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Abstract: This paper considers the one-sample sign test for population quantiles in general ranked set sampling, and proposes a weighted sign test because observations with different ranks are not identically distributed. It is shown analytically that optimal weight always improves the Pitman efficiency for all distributions. For each quantile, the sampling allocation that maximizes the sign test efficacy is identified and shown to not depend on the population distribution. Moreover, distribution-free confidence intervals for quantiles based on ordered values of optimal ranked set samples are discussed. [Copyright &y& Elsevier]

Abstract: A proof on the optimal arrangement of a linear consecutive-k-out-of- system, with , was given by Jalali et al. [2005. The optimal consecutive-k-out-of- line for . J. Statist. Plann. Inference 128, 281–287]. However, a corollary for the case was still incomplete. In this note we point out what is missing from the proof of that corollary and present a new proof using a different approach. [Copyright &y& Elsevier]

The availability of systems undergoing periodic inspections is studied in this paper. A perfect repair or replacement of a failed system is carried out requiring either a constant or a random length of time. In Model A, the system is assumed to be as good as new on completion of inspection or repair. For Model B, no maintenance or corrective actions are taken at the time of inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. Unlike that studied in a related paper by Sarkar and Sarkar (J. Statist. Plann. Inference 91 (2000) 77.), our model assumes that the periodic inspections take place at fixed time points after repair or replacement in case of failure. Some general results on the instantaneous availability and the steady-state availability for the two models are presented under the assumption of random repair or replacement time. [Copyright &y& Elsevier]