Life testing is an important method for evaluating components reliability by assuming a suitable lifetime distribution. Once the test is carried out by subjecting a sample of items of interest to stresses and environmental conditions that typify the intended operating conditions, the lifetimes of the failed items are recorded.

Due to time and cost constraints, often the test is stopped at a predetermined time (type I censoring) or a predetermined number of failures (type II censoring). If each item in the tested sample has the same chance of being selected, then the equal probability sampling scheme is appropriate, and this lead theoretically to the use of standard distributions to fit the obtained data.

If the proper sampling frame is absent and items are sampled according to certain measurements such as their length size age or any other characteristic. In such a case the standard distributions can not be used due to the presence of certain bias and must be corrected using weighted distributions. In the life testing, the lifetime distribution is not necessary homogenous and it can be a mixture of two ore more than two sampler lifetime distributions, each one represents a distinct case of failure.

Weighted distributions, mixture distribution, classical methods of estimation, bayesian methods..

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