Estimation for Product Life Expectancy Paramaters under Interval Censored Samples

Kaiwen Guo Department of Maths, Tianjin Polytechnic University Tianjin 300160, China Tel: 86-022-2459-0532 E-mail: guokaiwen04@126.com Abstract From basic consept for reliability theory, we computed the moment and maximum likehood estimation for product life expectancy paramaters by means of interval censor data. This is a feasible and efficient estimator for life parameters


Introduction
In survival analysis and reliable research, often because of the restriction of objective conditions, the time lapse could not be accurately observed values, which they can only be observed by their interval.Generally this kind of data is called interval censored data .In 1972 Hole and Walburg had the research and the application in the medicine clinical test domain to the interval censored data .In 1991 Keiding and walburg gave the definition of the interval censored data theoretically.When the survival variable turns to the product life, the products to maintain their performance time are an imporant quality indicator, such reliability and product life are linked each other.When the censored variable turns to a time variable, we assume that this variable be a continuous random variable, the probability density function have un-known parameters which need to be estimated.In this paper, by means of interval censored data, we gave the monment estimation and maximum likehood estimation.

Suppose that survival variable and the interruption variable all obey the single parameter exponential distribution
Let X be a survival variable, which is a continuous random variable, the probability density function of X is . Let Y be a survival variable, which is a continuous random variable, the probability density function of Y is . Suppose that survival variable obeys the single parameter exponential distribution, , where

Suppose that survival variable obeys the single parameter exponential distribution and the interruption variable obeys the even distribution
Let X be a survival variable, which is a continuous random variable, the probability density function of X is . Let Y be a survival variable, which is a continuous random variable, the probability density function of Y is . Suppose that survival variable obeys the even distribution, . Assume X and Y be mutually . Now we consider the monment estimation of interal , where . In the moment 0 0 = t we start to admit experimental n-products.In the moment 1 t , 2 t , …, i t , we remove for examination, these n-products in the product life have ended to remove, the remaining time puts the latter to continue testing.In the period of products lives be lost, but c-products lives haven't lost , then we give a reliability function , we have their maximum likehood estimation

Example
Let the product life obey the single parameter exponential distribution, we extract 12-products to carry on the experiment.When 8-products lives have already finished we stop experiment, the products lives closure time presses the arranged in order is 2, 10,18,36,60,180,720,2880, we discuss the maximum likehood estimate and the monment estimate solution.From the time order 2, 10, 18, 36, 60, 180, 720 and 2880, we

conclusion
The monment estimate and the maximum likehood estimate to obtain the product life only to be able to small partially to carry on the experiment, the sample which we can take are quite small, but the monment estimate and the maximum likehood estimate to the unknown parameter is a kind of feasible and efficient estimate method.
the overall Y.When we observe them actually, we can obtain the sample