In some situations in reliability and survival analysis, the life times of the units in an experiment depend on the number of times the units are switched on and off or the number of shocks they receive. On the other hand, the experiment may not terminate on an adequate time under the normal conditions. This paper proposes a Bayesian inference model for a simple step-stress model with Type-I censored sample. Assuming a cumulative exposure model with lifetimes being geometric distributed, the problems of point and interval estimation of studied in the Bayesian approach. Finally, an example is presented to illustrate the proposed procedure in this paper.

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