In the literature, there hasn’t been any work done on optimal **designs** for PH based ALT models with multiple step-stress plans. Since all of the previous works done are on simple step-stress for PH based ALT models, exploring optimal **designs** for PH based ALT models with multiple step-stress plans would be an area deserving of research. Due to the nature of the prediction made from ALT experimental data, attained under the stress levels higher than the normal design condition, extrapolation is encountered. In such case, the assumed model cannot be tested. For possible imprecision in an assumed PH model, the method of construction for **robust** **designs** is also needed to explore. Therefore, we are interested in constructing optimal and **robust** **designs** for multiple step-stress ALTs for PH models. For optimal **designs**, we consider the baseline hazard function to be either a simple linear or a quadratic form. For each case, we discuss the optimal multiple step-stress ALT **designs** under three di¤erent design criteria: D-optimality, A-optimality, and Q-optimality.

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Genetic and evolutionary algorithms have been applied to solve numerous problems in engineering design where they have been used primarily as optimization procedures. These methods have an advantage over conventional gradient-based search procedures because they are capable of finding global optima of multi-modal functions (not guaranteed) and searching design spaces with disjoint feasible regions. They are also **robust** in the presence of noisy data. Another desirable feature of these methods is that they can efficiently use distributed and parallel computing resources since multiple function evaluations (flow simulations in aerodynamics design) can be performed simultaneously and independently on multiple processors. For these reasons genetic and evolutionary algorithms are being used more frequently in design optimization. Deb 5 reviews numerous genetic and evolutionary algorithms

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method a instead a of for range wide a as and are: by notation tools Monte Carlo Distribution Analysis and Simplification form optimiza are: Optimization Theory for optimization includes[r]

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A Bayesian optimality procedure that works well under model uncertainty is used in the first stage and the second stage design is then generated from an optimality procedure that i[r]

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The genetic algorithm is very appropriate for construction of a design when the optimality criterion is crucial to work and/or where the experimental region is constrained such as in mixture experiments. We use the genetic algorithm developed by Limmun et al. (2013) to construct the model-**robust** **designs**. Throughout this paper, the chromosomes are encoded using real-value encoding instead of binary or another encoding. Real value encoding is flexible enough to allow a unique representation for every variable, compatible with other optimization algorithms (such as simulated annealing), easy to interpret, and can be modified to adjust for many applications. The reproduction process including blending, between-parent crossover, within-parent crossover, and mutation operators is a process that usually operates on the genes to produce offspring chromosomes. The success probabilities for these operators are , , and , respectively. A gene or set of genes is altered when a probability test is passed (PTIP). A probability test is a Bernoulli distribution with probability of success . If is a random deviate from a continuous uniform distribution on the interval 0,1 and 0 , then a probability test is passed and the operator is applied. Otherwise, the chromosome remains untouched. Furthermore, if a probability test is passed, a random variate ε from a normal distribution with a mean of 0 and a standard deviation of is added to a gene to form a new gene.

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• Two **robust** **designs** (i.e., **Robust**-SP and **Robust**-LPM) are developed to solve the “dual” **robust** min-max power problem. This problem is well-known nonconvex due to the infinitely many SINR constraints. For **Robust**-SP, we use the S-procedure to convert the problem into a rank-constrained semidefinite program (SDP), and then apply the SDP relaxation technique to find its (near-)optimal solution. Like [15], we give a computable CSI uncertainty bound which ensures the tightness of the SDP relaxation. For **Robust**-LPM, we consider a slightly conservative problem reformulation. Relying on a linear matrix inequality (LMI) representation for the cone of Lorentz-positive maps (LPMs), the new problem is shown to be equivalently transformed into a convex SDP which can be efficiently solved with guaranteed global optimality.

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We proposed **robust** THP transceiver **designs** that jointly optimize the THP precoder and receiver filters in multiuser MIMO downlink in the presence of imperfect CSI at the transmitter. We considered these transceiver **designs** under SE and NBE models for CSIT errors. For the SE model, we proposed a minimum SMSE transceiver design. For the NBE model, we proposed three **robust** **designs**, namely, minimum SMSE design, MSE-constrained design, and MSE-balancing design. We presented iterative algorithms to solve these **robust** design problems. The iterative algorithms involved solution of subproblems, which either have analytical solutions or can be formulated as convex optimization problems that can be solved eﬃciently. Through simulation results we illustrated the superior performance of the proposed **robust** **designs** compared to nonrobust **designs** as well as **robust** linear transceiver **designs** that have been reported recently in literature.

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attained by intelligently choosing axial distance in central composite **designs**. They have developed **designs** for a few number of factors and compared these **designs** with rotatable **designs** without establishing their superiority. There are other attempts, in the academic literature, focusing exclusively on the development of **designs** **robust** to other problems. Draper (1961), Ghosh (1982), Herzberg & Andrews (1975), Herzberg & Andrews (1976), Akhter & Prescott (1986), Akram (1993) are a few names in the list who presented several maneuvering to guard the design against missing observations. Akhter (1985), Akhter & Prescott (1986), Akram (1993) presented **designs** based on central composite **designs** employing a minimax criterion which works on down weighing the effect of a missing observation. There are other problems too for which **robust** **designs** exists. Schwabe (1995) studied robustness with respect to the underlying model. Zhou (2001) studied the **robust** against serially correlated observations. Toman (1992) and Toman & Gastwirth (1994) uses Bayesian methodology to incorporate the results of the first study (or studies) into the design of the follow up study. Park & Cho (2003) for example, developed **designs** **robust** for outliers and non-normal experimental data. Fellner (1986), Zhou and Zhu (2003) developed outlier **robust** **designs** to get more reliable estimates for variance components in random effects models.

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i j v (11) Thus, a design satisfying the conditions mentioned above may be successfully uti table design under violation of the homoscedasticity assumption sub- ject to the covariance structure being of the type (condi- tions of exact rotatability). Such a design is, therefore, **robust**, N, N 1 , 4

[3] and [4] developed eﬃcient spherical three-level **designs** appropriate for ﬁtting second-order (quadratic) response models. The **designs** are constructed by combining two-level (full or fractional) factorials with Balanced Incomplete Block **Designs** or Partially Balanced Incomplete Block **Designs**. In each block, a certain number of factors are put through all combinations for the factorial design, while the other factors are kept at the central values. Hence the **designs** do not contain any points at the vertices or face-center of the design region but rather at the center of the edges of the experimental space, thus avoiding extreme values for factor level combinations which may be impossible to test due to cost or physical process constraints [22]. The **designs** are rotatable or near-rotatable and require fewer experimental runs than the 3 𝑘 factorial technique. As the number of factor, increases, so does the run size of the **designs**. Additionally, the **designs** uses center runs to avoid singularity in the design matrix and to maintain favorable design qualities like good prediction variance [23]. Over the years, the **designs** have been improved in terms of rotatability, average prediction variance, D- and G-eﬃciency as in [17], [25], [31].

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In this case, the foundation pier of entire is structure is separated by means of Spherical Sliding Isolation Bearing and there is no medium by which waves of EQ reaches the Structure. So, it becomes purely EQ resistant **Designs**. If EQ happens even inside Surface of Earth, then even the structure is remained undamaged by EQ.

It is conjectured that if a multiplicative design has a multi- plicative dual, and if neither design belongs to a specific class of designs, then both are uniform [r]

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It is easily seen that the above plan is a BIBDs with parameters n = 15, b = 35, r = 7, k = 3, and λ = 1 when triplets of girls are treated as blocks. Other solutions to KTS{15) were provided by several authors, including Cayley ([Cay50]), Peirce ([Pei60]) and Davis ([Dav97]). The solution of a Kirkman triple System KTS(n) for all n ≡ 3 (mod 6) was provided by Raychaudhuri and Wilson ([RW71]). Steiner ([Ste53]) proposed the problem of arranging n objects in triplets (called Steiner's triple systems) such that every pair of objects appears in exactly one triplet. It is easy to see that Steiner's triples are in fact BIB **designs** with block size three. Later in 1853, Steiner discussed t -**designs** with k = t + 1 and λ = 1. When t = 2, these are triple systems with λ = 1. Thus, we call such **designs** Steiner triple systems. Put another way, they are 2-**designs** with parameters (n, 3, 1), and we denote such systems by S(2, 3, n). Unaware of Kirkman's work, Jakob Steiner ([Ste53]) reintroduced triple systems, and as this work was more widely known, the systems were named in his honor ([Ste53]).The existence question for which STS(n) does exist was first posed by W.S.B. Woolhouse (Prize question 1733, Lady's and Gentlemen's Diary 1844).The problem was solved in 1847 by Rev. T.P. Kirkman ([Kir47]) further established the existence of a Steiner triple system of order n which exists if and only if n≡ 1 , 3 (mod 6).

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All Intellectual Property rights existing in the designs, including designs, trade marks and copyright, remain the property of Crocodile Creek. Copyright exists in these designs and th[r]

Biplane, Incidence Mat, Self-orthogonal Linear Codes, 16, 11 Extended Binary Hamming Code, Weight Distribution, Automorphism Groups, Difference Set.. THEMATICS SUBJECT CLASSIFICATION I C[r]

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R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission... BLOCK STRUCTURE OF CERTAIN QUINTIC DESIGNS ... AN EXAMPLE OF [r]

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When starting new circuits, or editing existing ones, always use the New Project and Open Project commands. If you want to simulate **designs** with PSpice, it is critical that you work with project files rather than with design files. If you open the .DSN files directly for editing, you will not see the PSpice menu in Capture.

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The PCBoards-to-Layout translator converts **designs** (.PCA files) created in MicroSim PCBoards to design databases (.MAX files) that can be read by OrCAD Layout 9. You can translate PCB **designs** created in any version of MicroSim PCBoards. Footprint and padstack libraries from PCBoards cannot be translated for use with Layout. Translated circuit board **designs** contain all of the

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We deal with each of the theta graphs stated in the theorems. The lemmas in this section assert the existence of specific graph **designs** and decompositions of multipartite graphs. These are used as ingredients for the propositions of Section 2 to construct the decompositions of complete graphs required to prove the theorems. With a few exceptions, the details of the decompositions that constitute the proofs of the lemmas have been deferred to sections in the rather lengthy Appendix to this paper. If absent, the Appendix may be obtained from the ArXiv (identifier 1703.01483), or by request from the first author. In the presentation of our results we represent Θ(a, b, c) by a subscripted ordered (a + b + c − 1)-tuple (v 1 , v 2 , . . . , v a+b+c−1 ) Θ(a,b,c) , where v 1 and v 2 are the vertices

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