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, that means that 10% of the population
will have failed by 100 hours of operation.
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.
Complete data
A data set consisting only of failure times.
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.
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.
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.
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.
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.
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.
Reliability analysis
see Life data analysis
Reliability importance
see Importance measure
Reliability life data analysis
see Life data analysis
Statistics
The branch of mathematics that deals with the collection, organization, analysis
and interpretation of data.
Suspended data
see Censored data
