Optimization designs of the combined Shewhart-CUSUM control charts

This article presents the optimization design of the combined Shewhart chart and CUSUM chart ( chart in short) used in Statistical Process Control (SPC). While the optimization design effectively improves the overall performance of the chart over the entire process shift range, it does not increase difficulties in understanding and implementing this combined chart. A new feature pertaining to an additional charting parameter w (the exponential of the sample mean shift) is also investigated, with the hope of further enhancing the detection effectiveness of the chart. Moreover, this article provides the SPC practitioners with a design table to facilitate the designs of the charts. From this design table, the users can directly find the optimal values of the charting parameters, according to the design specifications. The design table makes the design of an chart as simple as the design of the simplest chart. In general, this article will help to enhance the detection effectiveness of the chart, and facilitate and promote its applications in SPC.     

On-line SPC with consideration of learning curve

This work identifies a link between on-line statistical process control (SPC) and the learning effect for the process standard deviation (PSD) caused by the quality improvement (QI) program. The learning curve (LC) is used to describe and forecast, and the exponentially weighted root mean square control chart is used to monitor the progress in reducing PSD. A modification of the quality control chart (QCC) that considers LC of PSD is proposed. The reduction rate of PSD may be large during the initial stage of the QI program, and influences QCC construction. Simulation is used to compare the shift-detecting ability of the Shewhart- control chart and EWMA- control chart, without- and with- consideration of LC. The EWMA- chart with consideration of LC performs best. In comparison, the Shewhart- chart without LC consideration has almost no shift-detecting ability when the shift magnitude of the process mean is small, leading to rendering quality control ineffective.     

Synthetic- control charts optimized for in-control and out-of-control regions

There are real industrial cases where small shifts in the quality of a productive process do not need to be detected, but, at the same time, it is necessary to maintain the performance of the control chart to detect large shifts which are considered important. In this paper the optimization, zero- and steady-state cases, of the synthetic- control chart is studied (standard, side-sensitive, group runs and side-sensitive group runs versions) with the aim of not detecting shifts in a region of admissible shifts (in-control region) and, at the same time, being able to detect shifts considered important (out-of-control region). Genetic algorithms have been employed to solve this optimization problem and user-friendly software has been developed with the objective of helping users to select the best synthetic- chart for the process. On the other hand, a comparison is made with the optimized EWMA chart for this in-control and out-of-control optimization problem.     

Economic design of two-stage non-central chi-square charts for dependent variables

Non-central chi-square charts are more effective than the joint and R charts in detecting small mean shifts or variance changes of a performance variable. However, the cost may be high to monitor a primary quality characteristic, such as the weight of each bag in a cement filling process. It is more economical to monitor a surrogate variable, for example, the milliampere of the load cell. When the correlation of the performance variable of surrogate variable exists, this article proposes a two-stage charting design to monitor either the performance variable or its surrogate variable in an alternating fashion rather than monitoring the performance variable alone. The proposed method simplifies process monitoring when users only concern about whether a process is in control or not. The application of the proposed method and the advantages of the proposed chart over the existing methods are presented through an example. Numerical results show that the proposed chart is insensitive on the correlation of the performance variable and surrogate variable even when the historical information on the correlation coefficient is not very accurate.     

The Monte Carlo Event Generator AcerMC version 1.0 with interfaces to PYTHIA 6.2 and HERWIG 6.3

The AcerMC Monte Carlo Event Generator is dedicated for the generation of Standard Model background processes at pp LHC collisions. The program itself provides a library of the massive matrix elements and phase space modules for generation of a set of selected processes: , , , , and complete electroweak process. The hard process event, generated with one of these modules, can be completed by the initial and final state radiation, hadronization and decays, simulated with either PYTHIA or HERWIG Monte Carlo event generator. Interfaces to both of these generators are provided in the distribution version. The matrix element codes have been derived with the help of the MADGRAPH package. The phase-space generation is based on the multi-channel self-optimizing approach as proposed in NEXTCALIBUR event generator. Eventually, additional smoothing of the phase space was obtained by using a modified ac-VEGAS routine in order to improve the generation efficiency.     

The formalism underlying EASYMAP: A precompiler for refinement-based exploration of hierarchical data organizations

In the computer science community, data structure design is mainly conducted at a high level of abstraction under the implicit assumption that the platform contains a monolithic memory. Exploiting platform-related knowledge such as available on-chip and off-chip memory sizes, the cache size, and the number of banks is mainly conducted in the system engineering community when the refined data structure has already been chosen. A convergence of both communities is desirable since this can lead to powerful optimizations.To achieve the convergence mentioned above, data-related transformations have been researched extensively in the recent past. Many of these transformations have a direct and large impact on memory footprint, execution time and energy consumption. Unfortunately, however, the most effective transformations are applied manually (e.g. in C code) and these result in a very time-consuming and error-prone design process. To overcome this burden, our general research goal is to develop a computer-aided design tool, called , that helps the designer to correctly construct the C code of an efficient but difficult-to-understand data structure. The formal design of is the topic of this article with the emphasis on , the internal language of . is based on a novel extension of Separation Logic’s spatial conjunction operator (∗), allowing it to concisely describe access operations of an irregularly accessed complex data organization. is the basic building block of ; it serves the purpose of automating ’s refinement process and proving that it is correct by construction.     

A weakest failure detector-based asynchronous consensus protocol for f<n

has been shown to be the weakest realistic failure detector class needed to solve the consensus problem in an asynchronous distributed system prone to f<n process crashes in which communication is by message-passing. However, the only protocol that is known to meet this bound is based on three layers of protocol construction, and is therefore not efficient. This paper presents a surprisingly simple and very efficient direct message-passing implementation of a -based consensus protocol, and proves its correctness.     

A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets

Fuzzy logic is frequently used in computing with words (CWW). When input words to a CWW engine are modeled by interval type-2 fuzzy sets (IT2 FSs), the CWW engine’s output can also be an IT2 FS, , which needs to be mapped to a linguistic label so that it can be understood. Because each linguistic label is represented by an IT2 FS , there is a need to compare the similarity of and to find the most similar to . In this paper, a vector similarity measure (VSM) is proposed for IT2 FSs, whose two elements measure the similarity in shape and proximity, respectively. A comparative study shows that the VSM gives more reasonable results than all other existing similarity measures for IT2 FSs for the linguistic approximation problem. Additionally, the VSM can also be used for type-1 FSs, which are special cases of IT2 FSs when all uncertainty disappears.     

Bottleneck flows in unit capacity networks

The bottleneck network flow problem (BNFP) is a generalization of several well-studied bottleneck problems such as the bottleneck transportation problem (BTP), bottleneck assignment problem (BAP), bottleneck path problem (BPP), and so on. The BNFP can easily be solved as a sequence of O(logn) maximum flow problems on almost unit capacity networks. We observe that this algorithm runs in O(min{m3/2,n2/3m}logn) time by showing that the maximum flow problem on an almost unit capacity graph can be solved in O(min{m3/2,n2/3m}) time. We then propose a faster algorithm to solve the unit capacity BNFP in time, an improvement by a factor of at least . For dense graphs, the improvement is by a factor of . On unit capacity simple graphs, we show that BNFP can be solved in time, an improvement by a factor of . As a consequence we have an algorithm for the BTP with unit arc capacities.     

On the number of control sets on projective spaces

The purpose of this paper is to provide an upper bound for the number of control sets for linear semigroups acting on a projective space . These semigroups and control sets were studied by Colonius and Kliemann (1993) who proved that there are at most d control sets. Here we apply the results of San Martin and Tonelli (1995) about control sets for semigroups in semisimple Lie groups and make a case by case analysis according to the transitive groups on P^d−1 which were classified by Boothby and Wilson (1975, 1979) in order to improve that upper bound. It turns out that in some cases there are at most d/2 or d/4 control sets.     

Optimal semi-online algorithms for scheduling problems with reassignment on two identical machines

In this paper, we consider semi-online minimum makespan scheduling problem with reassignment on two identical machines. Two versions are discussed. In the first version, one can reassign the last job of one machine that is based on the problem proposed by Tan and Yu (2008) [1], in which case the last job of each machine is allowed to be reassigned. An optimal algorithm which has the same competitive ratio is presented. In the second version we consider the combination of the next two conditions: the total size of all jobs is known in advance and one can reassign the last job of one machine. For this problem an optimal algorithm with competitive ratio is also given.