In many scientific studies, treatments are applied in a naturally ordered sequence, such as increasing or decreasing dose levels. Researchers are often interested in comparing the effects of successive treatments within these sequences. When treatment effects follow a normal distribution, [1] developed simultaneous confidence intervals (SCIs) for successive differences in treatment means, assuming equal but unknown variances. [2] later improved upon this approach by proposing more powerful SCIs under the same homoscedasticity assumption. In this paper, we extend [2] procedure methodology to settings where treatment variances are unequal and unknown. We propose new SCIs based on both one-stage and two-stage procedures for comparing successive treatment effects under heteroscedasticity. Furthermore, we introduce new criteria for the design-oriented two-stage procedure to eliminate selection bias. Critical values are obtained using a recursive integration method, which are then tabulated for one-sided and two-sided tests across different numbers of treatments and significance levels. We evaluate the finite-sample performance of the proposed methods through a simulation study, focusing on the size and power properties of both procedures. Finally, the practical usefulness of the approach is further demonstrated using a real data example.
