Limited Failure Censored Life Test Sampling Plan in Burr Type X Distribution

The Burr type X distribution is considered as a life time random variable of a product whose lots are to be decided for acceptance or otherwise on the basis of sample lifetimes drawn from the lot. The sample is divided into various groups in order to develop a group sampling plan in such a way that the life testing experiment is terminated as soon as the first failure in each group is observed. The acceptance criterion based on the theory of order statistics is proposed and is shown to be more economical than a criterion proposed in the earlier similar works

Ring opening of oxiranes catalyzed by Mn-Salen immobilized mesoporous materials

Mn-Salen immobilized mesoporous materials were found to be efficient solid catalysts for the nucleophilic ring opening of oxiranes with TMSN3, TMSCN and aniline

Friedel-Crafts sulfonylation of aromatics catalysed by solid acids: an eco-friendly route for sulfone synthesis

A mild and efficient catalytic method for Friedel-Crafts sulfonylation of arenes to the corresponding sulfones using a catalytic amount of reusable solid acid and arene- or alkanesulfonyl chlorides, sulfonic anhydrides and sulfonic acids as sulfonylating agents is described. Solid acids enable formation of a sulfone by the reaction of a sulfonic acid and an arene for the first time. In pursuit of the development of the best catalytic system, various metal-exchanged K10 montmorillonites and synthetic zeolites such as zeolite beta, zeolite Y and ZSM-5 have been screened for Friedel-Crafts sulfone synthesis. Fe3+-montmorillonite in the family of clays and zeolite beta in the family of zeolites exhibit higher activity. The activity is correlated to the presence of the right mix of Bronsted and Lewis acidic sites. The regioselective sulfonylation of toluene and naphthalene are studied in which para and beta selectivities are observed respectively

Polymer-anchored palladium catalyst in carbonylation of organic halides - the first example of triphase catalysis

Polymer-anchored palladium-catalysed carbonylation of organic halides affords oxo esters in reasonable- yields under solid-liquid-solid phase transfer conditions at mild pressure and short durations

Estimation and Testing in Type I Generalized Half Logistic Distribution

A generalization of the half logistic distribution is developed through exponentiation of its cumulative distribution function and termed the Type I Generalized Half Logistic Distribution (GHLD). GHLD’s distributional characteristics and parameter estimation using maximum likelihood and modified maximum likelihood methods are presented with comparisons. Comparison of Type I GHLD and the exponential distribution is conducted via likelihood ratio criterion

Likelihood Ratio Type Test for Linear Failure Rate Distribution vs. Exponential Distribution

The Linear Failure Rate Distribution (LFRD) is considered. The graphs of its probability density function are examined for selected parameter combinations. Some of them are similar to the well-known exponential distribution. Incidentally exponential distribution is one of the two component models of the LFRD model. In view of the simpler form of exponential model as applicable in inference, looking at the frequency curves of LFRD, a test statistic is proposed based on ratio of likelihood functions containing the standard forms of the density functions of both LFRD and Exponential to discriminate between LFRD and exponential models. The critical values and the powers of the test statistic are developed

The first example of heterogeneous oxidation of secondary amines by tungstate-exchanged Mg-Al layered double hydroxides: a green protocol

Tungstate exchanged Mg-Al layered double hydroxides a as recyclable heterogenised catalyst along with H2O2 as an oxidant for the oxidation of sec-amines to nitrones is developed for the first time, Reactions proceed at a fast rate in aqueous media in a single step at room temperature in good to excellent yields. The heterogenised catalyst showed higher activity (TOF) over their homogeneous analogues and other heterogeneous catalysts reported so far. The obtained catalysts were well characterised by various instrumental techniques such as FT-IR spectroscopy, thermal analysis (TGA and DTA), powder XRD and chemical analysis. The catalyst can be reused for six cycles with consistent activity and selectivity

Henry reactions catalysed by modified Mg-Al hydrotalcite: an efficient reusable solid base for selective synthesis of β-nitroalkanols

Henry reactions have been performed for the first time with suitably activated Mg-Al hydrotalcite as catalyst in quantitative yields in the liquid phase under mild reaction conditions and with low reaction times. Exclusive synthesis of β-nitroalkanols (3) is realised by the compatible basic Bronsted hydroxy sites of the modified hydrotalcite. Reusability with consistent activity and selectivity for a number of cycles is established indicating that the hydrated hydrotalcite employed here is a potentially eco-friendly catalyst which can replace soluble bases in commercial synthesis

A new bifunctional catalyst for tandem Heck-asymmetric dihydroxylation of olefins

A new bifunctional catalyst consisting of active palladium and osmium species anchored on silica gel through a mercaptopropyl spacer and a cinchona alkaloid respectively has been prepared for the first time and used in the heterogeneous tandem Heck-asymmetric dihydroxylation of olefins to afford diols with excellent yields and enantiomeric excesses (ee's) in presence of N-methylmorpholine Noxide or K3Fe(CN)6 as cooxidants

The first example of direct oxidation of sulfides to sulfones by an osmate molecular oxygen system

Osmate-exchanged Mg-Al layered double hydroxides catalysed the delivery of two oxygen atoms simultaneously via a 3 + 1 cycloaddition to sulfide to form sulfone directly for the first time, reminiscent of 3 + 2 cycloaddition in asymmetric dihydroxylation reactions