duane model
A reliability growth model similar to the AMSAA model that uses a relationship between cumulative test time and cumulative failures to develop a reliability growth profile.

Event space method
A method for determining the reliability of complex systems. With the event space method, all mutually exclusive events are determined. The reliability of the system is simply the probability of the union of all mutually exclusive events that yield a system success (the unreliability is the probability of the union of all mutually exclusive events that yield a system failure).

Exponential distribution
A lifetime statistical distribution that assumes a constant failure rate for the units being modeled.

Eyring model
An accelerated life testing model based on quantum mechanics for use when temperature is the accelerating factor.

Failure distribution
A mathematical model that describes the probability of failures occurring over time. Also known as the probability density function (pdf), this function is integrated to obtain the probability that the failure time takes a value in a given time interval. This function is the basis for other important reliability functions, including the reliability function, the failure rate function and the mean life.
   

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, i.e. 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.

Gaussian distribution  
see Normal distribution

General log-linear model  
An accelerated life testing model that can account for multiple non-thermal stresses as acceleration factors.

Generalized gamma distribution
While not as frequently used for modeling life data as other life distributions, the generalized gamma distribution does have the ability to mimic the attributes of other distributions such as the Weibull or lognormal, based on the values of the distribution's parameters. While the generalized gamma distribution is not often used to model life data by itself, its ability to behave like other more commonly-used life distributions is sometimes used to determine which of those life distributions should be used to model a particular set of data.

Gompertz model
A reliability growth model that models reliability values at different stages of development and produces an S-shaped reliability growth curve.

HALT
Highly accelerated life testing.

HASS 
Highly accelerated stress screening.

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.

Inverse power law
An accelerated life testing model commonly used when the accelerating factor is a single, non-thermal stress.

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.

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.

Life distribution
see Failure distribution

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.

Lloyd-Lipow model
A reliability growth model based on the number of trials and successes at each stage of product development.

Lognormal distribution
A lifetime statistical distribution that is often used to model products in which physical fatigue is the prominent contributor to the primary failure mode.

Maintainability
The probability that a failed unit will be repaired within a given amount of time. The term is also used to denote the discipline of studying and improving the maintainability of products, primarily by reducing the amount of time required to diagnose and repair failures.

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.

Mixed Weibull distribution
A variation of the Weibull distribution used to model data with distinct subpopulations that may represent different failure characteristics over the lifetime of a product. Each subpopulation has separate Weibull parameters calculated and the results are combined in a mixed Weibull distribution to represent all of the subpopulations in one function.

Modified Gompertz model
A reliability growth model that models based on a variation of the Gompertz model.

Monte Carlo simulation
A method of generating values from a known distribution for the purposes of experimentation. This is accomplished by generating uniform random variables and using them in an inverse reliability equation to produce failure times that would conform to the desired input distribution.

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.

MTTR
MTTR stands for mean time to repair and is represented by the mean life value for a distribution of repair times. (see Maintainability.)

NHPP
NHPP stands for non-homogeneous Poisson process, which is a simple parametric model used to represent events with a non-constant failure recurrence rate. This type of model is often used to model reliability growth and the reliability of repairable units.

Nonparametric analysis
A method of analysis that allows the user to characterize failure data without assuming an underlying failure distribution. This avoids the potentially large errors brought about by making incorrect assumptions about the distribution. However, the confidence bounds associated with nonparametric analysis are usually much wider than those calculated via parametric analysis. Additionally, predictions outside the range of the observations are not possible.

Normal distribution
A common lifetime statistical distribution that was developed by mathematician C. F. Gauss. The distribution is a continuous, bell-shaped distribution which is symmetric about its mean and can take on values from negative infinity to positive infinity.

Path-tracing method
A method for determining the reliability of complex systems. With this method, every path from a starting point to an ending point is considered. Since system success involves having at least one path available from one end of the reliability block diagram to the other, as long as at least one path is available, the system has not failed. The reliability of the system is simply the probability of the union of these paths.

Plotting paper
see Probability plotting paper

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.   

Probability plot
A type of plot that linearizes a distribution’s cdf, allowing the user to manually plot failure time vs. estimated unreliability. Provided that the plotted points fall on a relatively straight line (thus indicating that the chosen distribution is a good fit), the parameter estimates can be obtained from scales on the plot. This is a crude, time-consuming method of fitting a distribution to failure data, but it was practically the only method available prior to the widespread use of computers.

Probability plotting paper
A specially designed type of graph paper that allows the user to plot failure time vs. unreliability as a linear function. Plotting paper constructions varies from distribution to distribution. Probability plotting papers that have been generated by ReliaSoft's software are available on the Web at http://www.weibull.com/GPaper/index.htm.

Proportional hazards model
An accelerated life testing model that can account for multiple non-thermal stresses as acceleration factors.

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.

RBD
see Block diagram

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.

Reliability analysis
see Life data analysis

Reliability block diagram
see Block diagram

Reliability growth
The analysis of the change in reliability over time, usually applied to products under development. Reliability growth analysis provides the means by which the reliability, mean life or failure rate is tracked over time, allowing the user to predict future reliability values based on the current rate of growth of the reliability measurement of interest.

Reliability importance
see Importance measure

Reliability life data analysis
see Life data analysis

Reliability test design
The process of designing plans for reliability testing.

Reliability testing
Testing units to failure in order to obtain raw failure time data for life data analysis.

Repair
An action that restores a failed part or component to operating condition.

Repair distribution
A mathematical model that describes the probability of repairs occurring over time.

Repairable system
A system that can be restored to operating condition after a failure by the repair or replacement of one or more components.

Sequential testing
A testing methodology in which test units are tested consecutively instead of simultaneously.

Spares provisioning
The stocking of spare units or components based on the anticipated number of failures for a given mission or length of operation.

SPRT
SPRT stands for sequential probability ratio test. This is a type of accept/reject sequential testing in which accept/reject boundaries are defined by the user and units are sequentially tested until either the accept boundary or the reject boundary have been reached, and a decision is made about the suitability of the units.

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

Stress testing
Testing units at stresses higher than what would be encountered during normal operating conditions, usually to induce failures.

Stress-strength interference
A method by which the probability of failure of an item is calculated by superimposing the distribution of the item’s strength with the distribution of the stress it will encounter during normal usage.

Suspended data
see Censored data

System reliability
The reliability of an entire system, as opposed to the reliability of its components. The system reliability is defined by the reliability of the components as well as the way the components are arranged reliability-wise.

Temperature-humidity model
An accelerated life testing model used when the two accelerating factors are temperature and humidity.

Temperature-non-thermal model
An accelerated life testing model used when the two accelerating factors are temperature and another non-thermal stress factor.

Up time
The amount of time a repairable unit is operating per design.

Warranty analysis
The analysis of warranty and return data for the purpose of determining the reliability characteristics of a product.

Weibull distribution
A statistical distribution frequently used in life data analysis. Developed by Swedish mathematician Wallodi Weibull, this distribution is widely used due to its versatility and the fact that the Weibull pdf can assume different shapes based on the parameter values.