حسن رسائی

There exist many processes where the quality characteristic does not follow a normal distribution, and the conditions for the application of central limit theorem are not satisfied; for example, because collecting data in a subgroup is impossible or the distribution is highly skewed. Thus, researchers have developed the control charts according to the specific distribution that models the quality characteristic. In this paper, some control charts are designed to monitor an exponentially distributed lifetime. The life testing is conducted according to the failure censoring while during the test; once observing a failure item, it is replaced by a new one so that the total number of items inspected during the test remains constant. Under the condition of the test, it is discussed that the elapsed time until observing the r’th failure has Erlang distribution. According to the relation of Erlang and chi-square distributions, the chart limits are computed to satisfy a specified value of type I error. Examples are presented and the curves of average run length are derived for the one-sided and two-sided control charts. Also, a comparative study is conducted to show the performance and superiority of the proposed control charts.