Weibull analysis is synonymous with LDA (life data analysis) because the Weibull distribution is the most widely used to determine the relationship between reliability and the life span of the product or system. The primary advantage of this distribution is its ability to provide reasonably accurate analysis and failure forecasts with extremely small data samples.

Because the Weibull distribution can take a a variety of forms, it is effective in analyzing data from increasing, constant, and decreasing failure rate situations. This means that you can use it to analyze data collected during burn-in (infant mortality), useful life, or wear-out periods. The Weibull distribution is often used to study mechanical, chemical, electrical, electronic, material, and human failures.

Weibull analysis is typically used to determine the best-fit distribution for a set of failure data points collected during testing or field operation. The distribution that best fits these data points provides you with clues about the population from which they are drawn. While the best-fit distribution for any set of data points might be the Weibull distribution, it can be another failure distribution, such as the lognormal, normal, or exponential distribution.

The characteristics or parameters that describe and influence the behavior of the distribution vary from distribution to distribution. For example, while the shape (β) and characteristic life (η) parameters define the Weibull distribution, the mean (μ) and standard deviation (σ) parameters define the lognormal distribution, which is the second most frequently used distribution for LDA.

Ideally, Weibull analysis studies only one failure mode at a time. For example, the failure mode to analyze might be a crack, fracture, deformation, or fatigue due to such failure mechanisms as corrosion, excessive physical stress, high temperature, wear out, or infant mortality. The different data elements that you might analyze for a given failure mode include failure times, the number of failures during an interval, the number of suspended items, and the type of suspensions. Definitions of terms commonly used in LDA are defined in Weibull Analysis Terminology.

The lognormal distribution, which can also take a variety of forms, is extremely useful when the range of observed values in a data set spans several powers of 10. Additionally, this distribution is well suited to modeling data when the time to failure is from the multiplication of effects. For example, stress might cause a crack to form, but due to the crack, the stress increases, which then expands the crack until it causes part failure.

The lognormal distribution is frequently used to study metal fatigue, failure and repair times, chemical-processing equipment, transistors, mechanical devices, bearings, electrical insulation degradation, material characteristics, and non-linear, accelerating deterioration. Outside of engineering, the lognormal distribution is used to analyze personal incomes, inheritances, bank deposits, and the response of biological material to stimuli.

The Weibull module supports a variety of distributions for LDA. Choices include Weibull, Lognormal, Normal, Gumbel- (Lower), Gumbel+ (Upper), Exponential, Rayleigh, Gamma, Logistic, and Log-logistic. To perform LDA, you supply a set of data points. Using these data points, you estimate the parameters of one or more distributions to find the one that best fits this data. Once a data set is calculated, you can view various plots and generate reports to accurately determine product or system reliability.