a b s t r a c tThis paper deals with the optimal designing of step-stress partially accelerated life tests (PALTs) in which items are run at both accelerated and use conditions under censoring. It is assumed that the lifetime of the items follow truncated logistic distribution truncated at point zero. Truncated distributions arise when sample selection is not possible in some sub-region of the sample space. The logistic distribution is considered inappropriate for modeling lifetime data because left hand side of its distribution extends to negative infinity, and this could conceivably result in modeling negative times-to-failure. This has necessitated the use of truncated logistic distribution truncated at point zero for modeling lifetime data. Unlike the widely studied exponential, Weibull and lognormal life distributions, the failure rate of truncated logistic distribution is increasing and more realistically bounded below and above by non-zero finite quantity. The optimal change-time for the step PALT is determined by minimizing either the generalized asymptotic variance of maximum likelihood estimates (MLEs) of the acceleration factor and the hazard rate at use condition or the asymptotic variance of MLE of the acceleration factor. Inferential procedure involving model parameters and acceleration factor are studied. Sensitivity analysis is also performed.

A novel single-step process with chlorosulfonic acid catalyst for ultrasonic biodiesel synthesis using feedstock with high free fatty acid content is investigated.Jatropha curcas oil has been used as the model feedstock with methanol as alcohol. The distinct merit of chlorosulfonic acid is that it catalyzes both esterification and transesterification reactions. Moreover, chlorosulfonic acid also counteracts inhibition caused by water formed during esterification, which is the cause for very slow kinetics of acid catalyzed transesterification. In addition, sonication of the reaction mixture also causes strong micromixing and emulsification that enhances the transesterification kinetics. Statistical optimization of the process shows 93% yield for 8.5 wt % catalyst, 20:1 alcohol to oil molar ratio and temperature of 333 K. Peculiar feature of this process is that high yield is seen at moderate temperature and molar ratio, which are much smaller than that for conventional sulfuric acid catalyzed processes. The activation energy for the process (57 kJ/mol) is at least 33 lower than the energy for sulfuric acid catalyzed transesterification. The thermodynamic analysis reveals that the net Gibbs energy change for the single-step process is almost same as that for sulfuric acid catalyzed process.

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