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Polymers are used in the manufacturing of products for applications such as construction (buildings and furnishings), transportation (ground-based and outer space vehicles), and consumer and industrial goods (packaging, electrical and electronic equipment, medical devices, sports and leisure articles, and others). Thermal and various environmental exposures of polymers generally lead to the degradation and deterioration of the polymers [1 9]. Degradation of the polymers may be considered as any type of modi cation of a polymer chain involving the main-chain backbone or side groups or both. These changes are often of a chemical nature (requiring the breaking of primary valence bonds), leading to lower molecular weight, crosslinking, and cyclization. The following types of degradation can occur in a polymer due to the effects of the environmental factors [1 9]: Thermal Degradation initiated by high-temperature exposure Oxidative Degradation initiated by exposure to oxidizing agents including air Radiative Degradation initiated by exposure to radiative energy Mechanical and Ultrasonic Degradation initiated by machine-type operations (e.g., mastication, grinding, ball milling, roll milling, and ultrasonic vibrations) Chemical Degradation initiated by exposure to chemicals Biological Degradation initiated by exposure to living organisms, usually microorganisms, such as fungi and bacteria; fungi, including bacteria, widely distributed throughout the world in soil, water, and air

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Whatever the explanation, the combination of apparent convergence and lack of clear warning messages in many programs means that some users are likely to be misled about the viability of their parameter estimates 1044 Reporting of Parameter Estimates and Standard Errors Some programs do a good job of detecting and warning about complete separation but then fail to report any parameter estimates or standard errors (SPSS, STATA LOGIT) This might seem sensible since nonconvergent estimates are essentially worthless as parameter estimates However, they may still serve a useful diagnostic purpose in determining which variables have complete or quasi-complete separation 1045 Likelihood Ratio Statistics Some programs (SAS GENMOD, JMP) report optional likelihood-ratio chi-square tests for each coef cient in the model.

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Class A AIS This is the compulsory system tted by commercial shipping worldwide. It transmits a great deal of data, much of which, such as destination etc., is entered manually by the bridge crew and the rest, such as GPS position, is wired directly from the ship s equipment. The heading information from the compass system has often been found unreliable, as has the data that has been manually entered. The dynamic information is updated every 10 seconds for vessels up to 14 knots and every 2 seconds for vessels travelling at more than 23 knots and the transmitting power is 12.5 watts.

Unlike Wald chi-squares, which are essentially useless under complete or quasi-complete separation, the likelihood ratio test is still a valid test of the null hypothesis that a coef cient is equal to zero Thus, even if a certain parameter cannot be estimated, it may still be possible to judge whether or not it is signi cantly different from zero 105 DIAGNOSIS OF SEPARATION PROBLEMS We are now in a position to make some recommendations about how the statistical analyst should approach the detection of problems of complete or quasi-complete separation If you are using software that gives clear diagnostic messages (SAS LOGISTIC, STATA LOGIT), one-half of the battle is won But there is still a need to determine which variables are causing the problem and to get a better sense of the nature of the problem.

The histogram of an image is a plot of the pixel value (abscissa) against the frequency of occurrence of the pixel value in the entire image (ordinate). For an image with 256 possible gray levels, the abscissa of the histogram ranges from 0 to 255 levels. The total pixel count under the histogram is equal to M N (see Section 2.1.1). The histogram represents the frequency of pixel value distribution in the image, an important characteristic of the image (see Fig. 6.4B, D, E, for examples). 2.1.6 Image Display

Second, all optimal designs computed and shown in Tables 4.2., 4.4., 4.6., and 4.8. are concentrated in less than the available eight measurement points. One may wonder why for estimating the target parameter the eight measurement points have not all simply been taken as in Example 4.20, that is, at zn = 0, 2, and f i for a,u,and p, respectively. However, this would imply estimating three parameters using only one measurement point. As discussed in Section 4.9, this would make the Fisher information matrix singular and, therefore, the parameters unidentifiable. The improved precision of the estimates of the parameters of the expectation model also propagates to functions of the parameters. This is illustrated in the following example.

The second step (or the rst step with programs that do not give good warning messages) is to carefully examine the estimated coef cients and their standard.

Interferogram Eye or imaging system Monochromatic point light source Surface under test Beam splitter Concave collimating mirror

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