Bayes estimation for exponential distributions with common location parameter and applications to multi-state reliability models

This paper considers the estimation of the stress–strength reliability of a multi-state component or of a multi-state system where its states depend on the ratio of the strength and stress variables through a kernel function. The article presents a Bayesian approach assuming the stress and strength as exponentially distributed with a common location parameter but different scale parameters. We show that the limits of the Bayes estimators of both location and scale parameters under suitable priors are the maximum likelihood estimators as given by Ghosh and Razmpour [15 M. Ghosh and A. Razmpour, Estimation of the common location parameter of several exponentials, Sankhyā, Ser. A 46 (1984), pp. 383–394. [Google Scholar]]. We use the Bayes estimators to determine the multi-state stress–strength reliability of a system having states between 0 and 1. We derive the uniformly minimum variance unbiased estimators of the reliability function. Interval estimation using the bootstrap method is also considered. Under the squared error loss function and linex loss function, risk comparison of the reliability estimators is carried out using extensive simulations.     

COVID-19 vaccine rollout—scale and speed carry different implications for corruption

The sanctioning of different coronavirus vaccines (with some approved by regulators for public delivery, and others in the pipeline) has met with relief by many sections of the public and the government. However, partly due to the damages associated with the pandemic and the ensuing euphoria over vaccines’ arrival, some of the challenges are mostly being ignored or are not recognized. This paper identifies some pitfalls and drawbacks in vaccine delivery. We argue that the somewhat unique tension between the speed of vaccine delivery and its scale can create opportunities for corrupt behavior that are often at odds with effective means to check abuse. While data on instances of abuse will emerge over time, it is useful to point out different avenues of abuse so that some preventive government actions can be undertaken. Specifically, we argue that the potential for out of turn delivery of vaccines and the stockpiling by unauthorized agents creates incentives for corruption, with the public or bureaucrats initiating corrupt transactions. An understanding of the potential avenues for corruption should guide the formulation of appropriate corruption-control policies and similar challenges that will be faced by policy makers in addressing future pandemics.     

Moment identity for discrete random variable and its applications

In this paper, we obtain a moment identity applicable to a general class of discrete probability distributions. We then derive the corresponding identities for modified power series, Ord and Katz families. It is noted that the proposed identity has potential applications in different fields.     

Implementing lean sigma in an Indian rotary switches manufacturing organisation

The manufacturing organisations have been witnessing a transformation in the manufacturing paradigm. Lean sigma and six sigma are the two business process improvement strategies widely employed by organisations to enhance their manufacturing performance. To achieve dramatic result in cost, quality and time, best strategies need to be applied to enhance the process performance. Lean sigma and six sigma are two powerful and effective strategies, enabling the organisation to overcome their weakness and for retaining their improvement. Lean sigma combines the variability reduction tools and techniques drawn from six sigma with the waste and non-value added elimination tools and techniques from lean manufacturing to achieve savings in the organisations. This study uses an integrated lean sigma framework to reduce the defects occurring in the final product, thereby contributing savings to the organisation. The proposed framework integrates lean tools within six sigma methodology to enhance the bottom-line results and to win customer loyalty. The implementation of the proposed framework shows dramatic improvement in key metrics and substantial financial savings to be generated by the organisation.     

Estimation for an inverted exponentiated Rayleigh distribution under type II progressive censoring

In this paper, we consider estimation of unknown parameters of an inverted exponentiated Rayleigh distribution under type II progressive censored samples. Estimation of reliability and hazard functions is also considered. Maximum likelihood estimators are obtained using the Expectation–Maximization (EM) algorithm. Further, we obtain expected Fisher information matrix using the missing value principle. Bayes estimators are derived under squared error and linex loss functions. We have used Lindley, and Tiernery and Kadane methods to compute these estimates. In addition, Bayes estimators are computed using importance sampling scheme as well. Samples generated from this scheme are further utilized for constructing highest posterior density intervals for unknown parameters. For comparison purposes asymptotic intervals are also obtained. A numerical comparison is made between proposed estimators using simulations and observations are given. A real-life data set is analyzed for illustrative purposes.     

A goal programming model for paper recycling system

The conflict between economic optimization and environmental protection has received wide attention in recent research programs for waste management system planning. This has also resulted in a set of new waste management goals in reverse logistics system planning. The purpose of this analysis is to formulate a mixed integer goal programming (MIGP) model to assist in proper management of the paper recycling logistics system. The model studies the inter-relationship between multiple objectives (with changing priorities) of a recycled paper distribution network. The objectives considered are reduction in reverse logistics cost; product quality improvement through increased segregation at the source; and environmental benefits through increased wastepaper recovery. The proposed model also assists in determining the facility location, route and flow of different varieties of recyclable wastepaper in the multi-item, multi-echelon and multi-facility decision making framework. The use of the model has been illustrated through a problem of paper recycling in India.     

Simultaneous estimation of ordered parameters

The problem of estimating ordered parameters is encountered in biological, agricultural, reliability and various other experiments. Consider two populations with densities f₁(x₁-ω₁) and f₂(x₂-ω₂) where ω₁#ω₂. The estimation of ω₁,ω₂) with the loss function, the sum of squared errors, is studied. when f_i is the f_i(,_i,,_i ²) density with ,_i known, i=1,2; we obtain a class of minimax estimators. When ω₁ #ω₂ we show some of these estimators are improved by the maximum likelihood estimator. For a general f_i we give sufficient conditions for the minimaxity of the analogue of the Pitman estimator.     

Selecting the t-best cells in a multinomial distribution

The problem of selecting the t-best cells in a multinomial distribution with t + k cells, k > 1, 2 <= t is considered under the fixed sample-size indifference zone approach. The least favourable configuration is derived for the usual procedure of selection, for large values of N (the sample size). The result settles Conjecture I (for large N) and Conjecture IV of Chen and Hwang (Commun. Statist. - Theory Meth. 13 (10), 1289-1298, 1984) in the affirmative.     

Comparison of estimators of a dispersion matrix under generalized pitman nearness criterion

Some equivariant estimators of the dispersion matrix of a multivariate normal population are compared using the generalized Pitman nearness criterion based on the entropy loss function. It is shown that, under the group of lower triangular transformations, a best equivariant estimator does not exist. Existence of best estimators in certain subclasses are discussed and the performances of two commonly used estimators are compared. Some properties of central chi-square distributions are obtained and used to derive the main results.