A Statistical Design Consideration in Robotic Systems
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Stan A h , PhD Senior Research Fellow Areti Manola MS Senior Biostatistician Ramendro Pandey, PhD Technical Team Leader
John Troisi. AS Associate Scientist The lohnson & lohnson Pharmaceutical Research & Development L.L.C. Raritan. New Jersey
A Statistical Design Consideration in Robotic Systems
Damaraju Raghavarao, PhD Professor, Stat is tics Department. Temple University, Philadelphia, Pennsylvania
Key Words Robotic systems; Carryover effect; designs Correspondence Address Stan Altan. PhD, Senior Research Fellow, The Johnson &Johnson Phwmceutical Research S. Development L.L.c., Rantan, NI 08869 [email protected]).
INTRODUCTION When robotic machines are used to collect samples in a serial order, such as in automated sample preparation for the analytical determination of impurities, the residue of one sample may be carried to subsequent samples. During method validation, the statistical analysis must consider these carryover effects in order not to bias the results. For simplicity, we assume that the carryover effect persists to the subsequent sample and no further. If there are v distinct samples, the replicates of the sample should be arranged in a sequence such that any two distinct samples occur together equally often, say once. In the statistical literature, Finney and Outhwaite (1,2) introduced two types of serially balanced sequences. The treatments are arranged in a series of complete blocks in such a way that the residual effect of any treatment occurs the same number of times in conjunction with the direct effect of each treatment including itself (type 1 sequences) or of each other treatment (type 2 sequences). Sampford (3) investigated the constructions of these sequences systematically and Nair (4) extended their results to higher order residual effects. Monod (5)constructed serially balanced factorial sequences using orthogonal arrays, which are useful when the
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The use of automated sample preparation machines requiring sequences of different samples distinguishable by strength, for example, or treatments, has raised the question of how the samples should be ordered in view of possible carryover effects. The use of serially balanced sequences is advocated in this context where the residual effect of each treatment occurs one or more times with the direct effect of every other treatment and possibly itself. Such designs permit the study of carryover effects as well as treatment effects concurrently, thus obviating the need to do separate studies for carryover and treatment effects. The designs given in this paper have minimum length. Several examples are illustrated and the analysis is sketched for these experiments.
number of treatments is of the form s". where s is two or three and n is a positive integer. For analyzing the data from an automated sample preparation machine, complete blocking of distinct samples is not really needed and type 2 sequences are adequate. We give a simple construction of type 2 sequences balanced for residual effects of minimal length in the next section and
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