Weibull analysis
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This document discusses Weibull analysis, which is commonly used in reliability engineering. The Weibull distribution can take on many shapes depending on the value of the β parameter. Weibull analysis is useful for mechanical reliability due to its versatility. The document defines the Weibull probability density function and describes how it is used to derive reliability metrics like failure rate and mean time to failure. Examples are provided to demonstrate how Weibull analysis can be used to determine failure percentages and mean time to failure for products.
Weibull analysis
- 1. Weibull Analysis The Weibull distribution is one of the most commonly used distributions in Reliability Engineering because of the many shapes it attains for various values of β. Weibull analysis continues to gain in popularity for reliability work, particularly in the area of mechanical reliability, due to its inherent versatility. The Weibull probability density function (Failure/Time Distribution) is given by t −γ β β t − γ β −1 − ( η ) f(t) = ⋅ ( ) ⋅e t = Time to Failure η η β = Shape parameter η = Scale parameter γ = Location parameter (locates the distribution along the abscissa. When the distribution starts at t=0, or at the origin, γ = 0 ) The useful metrics (Reliability, Failure Rate, Mean Time To Failure) that are derived from the above f(t) function are shown in Page 2 Data Requirements Plotting Procedures Life data that is relevant to the failure mode is • Order data from lowest to highest failure time critical • Individual Data • Estimate percent failing before each failure • Total Units time (median ranks) • Number of observed failures • Draw best line fit through data points plotted • Item Time to Failure • Grouped Data on Weibull paper • Total Units • Estimate Weibull parameters β and η from the • Number of groups graph • Failures in Group • Group End Time Note: Parameters β & η can be easily derived from a Weibull Software package, without going through the above procedure Example A manufacturer estimates that its customers will operate a product, a portable A.C. Power Generator for 3000 hours per year, on average. The company wants to sell the Generator with a 1-year warranty, but needs to estimate the percent of returns that will be experienced in order to assess the warranty cost. Also wants to determine the Mean Time To Failure of the Generator. The manufacturer authorizes a test program using 10 random samples of the product. Times ( Hours) to failure for 10 samples are: 1:18200, 2:9750, 3:6000, 4:10075, 5:15000, 6:5005, 7:13025, 8:9500, 9:15050, 10:7000 Analysis Results are in Page 2; Using the Plot & Equations in Page 2 (1) Determine % of expected failures in the warranty period using the Plot and the R(t) Equation. (2) Determine the Mean Time To Failure Answers: (1) 3%; (2) 10929 Hours Hilaire Ananda Perera ( http://www.linkedin.com/in/hilaireperera ) Long Term Quality Assurance
- 2. Use Of Weibull Analysis β = 2.58 Q(t) = Probability of Failure as a percentage η = 12310 Hours t −( ) β β = Shape Parameter η Reliability Function R(t) = e η = Scale Parameter β t β −1 t = Operating Time Failure Rate Function λ(t) = ( ) Γ( β -1 +1) is the Gamma η η Function evaluated at the value of (β -1 +1) 1 Mean Time To Failure m = ηΓ ( + 1) β NOTE: Mean Time To Failure is the inverse of Failure Rate only when β = 1 Hilaire Ananda Perera ( http://www.linkedin.com/in/hilaireperera ) Long Term Quality Assurance
- 3. Interpreting The Weibull Plot Value of β Product If this occurs, suspect the following Characteristics β<1 Implies infant • Inadequate stress screening or Burn-In mortality. If • Quality problems in components product survives • Quality problems in manufacturing infant mortality, its • Rework/refurbishment problems resistance to failure improves with age β=1 Implies failures are • Maintenance/human errors random. An old • Failures are inherent, not induced part is just as good • Mixture of failure modes (or bad) as a new part β>1&<4 Implies early • Low cycle fatigue wearout • Corrosion or erosion failure modes • Scheduled replacement may be cost effective β>4 Implies old age • Inherent material property limitations (rapid) wearout • Gross manufacturing process problems • Small variability in manufacturing or material Ref: RAC Reliability Toolkit Hilaire Ananda Perera ( http://www.linkedin.com/in/hilaireperera ) Long Term Quality Assurance