**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series B, Pt. 2, pp. 231--239

**RESTRICTED REGION SIMPLEX DESIGNS FOR MIXTURE EXPERIMENTS IN THE PRESENCE OF PROCESS VARIABLES**

By

M. S. RAMCHANDRA MURTHY and P. LAKSHMI MANGA, *Osmania University*

SUMMARY. In the study of experiments with mixtures, the component proportions x_{i}(i = 1, 2, ...q) satisfy ${x _ i}\leq 0$, $(\sum_{i}^{q} x_{i}=1$. The factor space is a (q-1) dimensional simplex. When the q component proportions are constrained by $m_{i} \leq x_{i} \leq M_{i]}(i = 1, 2, ..., q) the region of exploration is a restricted region of the simplex are denoted by RRSD. RRSD in the presence of process variables are denoted by M X P RRSD. In this paper, two M X P RRSDs are constructed.

*AMS (1980) subject classification.* 62K, 62K99.

*Key words and phrases.* Extreme vertices design, mixture variable, process variable, transformation.