In this paper, two-stage and Purely Sequential estimation procedures are considered to construct fixed-width confidence intervals for the reliability parameter under the stress-strength model when the stress and strength are independent exponential random variables with di erent scale parameters. The exact distribution of the stopping rule under the Purely Sequential procedure is approximated using the law of large numbers and Monte Carlo integration. For the two-stage Sequential procedure, explicit formulas for the distribution of the total sample size, the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress-strength model are provided. Moreover, it is shown that both proposed Sequential procedures are finite, and in exceptional cases, the exact distribution of stopping times is degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally using real data, the procedures are clearly illustrated.

In this paper a new Sequential Sampling plan is introduced in which the acceptable quality level (AQL) and the lot tolerance percent defective (LTPD) are a fuzzy number. This plan is well defined, since, if the parameters are crisp, it changes to a classical plan. For such a plan, a particular table of rejection and acceptance is calculated and compared with the classical one.

Background and Objectives: Cylindrical scanning technique is a well-established indirect measurement method to characterize a wide range of antenna patterns such as fan-beam antennas and phased array antennas with versatile radiation patterns.Methods: Cylindrical scanning technique which is based on the nearfield-to-far-field transformation based on cylindrical mode coefficients (CMCs), cannot predict the antenna radiation pattern with a very narrow beamwidth in the azimuth plane accurately, because a remarkable error occurs during the calculation of the derivative of high-order Hankel functions in the CMCs extraction. We aim to address this issue and introduce a simple yet rigorous technique namely the Sequential Sampling method (SSM) in conjunction with the two-dimensional Fast Fourier Transform (2D-FFT) to efficiently calculate the far-field radiation pattern of a super-directive antenna with a very narrow beamwidth in the azimuth plane. Briefly, the SSM offers several sequences of progressive azimuth angles and the corresponding order of Hankel functions in such a way that CMCs fully span 360 degrees of azimuth angles (φ) in the cylindrical coordinate system in each sequence. Afterward, by putting the far-field obtained by these sequences together, the final radiation pattern will have a high angular resolution. This technique can also be applied to determine the necessary criteria in the data acquisition step which should be satisfied to precisely measure the radiation pattern of super-directive antennas. These criteria are the maximum acceptable Sampling resolution and the minimum value of the required azimuth angle (φ) in the data acquisition step if the far-field pattern is merely desired on the front side of the antenna. Results: For verifications, the far-field radiation pattern of an electrically large slot array antenna including 81×15 slots is calculated at 8.75 GHz by the proposed technique and the results are compared with the array theory. The results show that the azimuth pattern can accurately be measured as small as 0.1° resolution by the SSM.Conclusion: By comparing the results obtained by the proposed method and the traditional cylindrical scanning method, it can be inferred that the far-field pattern of an antenna with narrow beamwidth in the azimuth plane can easily be characterized by a cylindrical scanning system without any huge computational burden

We extend the method of adaptive two-stage Sequential Sampling to include designs where there is more than one criteria used in deciding on the allocation of additional Sampling e ort.These criteria, or conditions, can be a measure of the target population, or a measure of some related population. We develop Murthy estimator for the design that is unbiased estimators for the population mean, and propose another, more efficient, estimator. We investigate asymptotic properties of this estimator. We use a simulation study to investigate design properties of the multi-criteria adaptive stratified Sequential Sampling scheme and also some estimator properties under the design.