Discrete distributions have played an important role in the reliability theory. In order to obtain Bayes estimators, researchers have adopted various conventional techniques. Generalizing the results of Maiti (1995), Chaturvadi and Tomer (2002)
A new lifetime distribution for modeling system lifetime in series setting is proposed that embodies most of the compound lifetime distribution. The reliability analysis of parent and of sub-models has also been discussed. Various mathematical properties that include moment generating function, moments, and order statistics have been obtained. The newlyproposed distribution has a flexible density function; more importantly its hazard rate function can take up different shapes such as bathtub, upside down bathtub, increasing, and decreasing shapes. The unknown parameters of the proposed generalized family have been estimated through MLE technique. The strength and usefulness of the proposed family was tested on a real life data set and it is quite clear from the statistical analysis that proposed family offers a better fit.
Planning a highly reliable and efficient system has always been a primary interest for reliability engineers by devising the powerful design strategy and employing effective repair and replacement policy. Keeping in view this, the basic aim of this paper is to analyze the reliability of a system which comprised of two units A and B in which unit A is functional and B is held standby. Unit A after failure may be controlled or uncontrolled. The failed unit undergoes for repair in the controlled unit. If the repair of a unit is not controlled then it is replaced by a new one. Upon the breakdown of operational unit A, unit B come becomes active instantaneously. Unit B after failure is repaired by regular repairmen. System failure takes place when both the units quit serving. The unit serves as good as a fresh after preventive repair and replacement policy. The regenerative point technique has been used to obtain the expression for several reliability measures. Finally, the graphical behavior of MTSF and profit of the present model has been observed for arbitrary values of parameters and costs.
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