Benign failures

Failures that are known to experts but are not identified by the end user during the normal operation of the component or system. Benign failures are at the opposite end of the spectrum from dramatic failures, where catastrophic events are obvious and easily identified. Benign failures are failures that are often overlooked and not counted as failures.

Characteristic life

The characteristic life (η) of a distribution shows the point in the life of the component or system where the failure probability is independent of the parameters of the failure distribution. For a Weibull distribution, the characteristic life is the time at which 63.2% of the population is expected to have failed.

Confidence

Confidence measures the statistical accuracy of estimated values. It is the relative frequency that the statistically-derived interval estimate contains the true unknown value being estimated. To calculate confidence, you specify a confidence type, level, and method. The confidence level is a percentage value known as the degree of confidence.

Confidence bound

A range of potential values within which the parameters for a selected distribution are likely to fall with a given percentage of certainty. Bounds may be set above and/or below the resulting parameters, or they may consist of an interval, which is bounded above and below. Selection of the bounds to use in the analysis determines the confidence type. For more information, see Confidence Types.

Confidence interval

Bounds that assign a closed range between which the true analysis value is expected to fall with a given percentage of certainty. For example, a 90% confidence level between two values, X and Y, means that 90% of the population falls within the interval between X and Y, and 10% of the population falls outside this interval (with 5% below X and 5% above Y).

Correlation coefficient

A statistical measure that describes how well the regression line “fits” the data points on a probability plot. The correlation coefficient is also known as the coefficient of determination. It is represented by ρ (Rho). The closer ρ is to 1, the better the fit. To determine the goodness of fit, the X and Y values determined by rank regression are used to describe the linear relationship between time and the cumulative percentage of failure (unreliability) on the probability plot for all distributions but exponential. For the exponential distribution, the plot describes the linear relationships between time and the cumulative percentage of successful operation (reliability).

Data set

A set of failure data points to analyze. In the System file, you can insert any number of data sets and then perform best-fit analysis to determine the distribution to use for the analysis. The best-fit distribution for a data set provides clues about the population from which its data points are drawn.

Data type

Data sets can be set up for standard parametric analysis as well as special case analysis, which includes non-parametric and/or reliability growth analysis as well as warranty and degradation analysis. For more information, see Special Cases of Life Data Analysis (LDA).

Failure mode

A way in which a product or system can fail. Ideally, a Weibull analysis studies only one failure mode at a time.

Failure distribution

A statistical distribution technique for modeling the occurrence of failures during a time period when the product or system was operational. For the Weibull module, supported distribution choices are: Weibull, Lognormal, Normal, Gumbel- (Lower), Gumbel+ (Upper), Exponential, Rayleigh, Gamma, Logistic, and Log-logistic. For more information, see Failure and Repair Distributions.

Failure usage scale

Reflects the age of the product or system upon failure. Usage can be tracked in a variety of ways. For example, usage may be defined in number of hours, revolutions, or duty cycles. For an automobile tire, usage might be measured in thousands of miles. For burner and turbine parts, usage might be measured as a function of time spent operating at a high temperature or in the number of cold-to-hot-to-cold cycles that have occurred. Often times, physics-of-failure analyses can help to determine the parameter by which to measure the usage of a particular component or assembly.

Hazard rate

A measure of an item’s tendency to fail in the infinitesimal interval represented by t1 and t2, given survival until t1. Hazard rate is also known as instantaneous failure rate and conditional failure rate. When the slope is less than 1 (infant mortality), analyses have decreasing hazard rates as age increases. When the slope is equal to 1 (exponential distribution), analyses have a constant hazard rate. When the slope is greater than 1 (wear-out distributions), analyses have increasing hazard rates as age increases. The greater an item’s hazard rate, the greater its probability of impending failure.

Likelihood function

Measures the relative credibility of parameter values based on data or observations. Using the MLE (maximum likelihood estimation) method, possible parameter values are systematically and iteratively tested against the observed data. The equation for the likelihood function differs for each distribution and data type.

Non-parametric analysis

A form of analysis that does not assume an underlying distribution but which constructs a prediction according to information derived from the data. Because making incorrect assumptions in a parametric analysis can potentially result in large errors, some practitioners recommend beginning with a non-parametric analysis. Because the confidence bounds associated with non-parametric analysis are usually much wider than those for parametric analysis, once non-parametric results are calculated, you can save them to a free-form data set and then perform parametric analysis.

Parametric analysis

A form of analysis that assumes that data comes from a type of probability distribution and makes inferences about the parameters of the distribution. If these assumptions are correct, parametric methods can produce more accurate and precise estimates than non-parametric estimates.

Probability plot

A plot of the failure rate for the data points in the data set, which provides insight into the failure mode. This graphical representation also helps to identify whether the best-suited distribution and/or parameters have been selected for the data set. For example, if the probability plot does not closely fit the data points, you can make distribution and/or parameters changes to see if a better fit can be found. Once you are satisfied with the fit, you can use the resulting analysis to spot trends and accurately estimate future failures. The y-axis values for all distributions but exponential is unreliability. The y-axis values for the exponential distribution is reliability.

Reliability growth analysis

Analyzes the growth of reliability as a function of time, especially during product development. You use the plot generated from this special case of analysis as an aid in forecasting failures as a function of either additional test time or calendar time, thereby making planning for redesign and test resources easier. Use of both the Duane and Crow/AMSAA models are supported for reliability growth analysis. For more information, see Reliability Growth Analysis.

Scale parameter

The measurement along the x-axis of the probability plot that determines the statistical dispersion or range of the probability distribution. As this value decreases, the distribution shrinks towards its beginning point. As this value increases, the distribution broadens away from its beginning point. If the threshold parameter is equal to 0, the scale parameter is also known as the characteristic life.

Shape parameter

Controls the shape of the distribution, which indicates if the failure rate is increasing, decreasing, or constant. Not all failure distributions have a shape value. For example, the normal distribution does not have a shape value because it always has the same shape. For the Weibull distribution, the shape parameter is β (beta). By using different values for β, the Weibull distribution can assign many different shapes to its cumulative distribution function, probability density function, and hazard rate, which is why this distribution is so well suited to LDA. The greater the value for β, the steeper the curve becomes, indicating that failures are occurring more frequently. The smaller the value for β, the less steep the curve becomes, indicating that failures are occurring less frequently.

Slope parameter

Indicates the slope of the line among all of the data points in the probability plot. For most distributions, the slope parameter is equal to the shape parameter.

Suspensions

Units under test that do not fail during the duration of the test. Suspensions also include units that fail either before the test begins or after it ends. Additionally, suspensions include units that fail during the test due to a failure mode other than the one under test. For more information, see Suspensions.

Threshold parameter

A value used to shift the start time of a probability plot from zero. The threshold parameter for a distribution is γ (gamma). A positive value indicates a failure-free period where the probability of failure is negligible. A negative value indicates a loss of some life (reliability) before service officially begins. The threshold parameter is also referred to as the location parameter or minimum life parameter. For more information, see Threshold Parameter.