Lifetime data has two distinguishing features: they are usually censored and have non-normal distributions. Generally speaking, censoring schemes can be classified into (i) censoring schemes with replacement and (ii) censoring schemes without replacement. Replacement during a life testing means that once observing a failure item, it is replaced by a new one. While there is a relatively large body of literature regarding control charts under censoring schemes without replacement, i.e., the second type schemes, designing control charts for the first type schemes has not yet received considerable attention. In this paper, two types of control charts are developed to monitor the lifetime data of an exponentially distributed item. To obtain the information of the lifetime data, failure censoring is conducted: n items are randomly selected and put on the test simultaneously. The test continues until observing r (r≤n) failures. During the test, once observing a failure time, it is replaced by a new one. Development of Shewhart type and exponentially weighted moving average control charts under failure censoring with replacement is the main novelty of the current study. Comparative and simulation studies are conducted. ARL curves are also derived with respect to different parameters of the process.
