An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.     

Computer-Generated Change-Over Designs for Correlated Observations

Change-over designs with independently distributed errors in the model have been studied extensively in the literature. Martin and Eccleston (2001 Martin , R. J. , Eccleston , J. A. ( 2001 ). Optimal and near optimal designs for dependent observations . Statist. Applic. 3 : 101 – 116 . [Google Scholar]) gave an algorithm for the generation of efficient change-over designs when the errors are correlated. This article proposes an algorithm for the generation of efficient change-over designs for estimation of direct effects of treatments in the presence of first-order residual effects in the model and when the errors are correlated.     

Reliability Properties of Systems with Two Exchangeable Log-Logistic Components

In this article, we study the reliability properties of systems under bivariate log-logistic model which comes out from a particular stress-strength analysis. For this model, we obtain basic reliability characteristics of series and parallel systems and investigate their properties. We also derive distribution and moments of cold standby system under the abovementioned exchangeable model.     

Adaptive Crossover Design for Normal Responses

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achive a specific goal. In clinical trials our goal is to allocate a larger number of patients to the better treatment. In the present paper, we use a response adaptive design in a two-treatment two-period crossover trial where the treatment responses are continuous. We provide probability measures to choose between the possible treatment combinations AA, AB, BA, or BB. The goal is to use the better treatment combination a larger number of times. We calculate the allocation proportions to the possible treatment combinations and their standard errors. We also derive some asymptotic results and provide solutions on related inferential problems. The proposed procedure is compared with a possible competitor. Finally, we use a data set to illustrate the applicability of our proposed design.     

On the Use of Semi-folding in Regular Blocked Two-level Factorial Designs

In this article, we consider experimental situations where a blocked regular two-level fractional factorial initial design is used. We investigate the use of the semi-fold technique as a follow-up strategy for de-aliasing effects that are confounded in the initial design as well as an alternative method for constructing blocked fractional factorial designs. A construction method is suggested based on the full foldover technique and sufficient conditions are obtained when the semi-fold yields as many estimable effects as the full foldover.     

A-optimal designs for heteroscedastic multifactor regression models

Abstract

This paper searches for A-optimal designs for Kronecker product and additive regression models when the errors are heteroscedastic. Sufficient conditions are given so that A-optimal designs for the multifactor models can be built from A-optimal designs for their sub-models with a single factor. The results of an efficiency study carried out to check the adequacy of the products of optimal designs for uni-factor marginal models when these are used to estimate different multi-factor models are also reported.     

On the quantile past lifetime of the components of the parallel systems

ABSTRACT

Let T_{1: n} ? T_{2: n} ? ??? ? T_{n: n} be ordered lifetimes of components of a parallel system. In this article, the α-quantile past lifetime from the failure of the component with lifetime T_{r: n} provided that the system has failed at or before time t has been introduced. Then, some properties of this measure have been studied.     

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACT

In this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 ? α ? β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

Optimal block designs for double cross experiments

ABSTRACT

This paper presents systematic methods of construction of optimal block designs for a double cross experiments for both even and odd values of “p” parental lines. The both even and odd values of designs are derived by using initial block of unreduced balanced incomplete block designs and initial block of row–column designs given by Bose et al. (1953 Bose, R.C., Shrikhande, S.S., Bhattacharya, K.N. (1953). On the construction of group divisible incomplete block design. Ann. Math. Stat. 24:167–195.[Crossref] , [Google Scholar]) and Gupta and Choi (1998 Gupta, S., Choi, K.C. (1998). Optimal row-column designs for complete diallel crosses. Commun. Stat. Theory Methods 27(11):2827–2835.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), respectively. In this attempt we have found some new universally optimal block designs for double cross experiments.     

Admissibility of a variance estimator in finite population sampling under Warner's randomized response plan with multiple responses

ABSTRACT

Let P be the proportion of individuals in a finite population possessing a sensitive attribute. We consider the problem of unbiased estimation of (i) the variance of a linear unbiased estimator of P and (ii) the population variance P (1—P) for a given probability sampling design under Warner's (1965 Warner, S.L. (1965). Randomized response - A survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60:63–69.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) randomized response (RR) plan when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample and prove the admissibility of a quadratic unbiased estimator for each.