Statistical Quality Control Methods for Exponentiated Fréchet Distribution | Book Publisher International

In this book, we study the different methods of statistical quality control based on a life distribution, namely as an exponentiated distribution of Fréchet (EFD). The maximum likelihood estimator and its asymptotic distribution are mainly concerned with estimating the reliability of R=P(Y< X) in the exponentiated Fréchet distribution proposed by Nadarajah and Kotz (2006) to construct an asymptotic confidence interval of R. It also studies the reliability estimate of the multi-component stress-strength model using the ML method together with asymptotic confidence intervals. The new acceptance sampling plan and economic reliability test plan were proposed by us. In order to ensure a percentile life when the life test is terminated at a pre-assigned time and when the observed number of failures does not exceed a given acceptance number, we developed sampling plans for finding the minimum sample size necessary.

An economic reliability test plan is taken into account and this plan yields the minimum ratio of termination time required to test the items to decide whether or not a lot submitted is good. For EFD, group acceptance sampling plans are constructed when the lifetime of the product is truncated by known percentile shape parameters. Parametric quantities of the plan, such as the number of groups g and acceptance number c, are determined by simultaneously considering the risk of the consumer and the risk of the producer. For EFD, a two-stage group acceptance sampling plan with known shape parameters has been developed. In order to ensure the quality of product life, we also developed a group acceptance sampling plan (GASP) for lot resubmission. We built the Process Capability Index attribute control chart and bootstrap confidence intervals.

We determined the control chart coefficient and discussed the average run length (ARL) behaviour of the proposed control chart. We also built capacity index confidence intervals using bootstrap methods through simulation. The standard bootstrap confidence interval (SB), the percentile bootstrap confidence interval (PB) and the bias-corrected percentile bootstrap confidence interval (BCPB) are considered three types of bootstrap confidence intervals and the performance of these bootstrap confidence intervals are compared using Monte Carlo simulation by considering their coverage probabilities and average widths.

Author (s) Details

Sridhar Babu Mothukuri
Department of Sciences, St. Mary’s College, 8-3-229, Near Yousufguda Check Post, Yousufguda, Hyderabad, Telangana – 500045, India. D. M. Dewaikar

Kanaparthi Rosaiah
Department of Statistics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur District, Andhra Pradesh, India.

Gadde Srinivasa Rao
Department of Mathematics and Statistics, The University of Dodoma, Tanzania.

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Keywords - Exponentiated Fréchet distribution, stress-strength model, multi-component stressstrength,

acceptance sampling, producer’s risk, consumer’s risk, group acceptance

sampling, resubmitted lot, attribute control chart, process capability index, bootstrap

confidence interval.

Discussion on World-Universe Model—Alternative to Big Bang Model | Chapter 5 | New Insights into Physical Science Vol. 9

 A comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of Standard Cosmology is given in this manuscript. The BBM analysis performed reveals that the Traditional Cosmology Four Pillars are model-dependent and not large enough to sustain the model. One of the most important BBM problems is the angular momentum problem. Normal Cosmology is unable to clarify how galaxies and extra-solar structures have gained their major orbital and rotational angular momentum, and why Jupiter's orbital momentum is substantially greater than the Sun's rotational momentum. The only cosmological model in nature that is consistent with the Law of Angular Momentum Conservation is WUM. WUM describes the Origin of the Universe in depth to be consistent with this Universal Law. The model incorporates the Dark Epoch (0.4 billion years from the creation of the world) where only Dark Matter Particles (DMPs) existed and Luminous Particles (DMPs) existed. The Epoch (ever since for 13.8 billion years). In our opinion, the transition from the Dark Epoch to the Luminous Epoch due to the Rotational Fission of Overspinning Dark Matter (DM) Supercluster Cores is the Big Bang discussed in Traditional Cosmology. From the fourth spatial dimension, WUM envisions Matter being transported from the Cosmos into the Earth by DMPs. A byproduct of DM annihilation is Ordinary Matter. In contemporary cosmology and astrophysics, WUM solves a variety of physical problems by DMPs and their interactions: the problem of angular momentum in birth and subsequent evolution of galaxies and extrasolar systems; Fermi Bubbles-two large structures above and below the galactic core in gamma-rays and X-rays; the diversity of gravitationally rounded particles in the solar system; some pp. WUM discloses and measures the inter-connectivity of key cosmological parameters, which are in good accordance with the current results of their measurements. The model requires considerable further elaboration, but it can already serve as the basis for a new physics proposed by Paul Dirac in 1937 in its present form. All physical societies should build the model into a well-elaborated theory.

Author (s) Details

Vladimir S. Netchitailo
Biolase Inc., Cromwell, CA, USA.

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Optimization of a Three-Axes Teslameter for the Calibration of the Next Generation Undulators | Chapter 4 | New Insights into Physical Science Vol. 9

 There are many commercial and scientific uses for the measurement of a three-axis magnetic field with high spatial resolution. One particular experimental application includes characterising in free electron lasers the field map of insertion devices. This work presents the development of a new, reduced form-factor, digital teslameter with three axes. At the Paul Scherrer Institute (PSI) for the Athos soft X-ray beamline, this instrument will be used to classify the SwissFEL insertion units. The setup would move along the full length of the undulator along with a Hall probe at the middle of the cross-sectional region of the undulator on a specially designed basis. Minimal vibration device, thereby obtaining a complete map of the magnetic field in the three-axes. For the three-axis interface to a Hall probe, the teslameter integrates analogue signal conditioning, a linear absolute encoder interface and a high resolution 24-bit analog-to-digital converter. This compares with the old instrumentation setup used, consisting only of analogue circuitry with digitization performed by proprietary hardware externally to the instrument. The new instrument also offers a very detailed map of the magnetic field in the μT range with simultaneous location encoder readings at an accuracy of ±3 μm. The innovation of the instrument is the provision of an integrated optimised solution with a very compact size and efficiency comparable to the best state-of-the-art teslameters currently on the market. Initially, a brief history on magnetic field instrumentation is given, followed by the actual creation of the novel teslameter hardware. It follows the standardised calibration method that is critical to optimising this precision instrument's efficiency. Among other parameters, the output results obtained outline the instrument's noise, measurement accuracy, repeatability and frequency response. These are studied in order to eventually establish an informative understanding of the magnetic properties of insertion devices that need to be modelled and characterised.

Author (s) Details

Johann Cassar
Faculty of Engineering, University of Malta, Msida, MSD 2080, Malta.

Andrew Sammut
Faculty of Engineering, University of Malta, Msida, MSD 2080, Malta.

Nicholas Sammut
Faculty of ICT, University of Malta, Msida, MSD 2080, Malta.

Marco Calvi
Photon Science Division of the Paul Scherrer Institute, 5232 Villigen PSI, Switzerland.

Sasa Dimitrijevic
Sentronis ad, 18115 Nis, Serbia.

Zarko Mitrovic
Sentronis ad, 18115 Nis, Serbia.

Sasa Spasic
SENIS, Hertizentrum 11, 6300 Zug, Switzerland.

Dragana Popovic Renella
SENIS, Hertizentrum 11, 6300 Zug, Switzerland.


Radivoje S. Popovic
SENIS, Hertizentrum 11, 6300 Zug, Switzerland. 


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Emphasizing the World-Universe Model Predictions | Chapter 6 | New Insights into Physical Science Vol. 9

The World-Universe Model (WUM) suggested a mainly different way in 2013 to solve the problem of the accuracy of Newtonian Constant of Gravitation measurement and made some estimates of primary cosmological parameter values. A self-consistent collection of time-varying values of the World's Primary Cosmological Parameters was discovered by WUM: Gravity Parameter, Hubble Parameter, World Age, Microwave Background Radiation Temperature, and Intergalactic Plasma Concentration. WUM solved the Missing Baryon problem on the basis of the interconnectivity of these parameters and estimated the values of the following cosmological parameters: gravitation G, intergalactic plasma concentration, proton relative energy density in the medium, and proton relative energy density in the medium. minimum energy of photons, which were experimentally confirmed in 2015-2018. Between 2013 and 2018, the relative standard uncertainty of G measurements decreased x6. The set of values obtained by WUM was recommended for consideration in CODATA Recommended Values of the Fundamental Physical Constants 2014. The Model allows for precise calculation of values that were only measured experimentally earlier and makes verifiable predictions.

Author (s) Details

Vladimir S. Netchitailo
Biolase Inc., Cromwell, CA, USA.

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Investigation on the Consequences of a Strengthened Newtonian Gravity at Short Distances | Chapter 2 | New Insights into Physical Science Vol. 9

 In the middle ages, especially in astronomy and mechanics, the construction of the theory of movement of the solar planet system was a triumph of science. The confrontation that lasted for centuries between proponents of the Ptolemaic geocentric system and the heliocentric system of Aristarchus-Copernicus ended with the victory of the latter. A central interaction of bodies that is greater than Newtonian at short distances is considered. It is demonstrated that the velocity of escape from a body is essentially more than the velocity of escape provided by the theory of Newton. According to Newton's theorem, the Universal force Gravity is central, each mass m is attracted with force by another mass M in the Universe, The distance between the masses is inversely proportional to the quadrate and is directed along the axis, The cores of the masses bind. The relation of the latest core relationship with the A black hole's gravitational radius is observed. The gravitational radius of a black hole is shown to be They may be arbitrarily tall. The Black Hole (Dark Body) gravitation does not follow the classical It obeys the law of the essentially strong central gravitation (Newtonian) law of Gravitation.

Author (s) Details

Lenser Aghalovyan
Institute of Mechanics of National Academy of Sciences of Armenia, Yerevan, Armenia.

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Illustrating an Efficient 3-D Ray Tracing Method for Prediction of Indoor Radio Propagation at 28 GHz in 5G Network | Chapter 1 | New Insights into Physical Science Vol. 9

 The fifth generation networks would be dominated by millimetre wave technology due to the obvious The benefit of higher frequency and thus broader spectrum bands. The Indoor Radio Wave in this article The 28 GHz propagation is studied by the development of effective three-dimensional ray tracing (ETRT) Process. The ETRT model based simulation programme has been tested by measurement results. Important agreement between simulation and measurement has been shown by the obtained signal strength indication and path loss. The proposed ETRT method has greater agreement with measurement data compared with the traditional shooting bouncing ray tracing method. Appropriate agreement on the proposed approach is reached on the basis of a detailed comparison. Further research into the 28 GHz mmWave indoor mobile network networks is expected to direct the results of this research.

Author (s) Details

Ferdous Hossain
Faculty of Engineering and Technology, Multimedia University, Melaka, 75450, Malaysia.


Tan Kim Geok
Faculty of Engineering and Technology, Multimedia University, Melaka, 75450, Malaysia.


Tharek Abd Rahman
Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia.


Tan Choo Peng
Faculty of Information Science and Technology, Multimedia University, Melaka 75450, Malaysia.


Dr. Hin-Yong Wong
Faculty of Engineering, Multimedia University, Cyberjaya 63100, Malaysia.


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Relativity with a Preferred Frame | Chapter 3 | New Insights into Physical Science Vol. 9

 The theory named 'special relativity (SR) with a preferred frame' integrates the preferred frame into special relativity while preserving the basic symmetry of space-time that expresses itself as Lorentz invariance in the regular SR. At the cost of the right to allocate the one-way speeds of light that exist in special relativity, the synthesis of such apparently contradictory principles as the nature of the chosen frame and the theory of relativity is feasible. A degree of anisotropy of the one-way speed acquires significance in the established context of a feature of the genuinely existing anisotropy induced by the movement of an inertial frame relative to the chosen frame. The anisotropic special relativity kinematics was generated on the basis of the principles of symmetry: (1) space-time transformations between inertial frames leave the invariant equation of anisotropic light propagation and (2) a group structure has a set of transformations. Modified kinematics is applied to particle dynamics based on the modified spacetime symmetry' principle, which enables the theory to be built along the lines of the standard theory of relativity. The theory can also be generalised to the general relativity (GR) definition, which like the traditional GR, is based on the principle of equivalence, but with the local symmetry of space-time properly modified. The chosen frame is identified with an asking frame of cosmology or the CMB frame to align the theory to the observational evidence, indicating that the theory should be applied on cosmological scales. The following applications are considered: the distribution of the CMB temperature as seen by an observer moving with respect to the CMB frame; the interactions with the CMB photons of the Ultra High Energy Cosmic Rays (UHECR); cosmological models. Applying changed SR Kinematics to the problem of measuring the distribution of the CMB temperature results in a relationship in which the angular dependence is measured. It coincides with that observed on the basis of the standard theory of relativity, but in the observer velocity, the mean temperature is corrected by the second order terms. The application of modified relativistic dynamics to the explanation of UHECR interactions with universal diffuse background radiation results in the Greisen-Zatsepin-Kuzmin (GZK) energy suppression threshold due to pion photoproduction by UHECR protons depending on the distance to the particle source (cosmological redshift ⁇ ). This impact may contribute to the interpretation of Auger's recently published data on the UHECR mass composition. The application of the modified GR to cosmology results in a correction of the luminosity distance - redshift relation such that the deceleration parameter observed can be negative as it is derived from the data for type Ia supernovae. Within the matter-dominated cosmological model of Friedman-Robertson-Walker, the observed negative values of the deceleration parameter can be clarified. Without adding dark energies to the universe. A variety of other observations may also be well adapted to the cosmological model resulting from the GR based on the SR with a privileged frame, such as Baryon Acoustic Oscillations and Cosmic Microwave Background. The 'relativity with a chosen frame designed to reconcile the theory of relativity with the nature of the preferred cosmological frame, thus offers explanations of both the groundbreaking SNIa data and the recently published Auger data on mass composition without the implementation of new physics and with the only new universal constant, which in all applications is within the same range.

Author (s) Details

Georgy I. Burde
Alexandre Yersin Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben- Gurion, Israel.

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