Practical System Reliability (original) (raw)
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Mathematical Models of Reliability in Technical Applications
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This master's thesis is describing and applying parametric and nonparametric reliability models for censored data. It shows the implementation of reliability in the Six Sigma methodology. The methods are used in survival/reliability of real technical data.
How Reliable is Reliability Function
According to Knezevic [1] the purpose of the existence of any functional system is to do work. The work is done when the expected measurable function is performed through time. However, experience teaches us that expected work is frequently beset by failures, some of which result in hazardous consequences to: the users; the natural environment; the general population and businesses. During the last sixty years, Reliability Theory has been used to create failure predictions and try to identify where reductions in failures could be made throughout the life cycle phases of maintainable systems. However, mathematically and scientifically speaking, the accuracy of these predictions, at best, were only ever valid to the time of occurrence of the first failure, which is far from satisfactory in the respect of its expected life. Consequently, the main objective of this paper is to raise the question how reliable are reliability predictions of maintainable systems based on the Reliability Function.
2014
In this paper a two unit standby system with single repair facility has been considered. When a working unit fails, it is immediately taken over by standby unit and repair on the failed unit is started immediately. Taking two types of distribution, namely, Weibull and Erlangian, various system effectiveness measures such as MTSF, Availability and Busy Periods are compared and results are interpreted numerically. Regenerative Point Technique and Semi-Markov process have been employed in this paper to find the results. Results are supported with numerical data also. Failure time distributions are taken to be exponential whereas the repair times are particular. The result obtained from this can be applied to study complex system where small change in the value of one variable affects the system measures to a great extent. Key words: MTSF, availability, busy period, regenerative point technique, Semi-Markov process.
Journal of Advances in Mathematics and Computer Science
As a random variable, the survival time or Time to Failure (TTF) of a certain component or system can be fully characterized by its probability density function (pdf) fT (t) or its Cumulative Distribution Function (CDF) FT (t). Moreover, it might be also identified by transform functions such as the Moment Generating Function (MGF) and the Characteristic Function (CF). In reliability engineering, additional specific equivalent characterizations are used including the reliability function (survival function) which is the Complementary Cumulative Distribution Function (CCDF), and the failure rate (hazard rate), which is the probability density function normalized w.r.t. reliability. In prognostics, a prominent emerging subfield of reliability engineering, the characterizing functions are still supplemented by other specifically tailored ones. Notable among these is the Mean Residual Life (MRL) (also know as the Remaining Useful Life (RUL)). The purpose of this paper is to compile and interrelate the most prominent among these
Interval-Valued Parametric Distribution Functions: Application to System Reliability Analysis
Journal of Mathematical Extension, 2015
A lot of methods and models in classical reliability theory assume that all parameters of lifetime density function are precise.But in the real world applications imprecise information is often mixed up in the lifetimes and/or parameters of systems.However, the parameters sometimes cannot be recorded precisely due to machine errors, experiment, personal judgment, estimation or some other unexpected situations.When parameters in the lifetime distribution are interval-valued, the conventional reliability system may have difficulty for handling reliability function.Therefore, estimation methods for reliability characteristics have to be adapted to the situation of interval-valued parameters of life times in order to obtain realistic results.In this regard, the present paper will discuss the system reliability for coherent system based on a new notion of random variable withinterval-valued parameters.The concepts of probability density function and cumulative distribution function of ...
Comparison of reliability models
2009
Many stochastic models have been used in solving reliability problems, motivated by a high degree of variability or randomness of the studied phenomena. Therefore different types of stochastic laws derived from the basic distributions are proposed for modelling a hazard-rate function too. The main contribution of the present paper is to proposed new adaptive hazard rate functions, derived from classical models. A numerical example is provided for the introduced models and comparison is also discussed. It can be seen that these new adaptive functions are competitive models for describing the bathtub-shaped failure rate of the lifetime data.
Formal lifetime reliability analysis using continuous random variables
Logic, Language, Information and …, 2010
Reliability has always been an important concern in the design of engineering systems. Recently proposed formal reliability analysis techniques have been able to overcome the accuracy limitations of traditional simulation based techniques but can only handle problems involving discrete random variables. In this paper, we extend the capabilities of existing theorem proving based reliability analysis by formalizing several important statistical properties of continuous random variables, for example, the second moment and the variance. We also formalize commonly used reliability theory concepts of survival function and hazard rate. With these extensions, it is now possible to formally reason about important reliability measures associated with the life of a system, for example, the probability of failure and the mean-time-to-failure of the system operating in an uncertain and harsh environment, which is usually continuous in nature. We illustrate the modeling and verification process with the help of an example involving the reliability analysis of electronic system components.
Representing the mean residual life in terms of the failure rate
Mathematical and Computer Modelling, 2003
In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem-namely that of expressing the mean residual life in terms of the failure rate-typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.
On discrete failure-time distributions
Reliability Engineering & System Safety, 1989
Different classes of discrete life distributions are defined parallel to the continuous life distributions. Some implications known to be present in continuous life distributions are shown to exist among discrete life distributions. Some test statistics of geometric distribution property versus other classes o f failure-time distribution are proposed. Critical points of these statistics, based on simulations are presented. Powers of these tests against increasing failure rate (IFR) and decreasing failure rate (D FR) distributions are also calculated.