This paper discusses the hazard rate order of the fail-safe systems arising from two sets of independent multiple-outlier scale distributed components. Under certain conditions on scale parameters in the scale model and the submajorization order between the sample size vectors, the hazard rate ordering between the corresponding fail-safe systems from multiple-outlier scale random variables is established. Under certain conditions on the Archimedean copula and scale parameters, we also discuss the usual stochastic order of these systems with dependent components.

In this paper, a nonparametric test based on incomplete data is proposed to investigate the usual stochastic order  using an extension of Banerjee statistic for Type I censored data. This extension is optimized with weight coefficients based on Simpson's rule and the bootstrap method with 10000 iterations to estimate the empirical distribution of the proposed test statistic. The empirical distribution of the statistic under censoring is studied, and the power of the test is evaluated using Monte Carlo simulations against the Lehmann alternative model.