Reliability and failure rate of electronic system using mixture Lindley distribution

What is it about?

In this study, a statistical method was applied on the lifetime of electronic system contains 20 electronic unit, each unit include two electronic components having Lindley distributions in order to estimate the reliability and failure rate of the electronic system by using mixture Lindley distribution. The study dealt with the method of combining two Lindley distributions and produced the mixture Lindley distribution by including a mixing parameter which represents the proportions of the mixing of two components Lindley distributions. The maximum likelihood method was chose to estimate the values of the parameters for the mixture Lindley distribution. In addition the probability density function, cumulative distribution function, reliability function and failure rate of the mixture Lindley distribution were obtained. On the other hand, a numerical application was prepared to illustrate the implementation of mathematical procedures and obtain the required numerical results. Moreover this study enables the researchers and helps them to apply it in the field of their specialization.

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Why is it important?

The numerical results in this study show that the estimated parameters of the mixture Lindley distribution with different values of mixing parameter were good estimators because there are no significant differences for each of the reliability and failure rate in two Lindley distributions of two components in the electronic unit and mixture Lindley distribution with different values of mixing parameter. In addition, the reliability and failure rate in the mixture Lindley distribution are not affected by the different values of the parameter missing, as there is a strong inverse relationship between each of the reliability and failure rate and this means that the mixture Lindley distribution achieved a good results. The method used in this study to deduce the mixture Lindley distribution by the combining two Lindley distribution enable the researchers to apply it in the field of specialization with other distributions in order to deal with one mixture distribution, instead of two or more distributions and obtain the reliability and failure rate of the electronic system which contains any number of electronic units which each unit include different numbers of electronic components.