Download Weibull Models by D. N. Prabhakar Murthy, Min Xie, Renyan Jiang PDF

By D. N. Prabhakar Murthy, Min Xie, Renyan Jiang

A accomplished standpoint on Weibull versions

The literature on Weibull types is sizeable, disjointed, and scattered throughout many various journals. Weibull versions is a complete consultant that integrates all of the diverse aspects of Weibull versions in one quantity.

This e-book may be of significant aid to practitioners in reliability and different disciplines within the context of modeling information units utilizing Weibull versions. For researchers attracted to those modeling concepts, routines on the finish of every bankruptcy outline power themes for destiny examine.

Organized into seven exact components, Weibull versions:

  • Covers version research, parameter estimation, version validation, and application
  • Serves as either a instruction manual and a learn monograph. As a guide, it classifies the several types and offers their homes. As a examine monograph, it unifies the literature and offers the implications in an built-in manner
  • Intertwines thought and application
  • Focuses on version id sooner than version parameter estimation
  • Discusses the usefulness of the Weibull chance plot (WPP) within the version choice to version a given info set
  • Highlights using Weibull versions in reliability theory

Filled with in-depth research, Weibull versions pulls jointly the main suitable details in this subject to provide all people from reliability engineers to utilized statisticians concerned with reliability and survival research a transparent examine what Weibull types can supply.

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Extra info for Weibull Models

Example text

7) is the standard (one-parameter) exponential distribution. This can also be obtained as a special case of the standard Weibull model with the shape parameter b ¼ 1. 6) is often referred to as the power law transformation that links the Weibull and exponential distributions. 8. Model I(b)-2 The model is obtained using the transformation   ZÀt T ¼ b ln Z a ð2:8Þ MODIFICATION/GENERALIZATION OF WEIBULL DISTRIBUTION 23 and is given by  GðtÞ ¼ 1 À exp Àexp tÀt Z ! À1

The two possible shapes for the density function are as follows:  Monotonically decreasing  Unimodal A parametric study is a characterization of the shapes in the two-dimensional parameter plane. It is easily seen that the shape of the density function depends 51 STANDARD WEIBULL MODEL only on the shape parameter b and the scale parameter has no effect. The results are as follows:  For b 1 the density function is monotonically decreasing (type 1 in Fig. 1).  For b > 1 the density function is unimodal with the mode at tm ¼ a½ðb À 1Þ=bŠ1=b (type 2 in Fig.

As a result, they are either a function of the independent variable (t) or some other variables (such as stress level), or are random variables. These lead to the following three subgroups. Type IV(a) Parameters are functions of the variable t (time-varying parameters if t represents time). ). 5 Parameters are random variables (Bayesian models). Type V Models: Discrete Weibull Models In the standard Weibull model, the variable t is continuous and can assume any value in the interval ½0; 1Þ. As a result, T is a continuos random variable.

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