Contact: Wes Fulton 1-310-548-6358
Weibull analysis is the leading method in the world for fitting and analyzing life data.
Ex: A project engineer reports three failures of a component in service operations during a three month period. The program manager asks, "How many failures will we have in the next quarter, six months, and a year?" "What will it cost?" What is the best corrective action to reduce the risk and losses?
Ex: After an engineering change, how many units must be tested for how long, without any failures, to verify that the old failure mode is eliminated, or slightly improved with 90% confidence?
Ex: The cost of an unplanned failure component, subject to a wear out failure mode, is twenty times the cost of a planned replacement. What is the optimal replacement interval?
The primary advantage of the Weibull analysis is the ability to provide reasonably accurate failure analysis and failure forecasts with extremely small samples. Another advantage is that it provides a simple and useful graphical plot of the failure data.
The Horizontal scale is a measure of life or aging. Start/Stop cycles, mileage, operating time, landings or mission cycles are examples of aging parameters.
The Vertical Scale is the cumulative percentage failed. The tow defining parameters of the Weibull line are the slope, beta and the characteristic life, eta.
The slope of the line, beta, is particularly significant and may provide a clue to the physics of failure. The relationship between the slope and generic failure classes will be discussed later.
The characteristic life, eta, is the typical time to failure in Weibull analysis.
All the information in this Website it cited from Dr Abernethy's
The New Weibull Handbook.
Reliability & Statistical Analysis for predicting Life, Safety, Survivability, RIsk, Cost and Warranty Claims.
Discrete or counted data was originally used to measure reliability, Tests would be categorized as success or failure. Receiving inspection data would count good parts versus defective parts. This data is modeled with the binomial and Poisson distributions. The results are imprecise unless enormous samples sized are employed.
Ideally each Weibull Plot depicts a single failure mode.
To determine failure time precisely, there are three requirements:
-A time origin must be unambiguously defined
-A scale for measuring the passage of time must be agreed
-The meaning of failure must be entirely clear
The age of each part is required, both failed and unfailed. The units of age depend on the part usage and the failure mode.
For example, low cycle and high cycle fatigue may produce certain cracks leading to rupture. The age would be fatigue cycles. The age of the starter may be the number of starts. Usually the knowledge of the physics of failure will produce the age scale. When there is uncertainty, several age scales are tried to determine best fit.
The slope of the Weibull plot, beta, determines which member of the family of Weibull failure distributions best fits or describes the data. The slope also indicated which class of failures is present:
Beta < 1.0 indicated infant mortality
Beta = 1.0 means random failures (independent of age)
Beta > 1.0 indicates wear out failures
The Weibull plot shows the onset of the failure. For example, it may be of interest to determine the time at which 1% of the population will have failed.
Cumulative future failures are plotted against future months. This process provides information on whether the failure mode applies to the entire population or fleet, or to only one portion of the fleet, called the batch. After Alternative plans for corrective action are developed, the failure of forecasts are repeated. The decision maker will require these failure forecasts to select the best course of action, the plan with the minimum failure forecast or the minimum cost.
A further advantage of Weibull analysis is that is may be useful even with inadequacies in the data. Even bad Weibull plots are usually informative to engineers trained to read them.
Moderate size samples, twenty or more failures, are needed to accurately discriminate between Webull and other methods of distribution. With less than 20 failures the Weibull is the best choice, and therefore, best practice.
When a redesign is made to correct an existing failure mode, tests are made to show the new design is an improvement. The tests are required as not all redesigns are improvements. How many units must be tested without failure, for how long, to substantiate that the new design is significantly better than the existing design? Alternatively, the test objective may be to demonstrate a design requirement expressed as a reliability or probability of failure at some design life.
The success data from the test may be used to determine a lower confidence bound for the Weibull line for new design called "Weibayes" line. The test design criteria may allow zero failures, or zero or one failure, as alternatives. "Sudden Death" testing is another useful technique. Zero failure test plans have the absolute minimum test time.
The Weibull plot is extremely useful for maintenance planning, particularly reliability centered maintenance. Beta tells the analyst whether or not scheduled inspections and overhauls are needed.
If Beta is less than or equal to one, over hauls are not cost effective. With Beta's greater than one, the overhaul period or scheduled inspection interval is read directly from the plot at an acceptable probability of failure.
For wear out failure modes, the cost of the unplanned failure is much greater the cost of a planned replacement, there is an optimum replacement interval for minimum cost.