When you have age-to-failure data by component, the analysis is very helpful because the b-values will tell you the modes of failure which no other distribution will do this When you have age-to-failure by system, the b-values have NO physical significance and the b-, h-values only explain how the system is functioning-this means you loose significant information for problem solving.The Weibull distribution is valid for 85-95 of all life data, so play the odds and start with Weibull analysis.The major competing distribution for Weibull analysis is the lognormal distribution.
For additional information read The New Weibull Handbook, 5th edition by Dr. Weibull Analysis For Reliability Software For AnalyzingRobert B. Abernethy and use the WinSMITH Weibull and WinSMITH Visual software for analyzing the data (both software are bundled for a reduce price as SuperSMITH ). Weibull Analysis For Reliability Free To ReceiveWe also have a magazine that is free to receive (U.S. Subscribing is free. This behavior makes it suitable for representing the failure rate of units exhibiting early-type failures, for which the failure rate decreases with age. It is a versatile distribution that can take on the characteristics of other types of distributions, based on the value of the shape parameter. This chapter provides a brief background on the Weibull distribution, presents and derives most of the applicable equations and presents examples calculated both manually and by using ReliaSofts Weibull software. The advantage of doing this is that data sets with few or no failures can be analyzed. It is called conditional because you can calculate the reliability of a new mission based on the fact that the unit or units already accumulated hours of operation successfully. If, then, the median life, or the life by which half of the units will survive. Depending on the values of the parameters, the Weibull distribution can be used to model a variety of life behaviors. We will now examine how the values of the shape parameter,, and the scale parameter,, affect such distribution characteristics as the shape of the curve, the reliability and the failure rate. Note that in the rest of this section we will assume the most general form of the Weibull distribution, (i.e., the 3-parameter form). The appropriate substitutions to obtain the other forms, such as the 2-parameter form where or the 1-parameter form where constant, can easily be made. This is because the value of is equal to the slope of the regressed line in a probability plot. Different values of the shape parameter can have marked effects on the behavior of the distribution. In fact, some values of the shape parameter will cause the distribution equations to reduce to those of other distributions. For example, when, the pdf of the 3-parameter Weibull distribution reduces to that of the 2-parameter exponential distribution or. The following figure shows the effect of different values of the shape parameter,, on the shape of the pdf. ![]() Consequently, it may approximate the normal pdf, and for 3.7, srcimagesmathd26d26570d1c4952e989b3af71688dec579.png it is negatively skewed (left tail). The way the value of relates to the physical behavior of the items being modeled becomes more apparent when we observe how its different values affect the reliability and failure rate functions. Note that for,, but for, This abrupt shift is what complicates MLE estimation when is close to 1. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of. The following figure shows the effects of these varied values of on the reliability plot, which is a linear analog of the probability plot. ![]() All three life stages of the bathtub curve can be modeled with the Weibull distribution and varying values of. The failure rate, decreases thereafter monotonically and is convex, approaching the value of zero as or.
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