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SUMMARYIt is often the case that some information is available on the parameter of failure time distributions from previous experiments or analyses of failure time data. The Bayesian approach provides the methodology for incorporation of previous information with the current data. In this paper, given a progressively type II censored sample from a Rayleigh distribution, Bayesian estimators and credible intervals are obtained for the parameter and reliability function. We also derive the Bayes predictive estimator and highest posterior density prediction interval for future observations. Two numerical examples are presented for illustration and some simulation study and comparisons are performed.

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Photoluminescent nanomaterials have immense potential for use in biological systems due to their excellent fluorescent properties and small size. Traditional semiconductor quantum dots are heavy-metal-based and can be highly toxic to living organisms, besides their poor photostability and low biocompatibility. Nano-sized carbon quantum dots and their surface-modified counterparts have shown improved characteristics for imaging purposes. We used 1,3, 6-trinitropyrene (TNP) and polyethylene glycol6000 (PEG6000) in a hydrothermal method to prepare functional polyethylene glycol6000/carbon nanodots (PEG6000/CDs) and analyzed their potential in fluorescent staining of different types of bacteria. Our results demonstrated that PEG6000/CDs stained the cell pole and septa of gram-positive bacteria B. Subtilis and B. thuringiensis but not those of gram-negative bacteria. The optimal concentration of these composite nanodots was approximately 100 ppm and exposure times varied across different bacteria. The PEG6000/CD composite had better photostability and higher resistance to photobleaching than the commercially available FM4-64. They could emit two wavelengths (red and green) when exposed to two different wavelengths. Therefore, they may be applicable as bioimaging molecules. They can also be used for differentiating different types of bacteria owing to their ability to differentially stain gram-positive and gram-negative bacteria.