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Optimal design of one‐sided exponential cumulative sum charts with known and estimated parameters based on the median run length

Quality and Reliability Engineering International, 2020
AbstractAs a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high‐quality processes. Considering both known and estimated parameter cases, the one‐sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run
YuLong Qiao, XueLong Hu, JinSheng Sun, Qin Xu   +3 more
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Estimates on polynomial exponential sums

Israel Journal of Mathematics, 2010
Let \(f(x)=a_1x^{k_1}+\cdots+a_rx^{k_r}\in \mathbb{Z}[x]\) be a polynomial of degree \(d\), and let \(q\) be a positive integer. Assume \((a_1,\cdots,a_r,q)=1\), and define \(e_q(x)=e^{2\pi i \frac{x}{q}}\). This paper estimates exponential sums of the form \[ \sum_{1\leq x< q;~(x,q)=1}e_q(f(x)) \quad \text{and}\quad \sum_{1\leq x\leq q}e_q(f(x ...
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Parameter estimation of monomial-exponential sums in one and two variables

Applied Mathematics and Computation, 2015
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FERMO, LUISA, VAN DER MEE, CORNELIS VICTOR MARIA, Seatzu S.   +2 more
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On a variant of sum-product estimates and explicit exponential sum bounds in prime fields

Mathematical Proceedings of the Cambridge Philosophical Society, 2009
AbstractLet Fp be the field of a prime order p and F*p be its multiplicative subgroup. In this paper we obtain a variant of sum-product estimates which in particular implies the bound for any subset A ⊂ Fp with 1 < |A| < p12/23. Then we apply our estimate to obtain explicit bounds for some exponential sums in Fp.
Bourgain, J., Garaev, M. Z.
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On Hua's estimates for exponential sums

Mathematika, 1987
Let f(x)\(\in {\mathbb{Z}}[X]\), \(e_ q(t)=\exp (2\pi i/q)\) and \(S(q,f)=\sum _{0\leq ...
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Estimates on exponential sums related to the Diffie–Hellman Distributions

GAFA Geometric And Functional Analysis, 2005
This important paper investigates the structure of sets in \( \mathbb F_p \) and \( \mathbb F_p \times \mathbb F_p \) with small product set, where ``small'' is meant in the not too restrictive sense \(| H \cdot H| < | H| ^{1+\tau }\) with a suitably small \(\tau \).
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Estimates of hybrid exponential sums on quasiprojective varieties over finite fields

Mathematika, 1996
Recently, \textit{E. Bombieri} and \textit{S. Sperber} [Acta Arith. 69, 329-358 (1995; Zbl 0826.11040)] have jointly created a new construction for estimating exponential sums on quasiprojective varieties over finite fields. In this paper we apply their construction to estimate hybrid exponential sums on quasiprojective varieties over finite fields. In
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On Hua's Estimate for Exponential Sums

Journal of the London Mathematical Society, 1982
Loxton, John H., Smith, Robert A.
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On the estimates of double exponential sums

Acta Arithmetica, 2007
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Bounds for the Rate of Convergence in the Generalized Rényi Theorem

Mathematics, 2022
In the paper, an overview is presented of the results on the convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson random sums, including the case where the mixing law is itself a mixed ...
Victor Korolev
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