Designing of multiple deferred state sampling plan for generalized inverted exponential distribution

In this article, we propose a sampling plan called a multiple deferred state sampling plan for sentencing a lot based on the information of current and successive lot samples. Based on this sampling plan, the median life of the product is assured based on a time-truncated life test where the lifetime of the product follows the generalized inverted exponential distribution. The quality of the product is measured by its median life. The optimal parameters of the proposed plan are obtained by using the approach of two points on the operating characteristic curve. Tables are also constructed for determining the optimal parameters with various shape parameters. The implementation of the proposed plan is illustrated with examples. The performance of the proposed plan is compared with the performance of existing sampling plans under the generalized inverted exponential distribution.     

Designing of two mixed variable lot-size sampling plans using repetitive sampling and resampling based on the process capability index

In this article, we propose two types mixed variable lot-size sampling plans using the process capability index. The first one is the mixed variable lot-size repetitive sampling plan and the other is the mixed variable lot-size sampling plan for resubmitted lots. The design methodology of the proposed mixed sampling plans for symmetric and asymmetric fraction nonconforming cases is presented. Tables are constructed to determine the optimal parameters for practical applications. The industrial applications of the proposed mixed sampling plans are explained with illustrative examples. Comparison of the proposed sampling plans with other existing sampling plans is also made.     

Optimization of nonlinear process based on sequential extreme learning machine

In this paper, a new approach to the optimal control with constraints is proposed to achieve a desired end product quality for nonlinear processes based on new kernel extreme learning machine (KELM). The contributions of the paper are as follows: (1) In existing ILC algorithm, the model was built only between manipulated input variables U and output variables Y without considering the state variables. However, the states variables X_state are important in the industrial processes, which are usually constrained. In this paper, the variables are divided into state variables X_state, manipulated input variables U and output Y in the process of modeling. Then ΔU can be obtained by batch-to-batch iterative learning control separately. Kernel algorithm is added to ELM. (2) Constraints of state variables X_state and the input variables U are considered in the current version. PSO is used to solve the optimization problem. (3) Kernel trick is introduced to improve accuracy of ELM modeling. New KELM algorithm is proposed in the current version. The input trajectory for the next batch is accommodated by searching for the optimal value through the error feedback at a minimum cost. The particle swarm optimization algorithm is used to search for the optimal value based on the iterative learning control (ILC). The proposed approach has been shown to be effective and feasible by applying bulk polymerization of the styrene batch process and fused magnesium furnace.     

Interval Estimation Approach to Counting by Weighing: A Sequential Scheme

Abstract

Considerable time and energy involved in complete counting of large, but pre-specified, batch of N _s items could be saved by using weights of items. This article considers the case when the underlying distribution of weights, and its mean and variance are unknown. The problem is then reduced to that of finding an estimator of the mean and an optimal (small) sample size based on which a number [Ncirc] _n of items in the batch can be determined. Using a fixed-width interval criterion, Nickerson [Nickerson, D.M. Another look at counting by weighing. Commun. Statist. Simula. 1993, 22 (2), 323–343] derived an optimal sample size, but it depends on the unknown coefficient of variation. For this case, we propose a batch-type sequential sampling scheme which requires substantially fewer sampling operations and no prior knowledge of the coefficient of variation, but performs as well as Nickerson's and other available procedures in the literature. This shows that a little bit of sampling using substantially fewer sampling operations can significantly reduce the effort of complete counting.     

Construction of an Optimal Sequential Plan for Testing a Treatment for an Adverse Effect

Abstract

Classical sequential procedures that collect a single observation at a time are often found impractical, expensive, and time consuming. Sequentially planned procedures, or simply sequential plans, extend and generalize the concepts of sequential analysis by allowing observations to be collected in groups of variable sizes. After every group, all of the previously collected data are used to determine the next course of action. An optimal (Bayes) sequential plan minimizes the (Bayes) risk function that combines the decision loss, observation (variable) cost, and group (fixed) cost. In general, determining the optimal sequential plan remains an open and challenging problem mainly because it requires risk optimization over a huge and rather unstructured set of all sequential plans. This article demonstrates how to obtain the optimal solution for a particular class of problems that may arise in testing a treatment for a rare but severe adverse effect. This solution is obtained by studying a number of properties of the Bayes sequential plan such as transitivity and monotonicity. This allows one to reduce the search to a small, manageable set of sequential plans within which the optimal plan can be calculated.     

Determination of a new sampling system based on exponentially weighted moving average

In this article, a new sampling system based on an exponentially weighted moving average statistic is proposed for the inspection of normally distributed quality characteristics. The proposed sampling system can be applicable for compliance testing. The performance measures of the proposed system are derived and analyzed. Tables are also constructed for determining the optimal parameters of both known and unknown standard deviation cases. An optimization problem is formulated as a nonlinear program in order to construct the tables in which the objective function used is the minimization of the average sample number and the constraints are related to the probability of acceptance at acceptable quality level and limiting quality level under the operating characteristic curve. The efficiency and advantages of the proposed sampling system are discussed over the existing variables sampling plans. Extensive tables are provided for industrial applications. Implementation of the proposed sampling system is discussed with the help of a real-time industrial example.     

Determination of optimal quick switching system with varying sample size for assuring mean life under Weibull distribution

Conventional sampling plans are applied to dispose an individual lot or isolated lot that requires a large sample size. Consequently, the inspection time and cost needed to make a decision under conventional plans are high. In order to reduce the sample size and to inspect the series of lots with minimum cost and time, special purpose plans are utilized. In this article, we propose one of the special purpose plans, namely, a quick switching sampling system that is also known as a two-plan sampling system. Through this sampling system, the Weibull-distributed mean life of the product is ensured based on time-truncated life tests. The proposed system is designed with the intention of minimizing the average sample number using two points on the operating characteristic curve approach. The optimal parameters of the proposed system are determined for different combinations of producer’s risk and consumer’s risk. Implementation of the proposed system is also explained and the performance of the proposed system is compared with other existing plans. In addition, the effects of misspecification of shape parameters on optimal parameters and the probability of acceptance are discussed.     

Optimization of mesoporous alumina sol-gel synthesis by Taguchi and response surface methodology

Taguchi method (TM) and response surface methodology (RSM) have been employed to optimize three parameters, including the amounts of P123, the amounts of nitric acid and calcination temperature, in order to define an optimal setting for sol-gel synthesis of high surface area mesoporous alumina powder (MA). Herein, the comparison of the both statistical approaches has been examined and discussed considering the nitrogen adsorption as the response variable because this important character for mesoporous materials is exceedingly sensitive to the synthesis parameters. The BET surface area (S_BET) and pore volume of MA under Taguchi optimal condition were 323.5 m² g⁻¹ and 0.551 cm³ g⁻¹, respectively, by conducting confirmation test. Furthermore, the confirmation test showed high S_BET of MA (363.4 m² g⁻¹), which was in a good agreement with calculated S_BET result (431.25 m² g⁻¹) by a quadratic model under RSM optimal condition. Moreover, 3D response surface plots and 2D contour plots of desirability have been discussed to visualize the influence of input factors on response variable. It is also concluded that RSM shows more appropriate (12.33% higher S_BET than TM) and efficient optimal condition with determining a quadratic function as the relationship between S_BET and synthesis parameters.     

A GLR Control Chart for Monitoring the Process Mean with Sequential Sampling

Abstract

Variable sampling rate (VSR) control charts have been used where the sampling rate changes as a function of the data from the process. In this article we investigate a generalized likelihood ratio (GLR) control chart based on sequential sampling (the SS GLR chart). The objective of process monitoring is assumed to be the effective detection of a wide range of two-sided shifts in the process mean. The performance of the SS GLR chart is evaluated and compared with other control charts. The SS GLR chart has much better performance than that of the fixed sampling rate GLR chart. It is also shown that the overall performance of the SS GLR chart is better than that of the variable sampling interval (VSI) GLR chart and the VSR CUSUM chart. The SS GLR chart has the additional advantage that it requires fewer parameters to be specified than other VSR charts. The optimal parameter choices are given in the article, and regression equations are provided to find the limits for the SS GLR chart.     

Optimization of a tubular nylon 6 reactor with radial gradients

Optimal jacket-fluid temperature profiles for tubular Nylon 6 reactors (in the presence of radial gradients of temperature and concentration) have been obtained using an algorithm based on the continuous minimum principle developed for a distributed parameter system. A gradient search technique has been devised and implemented for obtaining these optimal profiles. The optimal temperature profiles are found to be at the maximum permissible temperature, T_max, at the beginning of the reactor and then slowly decrease to the minimum permissible temperature, T_min, near the end of the reactor. The effect of varying several parameters is also studied. The desired value of the chain length and the reaction time are found to be the parameters which effect the optimal profiles most significantly.     

Chromatography and Countercurrent Distribution: Features of the Optimum Phase-Volume Ratio

Abstract

It is commonly believed that the optimum solvent ratio in countercurrent distribution and chromatography may be expressed as V = V_U/V_L = (K_D1 K_Dπ ) ^?½. Here V_U and V_L are the volumes of mobile and stationary phases. This expression, proposed by Bush and Densen and widely accepted, leads to optimum separations only under special conditions. Under most commonly-encountered situations in chromatographic and countercurrent systems, better separations may be achieved by reducing V to the lowest practicable level. Measures of separation effectiveness include resolution, extent of separation, total percent impurity, and quantity factor, the latter two of which are herein developed. Computer simulation is used for testing existing separation parameters and developing new ones on a rational and scientific basis.     

A New Class of Distribution-Free Tests for Location Parameters

Abstract

A new class of distribution-free tests for the two-sample location problem is proposed. The tests are based on two-sample U-statistics. This class basically generalizes the tests proposed by Deshpande, J.V.; Kochar, S.C. Some competitors of Wilcoxon–Mann–Whitney test for location alternatives. Journal of Indian Statistical Association 1982, 19, 9–18. The proposed class of tests is also extended to the k (≥ 2)-sample problem for testing homogeneity of location parameters against ordered alternatives. This extension is based on linear combinations of two-sample U-statistics. Pitman asymptotic relative efficiencies (AREs) of the members of the proposed class(es) of tests relative to some of the existing tests are computed for a number of underlying distributions. It is shown that the proposed class of tests performs as good as or better than its competitors in literature.     

An optimal spectral model for phosphor-converted white light-emitting diodes used in the mesopic vision

White light-emitting diodes (WLEDs) for road lighting are required to have both the high scotopic to photopic ratio (S/P) and color rendering index (CRI). However, there is a trade-off between S/P and CRI, and WLEDs commonly having the S/P of 1.68-2.38 usually exhibit a low CRI. In this work, to provide a best solution to the trade-off problem we proposed an optimal spectral model for the phosphor-converted WLEDs (pc-WLEDs) aiming to figure out the optimal phosphor combination. The Monte Carlo Algorithms combined with the Genetic Algorithm were adopted to obtain the optimization of CRI and S/P by varying the spectral power distributions of WLEDs through adjusting the spectral parameters. Considering the spectral requirements of pc-WLEDs based on the mesopic vision, we chose CaAlSiN₃:Eu²⁺ and Y₃(Ga,Al)₅O₁₂:Ce³⁺ as the red- and green-emitting phosphors to prepare WLEDs with both high S/P and CRI, respectively. The simulation based on the optimal spectral model led to an optimal pc-WLED with a high S/P of 2.0-2.14, Ra > 80 and correlated color temperature (CCT) of 4000-5000 K, which matches very well with the experimental results of S/P = 2.064, Ra = 93.9, and CCT = 4981 K for the two-phosphor converted WLEDs. It implies that the optimal spectral model would be used effectively for the spectral design and phosphor selection for WLEDs.     

Molecular Weight Polydispersity Effects on Diffusion at Polymer/Polymer Interfaces

The effect of molecular weight distribution (MWD) on diffusion at symmetric polymer/polymer interfaces is investigated by rheological tools. A new model allowing the determination of a self‐diffusion coefficient of polydisperse polymer systems is presented. The model is based on the double reptation theory and Doi and Edwards' molecular dynamics applied to A/A polymers brought into intimate contact in the molten state. The material parameters for the model are obtained from linear oscillatory shear experiments, in which the dynamic shear modulus is measured in parallel plate geometry under a small amplitude of deformation as a function of time and frequency for a sandwich‐like assembly. The experiments were conducted on polystyrene (PS) blends with constant weight average molecular weight (M_w) but with variable number average molecular weights (M_n). The measured self‐diffusion coefficients showed that the presence of short molecules in the blend increases the mean value of the self‐diffusion coefficient and the magnitude of such increase can be quantitatively evaluated by the proposed model.     

Study of the CO2 adsorption isotherms on El Hicha clay by statistical physics treatment: microscopic and macroscopic investigation

ABSTRACT

CO₂ introduction in deep aquifers based on adsorption phenomena represents geological tanks that reduce CO₂ emission. Thus, investigating carbon dioxide adsorption on rocks is becoming more interesting. In our work, carbon dioxide adsorption on El Hicha clay is extensively studied. Experimental data for CO₂ adsorption on this clay are given for the first time. All the corresponding parameters are simulated and interpreted using the multilayer model with two interaction energies. The effect of the key parameters involved in the adequate model on the isotherm curves are thus elucidated and interpreted. The formulation of this model is based on statistical physic formalism. Several hypotheses involving some physicochemical parameters which describe perfectly the adsorption process are used.

The characteristic parameters of the adsorption isotherm such as the number of carbon dioxide molecules per site (n), the receptor site densities (N_M), the number of adsorbed layers (N_L) and the energetic parameters (-ε₁) and (-ε₂) are estimated for the studied systems by a nonlinear least square regression. These parameters are discussed and interpreted considering their temperature dependence. In order to provide new macroscopic interpretations of adsorption mechanisms, three thermodynamic functions are also determined such as the entropy, the internal energy and the free enthalpy of Gibbs from experimental data. Thus, we prove theoretically and experimentally that CO₂ adsorption on El Hicha clay is feasible, spontaneous and exothermic in nature.     

Solvent Extraction Studies for Platinum Recovery from Chloride Media by A N,N′‐ Tetrasubstituted Malonamide Derivative

Abstract: Solvent extraction studies for platinum recovery from chloride media have been carried out using N,N′‐dimethyl‐N,N′‐diphenyltetradecylmalonamide (DMDPHTDMA). Platinum can be effectively extracted by DMDPHTDMA in the presence of tin and can also be successfully stripped by an aqueous mixture of 4M HCl + 0.05M NaClO₃. The influence of different Sn:Pt feed ratios on the extraction system has been considered. Experimental parameters such as equilibration time, diluent, and temperature effects, extractant and hydrogen ion concentrations have been thoroughly investigated. The loading capacity of DMDPHTDMA for platinum has also been evaluated. Platinum extraction is proposed to occur via an ion‐pair association.     

A Scale Effect in the Durability of Oriented Thin-Wide Polypropylene Films during Oxidation under Load: Fracture Model of Stressed Polypropylene Films

Abstract

Studies have been made of the durability of oriented isotactic polypropylene (PP) films depending on their width during intensive oxidation (T = 130°C, P₀₂ = 20 kPa) under load. As the specimen width decreases under low stresses, mean durability is determined thermooxidative destruction rate at the nucleation sites the scale effect takes place. The durability values are found to be discrete multiples of integers for narrow specimens. The conclusion is drawn that the difference in polymeric specimen durability is determined by the concentration of defect zones, rather than by the versatility of their nature. The model of oriented PP films fracture under low-load oxidation conditions is proposed. This model is based on the dependence of durability on a number of oxidation destruction centers which are similar in nature (in the initiation rate) and cause specimen fracture while growing and joining together.     

Selection of Lead‐Free Piezoelectric Ceramics

Lead‐free piezoelectric ceramics are extensively investigated for the alternatives of lead‐based piezoceramics. (K,Na)NbO₃ (KNN), (Bi_0.5Na_0.5)TiO₃ (BNT), and (Bi_0.5K_0.5)TiO₃ (BKT)‐based ceramics are reported as promising piezoelectric material families. Several researchers have reported solid solution of these ceramics using various chemical and physical routes. In this study, we have rank these materials using multiple attribute decision making techniques. KNN‐LT‐LS and 0.7BNT‐0.2BKT‐0.1(Bi_0.5Li_0.5)TiO₃ are found to be top rank in all the materials of respective families under study. We have also reported Pareto‐optimal (nondominated) lead‐free piezoelectric ceramics for d₃₃ and T_c parameters.     

Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution

Abstract

In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and explicit formulas for the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated.     

Modeling and coordinative optimization of NO x emission and efficiency of utility boilers with neural network

An empirical model to predict the boiler efficiency and pollutant emissions was developed with artificial neural networks based on the experimental data on a 360 MW W-flame coal fired boiler. The temperature of the furnace was selected as an intermediate variable in the hybrid model so that the predictive precision of NO _x emissions was enhanced. The predictive precision of the hybrid model was improved compared with the direct model. Three optimal operational objects were proposed in order to minimize the fuel and environmental costs. Based on the neural network model and optimal objects, a genetic algorithm was employed to seek real-time solution every 30 seconds. Optimum manipulated variables such as excess air, primary air and secondary air were obtained under different optimal objects. The above algorithm interconnected with a distributed control system (DCS) formed the supervisory control and achieved real-time coordinated optimization control of utility boilers. This work was presented at the 6 ^th Korea-China Workshop on Clean Energy Technology held at Busan, Korea, July 4–7, 2006.