Weibull life time

Statistical Methods for Nonelectronic Reliability, Reliability Specifications, Special Application Methods for Reliability Prediction Part Failure Characteristics, and Reliability Demonstration Tests. Data is located in section 5.0 on Part Failure Characteristics. This section describes the results of the statistical analyses of failure data from more than 250 distinct nonelectronic parts collected from recent commercial and military projects. This data was collected in-house (from operations and maintenance reports) and from industry wide sources. Tables, alphabetized by part class/ part type, are presented for easy reference to part failure rates assuminng that the part lives are exponentially distributed (as in previous editions of this notebook, the majority of data available included total operating time, and total number of failures only). For parts for which the actual life times for each part under test were included in the database, further tables are presented which describe the results of testing the fit of the exponential and Weibull distributions. 

The plotted characteristic numbers of cycles to fracture were determined by the Weibull method [21]. Each point represents a test series of ten specimens. In the diagram it can be seen clearly that fretting fatigue leads to a distinct deterioration of the specimen strength and life time. The higher the maximum Hertzian stresses the clearer the decline of the strength and life time is. 

In Figure 10 the number of fracture cycles and the characteristic number of fracture cycles for the respective test series is plotted against the maximum principal stress on the tensile loaded side of the specimens. The characteristic number of fracture cycles was determined by the method developed by Weibull [21]. In the Woehler diagram it can be seen clearly that fretting fatigue leads to a distinct deterioration of the life time. The higher the maximum stresses the clearer the decline of life time is. At Fn = 10 N (Pmax = 2311 MPa) the life time decreases at a maximum base load of OR.max = 210 MPa for about 80%. at Fn = 20 N (pmtx -2912 MPa) the life time decreases for about 91% compared to to life time under the same maximum base loading. 

Using the Weibull distribution, plots are made from measured strength data. These data are arranged in ascending order and assigned numbers beginning with 1 and ending with n. The survival probability (or expected life-time) is usually... 

The properties required for thermal stress analysis Included Young s modulus, Poisson s ratio, thermal conductivity, thermal expansion coefficient and specific heat. The CARES analysis requires strength data (from which the Weibull parameters are calculated) and Poisson s ratio. Fracture toughness was also measured. Although this parameter is not required for the fast fracture prediction made by CARES, it 1s used in life-time prediction and is related to the properties used in the reliability analysis. Strength measurements, which are the basis of reliability predictions, are controlled by both the size of flaws inherent in ceramic materials and the fracture toughness. Toughness represents the ability of a material to tolerate flaws. 

If a ceramic can fail by subcritical crack growth, its life time when loaded with a certain stress can be calculated from equation (7.2). In section 7.2.6, we used a deterministic approach to do so, but by now we have learned that the failure stress values scatter and the probability of failure follows a Weibull distribution Pf(failure stress, must therefore also be distributed stochastically. 

As a part of the joint project Increasing the availability of wind turbines operational data and experience of wind turbines were processed and analysed (IWES 2009). The life times and maintenance periods in this availability analysis are generic but were mainly based on the values shown there. The Weibull distribution was always chosen as the life time distribution. 

Influence on life time The failure probability at the life time specified with the parameter MTTF is 63.2% for a constant failure rate (i.e. Weibull shape parameter = 1) or approximately 50% for an increasing failure rate (e.g. Weibull shape parameter b = 3.5). That means, at this time half (or even more than the half) of the component s population are expected to be failed. Because of this, the MTTF as a specification parameter is often criticized. 

These examples illustrate the application of Weibull plots to service failure data in order to predict the probability of failure before the end of the service life, coupled with a power law to relate time to failure to the applied electric stress (voltage). 

Here (simulated) in vitro release profiles that differ by at least 10% are shown (panels a and b), as well as the (simulated) resulting plasma concentration-time profiles for a drug with a 1-hr half-life (panel c) and 6-hr half-life (panel d). The simulated-release profiles are described by the following Weibull equation ... 

For an exponential distribution function, the mean time to failure and the characteristic time T are identical. When / = 1 the Weibull distribution represents the region of the working life. For fS > 1 the failure rate increases with time, as when the product is wearing out... 

A more common method for medical devices is to run the life test until failure occurs. Then an exponential model can be used to calculate the percentage survivability. Using a chi-square distribution, limits of confidence on this calculation can be established. These calculations assume that a failure is equally likely to occur at any time. If this assumption is unreasonable (e.g., if there are a number of early failures), it may be necessary to use a Weibull model to calculate the mean time to failure. This statistical model requires the determination of two parameters and is much more difficult to apply to a test that some devices survived. In the heart-valve industry, lifetime prediction based on S-N (stress versus number of cycles) or damage-tolerant approaches is required. These methods require fatigue testing and ability to predict crack growth. " ... 

If it can be demonstrated that an SIF device (e.g., a block valve) has dominant time-based failure mechanisms (i.e., they wear out), the random failure rate model can lead to erroneous conclusions and practices. For example, in calculating test intervals, a random model may lead to testing more frequently than actually required during the early life of the device and testing too infrequently during the later wear-out phase. Owners/operators should be aware that reliability models (e.g., Weibull) are available that divide failures into infant mortality, random, and wear-out modes. This guideline assumes failures are random. 

Outline Life of product population is predicted with the help of Weibull analysis in which a statistical distribution is attempted to fit into life data from a representative sample of units. Then same data set can be used for estimation of important life parameters/cbaracteristics such as reliability or probability of failure at a specific time, the mean life, and the failure rate. For Weibull data analysis, the following information are required ... 

A Weibull distribution is a generalized distribution, as each type of product population provides different types of information about the life of the product, and different life data analysis method may vary. It is quite normal that life will be in unit of time but it may not be the case always, for example, life of lubrication in automobile is dictated by kilometers miming of the vehicle and not in time units. Time is a common measure of life, so often referred to as times-to-failure. There could be different (e.g., three) types of life data, each type provides different information about the life of the product with complete data, the exact time-to-failure for the unit is known (e.g., the unit failed at 100 h of operation). With suspended or right censored data, the unit operated successfully for a known period of time and then continued (or could have continued) to operate for an additional unknown period of time (e.g., the unit was still operating at 100 h of operation).With interval and left censored data, the exact time-to-failure is unknown but it falls within a known time range [5] . Based on statistical methods, characteristic parameters are calculated to fit a life disnibution to a patticulat data set. Fot futthet details on this generalized statistical distribution, a standard book on statistics may be referred to. After the same is done one can use to get the following results ... 

A practical use of fitting a distribution to reliability data is to extrapolate to smaller failure rates or other environmental conditions. To simplify the equations, the expressions in the text refer to the mean life of the relevant portion of the assembly. If the constants that define the failure distribution are known, the time to reach a smaller proportion of failures may be readily calculated. For example, for failure modes that are described by a Weibull distribution, the time f to reach x% failures is given by ... 

Determine life distribution from accelerated life distribution. The accelerated life distribution should be determined by fitting the data with the appropriate statistical distribution, such as the Weibull or log-normal distribution. The life distribution in service can be determined by transforming the time axis of the life distribution using the acceleration model. This predicted life distribution in service can then be used to estimate the number of failures in the specified service hfe. 

This situation can often be improved from an analytical viewpoint via the application of Weibull statistics to the plant data [12,13], which assumes that the life of the component is dominated by the time spent in the early crack initiation and "short" crack growth phases... 

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