Failure time

Figure 7 gives the results of an experiment in which freestanding films were exposed to constant elevated temperatures in air-circulating ovens for periods of weeks to months the failure criterion was a 50% loss in tensile strength. Because the test is destmctive, each data point (failure time at a given... 

Assuming that the above test produces the following data (failure time in hours), 84.1 240.1 251.9 272.2 291.9, the MTBF is estimated by using equation 26 ... 

Point Estima.tlon, This is a Type II censored life-testing situation where n items ate placed on test and the test is terrninated at the time of the th failure. The life test produces the ordered failure times. .. /. The estimator for 9 is... 

A sequence of tests has been devised to evaluate antioxidants for use in automotive crankcase lubricants. The Indiana Stirring Oxidation Test (ISOT) JISK2514 is an example of a laboratory screening test. The oil is stirred at 165.5°C in the presence of air. Copper and iron strips are used as metal catalysts. The development of sludge, viscosity, and acidity are deterrnined periodically. Failure time is determined when the development of acidity requires... 

Tliis cliapter is concerned willi special probability distributions and tecliniques used in calculations of reliability and risk. Tlieorems and basic concepts of probability presented in Cliapter 19 are applied to llie determination of llie reliability of complex systems in terms of tlie reliabilities of their components. Tlie relationship between reliability and failure rate is explored in detail. Special probability distributions for failure time are discussed. Tlie chapter concludes with a consideration of fault tree analysis and event tree analysis, two special teclmiques lliat figure prominently in hazard analysis and llie evaluation of risk. 

Equation (20.4.3) defines tlie pdf of the Weibull distribution. Tlie exponential distribution, whose pdf is given in Eq. (20.4.1), is a special case of the Weibull distribution witli p = 1. Tlie variety of assumptions about failure rate and tlie probability distribution of time to failure tliat can be accommodated by the Weibull distribution make it especially attractive in describing failure time distributions in industrial and process plant applications. 

The reliability function corresponding to nonnally distributed failure time is given by... 

Figure 17 Correlation of failure time and melt flow rate MFR 190/5 of sharp notched bars under stress for unimodal homopolymer and copolymers, and bimodal copolymers. Source Ref. 130.

Figure 4-439. Approximate failure time of carbon steel is 5% NaCI and various parts per miiiion of hydrogen sulfide. (From Ref. [184].)...

In many engineering studies, field data are used which consist of failure times for failed units and differing current mnning times for unfailed units. Such data arise because units are put into service at different times and receive different amounts of use. 

For each failure time, calculate the corresponding cumulative hazard value, which is the sum of its hazard value and the hazard values of all preceding failure times. This calculation is done recursively by simple addition. For example, for the generator fan failure at... 

Plot each failure time vertically against its corresponding cumulative hazard value on the horizontal axis of the hazard paper. This was done for the 12 generator fan failures and is shown in Figure 62.7. 

Like all other methods for analyzing censored failure data, the hazard plotting method is also based on a certain assumption that must be satisfied if we are going to rely on the results. The assumption is that if the unfailed units were mn to failure, their failure times would be statistically independent of their censoring times. In other words, there is no relationship or correlation between the censoring time of a unit and the failure time. For example. 

Failure times are typically recorded to the nearest hour, day, month, hundred miles, etc. This is so because the method of measurement has limited accuracy or because the data are rounded. For example, if units are inspected periodically for failure, the exact time of failure is not known but only the period in which the failure occurred. For data plotting, the amount that failure times are rounded off should be considerably smaller than the spread in the distribution of time to failure. 

Ideally, no fewer than 20 failure times, if available, should be plotted from a set of data. Often, in engineering practice there are so few failures that all should be kept in mind so that conclusions drawn from a plot are based on a limited amount of information. Note that if only selected failures from a sample are to be plotted on hazard paper, it is necessary to use all of the failures in the sample to calculate the appropriate cumulative hazard values for the plotting positions. Wrong plotting positions will result if some failures in the data are not included in the cumulative hazard calculations. A similar comment applies to the calculation of plotting positions for probability plotting. 

Material Yield stress (MPa) Failure time (h) (MPa Vm) Iscc (MPa Vm) Plateau velocity (m/s)... 

The failure time presented is the approximate time to failure at an applied stress of 759b of the yield stress of the material. 

Tests in a Clj + Oj mixture at 427°C have shown that the worst elements for promoting susceptibility are Al, Sn, Cu, V, Cr, Mn, Fe and Ni, while the least harmful are Zr, Ta and Mo. a-phase alloys are generally more susceptible than )3-phase alloys. Heat treatment has not been examined extensively, but some heat treatments render some a-alloys more susceptible or change the mode of fracture. The general effect will depend upon the alloy and the heat-treatment cycle. Subsequent cold work can sometimes considerably lower susceptibility. Failure times decrease as either the testing temperature or initial stress value is raised. 

Figure 1 shows the hierarchical tree that corresponds to Table I. The scale at the top of the tree corresponds to the predicted time to failure in months. The conditions at the top of the tree are given by 71 C, 72%, and 8.3 suns and correspond to an expected failure time of approximately 16 months. The first split in the tree is associated with a temperature of 95 C on the left branch and 50 C on the right branch, which correspond to average predicted lifetimes of approximately four and 27 months, respectively. The next two splits are seen to be based on relative humidity and ultraviolet radiation. 

MTBF mean time between failure (time)... 

Fire retardant treatment, for wood, 26 348 Fire science, 11 450 Fire test methods, 11 449—450 Fire test terminology, 19 588 Fire-tube furnaces, 12 319—320, 327 Firing, of ferrites, 11 73 Firming agents, 12 32 as food additives, 12 57 First aid and rescue, 21 858 First aid, for nitric acid exposure, 17 192 First failure, time to, 26 987 First falling rate period, 23 67 First-generation ionic liquids, 26 837-838, 841, 865... 

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