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Percentile modification concerns with using only fraction of the sample observations in computation of the test statistic. The modification improves power of rank based tests given appropriate amount of percentile modification is performed. This paper addresses the problem of deciding amount of percentile modification in context of two sample, multivariate scale problem using data depth. We propose an adaptive test which decides amount of modification based on tail heaviness of the data. As a second approach, we define three test statistics on a group of percentile modified statistics using different combining functions, viz. a quadratic form, a maximum-type and a sum-type. With this strategy, the task of choosing a single optimum value as an amount of percentile modification becomes irrelevant. Monte-Carlo simulation is used to perform comparative power study. Adaptive test as well as sum-type and maximum-type statistics based on a group of percentile modified statistics yield attractive powers whereas quadratic form statistics do not show promising results. [ABSTRACT FROM AUTHOR]

If process is running for a long period in an in-control condition, it will reach in a steady-state condition. In order to study the long term properties of a control chart, it is appropriate to investigate the steady-state average time to signal. In this article, we discussed runs rules representation of a nonparametric synthetic control chart using sign statistic for detecting shifts in location parameter. We compared zero-state average time to signal with steady-state average time to signal of the synthetic control chart for symmetric and asymmetric distributions. We also present the m-of-m control chart using sign statistic. For comparison study, we computed average time to signal of the m-of-m control chart, the sign chart (1-of-1 chart) and the synthetic control chart for normal, Cauchy, double exponential and gamma distributions. Steady-state and zero-state performance of the m-of-m control chart with m = 2, 3 compared with the sign chart (1-of-1 chart) and synthetic control chart. The zero-state and steady-state average time to signal of the synthetic and the m-of-m control charts computed using Markov chain approach. [ABSTRACT FROM AUTHOR]