The sums of two exponential random variables are compared in the sense of likelihood ratio order. It is shown that, under some conditions, their likelihood ratio order does not exist and, if it exists, the complete comparison results can be determined.

In the design of the control chart, both the sample size m of and the control-limit factor k (the number of standard deviations from the center line) must be determined. We address this problem under the assumption that the quality characteristic follows an autocorrelated process with known...