In this paper we compare the residual lifetime of a used coherent system of age t0 with the lifetime of the similar coherent system made up of used components of age t. Here ‘similar’ means that the system has the same structure and the component lifetimes have the same dependence (joint...

Independent random samples are taken from two normal populations with means <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mu _1$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mu _2$$</EquationSource> </InlineEquation> and a common unknown variance <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\sigma ^2.$$</EquationSource> </InlineEquation> It is known that <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mu _1\le \mu _2.$$</EquationSource> </InlineEquation> In this paper, estimation of the common standard deviation <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> </InlineEquation> is considered with respect to...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

Let [Pi]1,[Pi]2,...,[Pi]k be k populations with [Pi]i being exponential with an unknown location parameter [mu]i and a common but known scale parameter [sigma], i=1,...,k. Suppose independent random samples are drawn from the populations [Pi]1,[Pi]2,...,[Pi]k. Let {Xi1,Xi2,...,Xin} denote the...

Independent random samples from k exponential populations with the same location parameter [theta] but different scale parameters [sigma]1, ..., [sigma]k are available. We estimate the quantile [eta]1 = [theta] + b[alpha]1 of the first population with respect to squared error loss. Sharma and...