REPAIR MODELS: USING WEIBULL DISTRIBUTION AS A CASE STUDY

ABSTRACT

This paper provides an insight into various forms of repair models and their implementation when failure of a system occurs. It also shows the basic maintenance policy to be implemented so as to avoid a total breakdown and finally the application of Weibull distribution to analyze the failure time of a system. The time to failure of a system is also talked about as well as its relationship to other statistical distributions, as well as highlighting the mathematical expression of some statistical properties such as the mean, variance, median, mode, failure rate function, survival function, hazard function, reliable life and the estimation of a Weibull distribution. The time to failure of a system data by (Al-Fawzan 2000) is used to compute the parameter estimate, and also to solve some statistical properties such as the survival function, hazard function (failure rates) for the Weibull distribution. It was  observed that the survival rate gradually decrease and while the hazard rate gradually increase as the failure time increases for the Weibull distribution, this simply means that the Weibull distribution can be used to analyze reliability problems. It was also observed that the Weibull distribution decay fast from the survival rates. Considering the two deciding statistical properties for Weibull distribution, we conclude that using the Weibull distribution fits reliability analysis.