A Review and Evaluation of Statistical Process Control Methods in Monitoring Process Mean and Variance Simultaneously

In this paper, first the available single charting methods, which have been proposed to detect simultaneous shifts in a single process mean and variance, are reviewed. Then, by designing proper simulation studies these methods are evaluated in terms of in-control and out-ofcontrol average run length criteria (ARL). The results of these simulation experiments show that the EWMA and EWMS methods are quite capable to detect large shifts in the means and variances. However, while the two EWMV procedures under study do not perform well, the Max-Min EWMA and Max-EWMA perform very well in all scenarios of mean and variance shifts

Extending the hypergradient descent technique to reduce the time of optimal solution achieved in hyperparameter optimization algorithms

There have been many applications for machine learning algorithms in different fields. The importance of hyperparameters for machine learning algorithms is their control over the behaviors of training algorithms and their crucial impact on the performance of machine learning models. Tuning hyperparameters crucially affects the performance of machine learning algorithms, and future advances in this area mainly depend on well-tuned hyperparameters. Nevertheless, the high computational cost involved in evaluating the algorithms in large datasets or complicated models is a significant limitation that causes inefficiency of the tuning process. Besides, increased online applications of machine learning approaches have led to the requirement of producing good answers in less time. The present study first presents a novel classification of hyperparameter types based on their types to create high-quality solutions quickly. Then, based on this classification and using the hypergradient technique, some hyperparameters of deep learning algorithms are adjusted during the training process to decrease the search space and discover the optimal values of the hyperparameters. This method just needs only the parameters of the previous two steps and the gradient of the previous step. Finally, the proposed method is combined with other techniques in hyperparameter optimization, and the results are reviewed in two case studies. As confirmed by experimental results, the performance of the algorithms with the proposed method have been increased 36.62% and 23.16% (based on the best average accuracy) for Cifar10 and Cifar100 dataset respectively in early stages while the final produced answers with this method are equal to or better than the algorithms without it. Therefore, this method can be combined with hyperparameter optimization algorithms in order to improve their performance and make them more appropriate for online use by just using the parameters of the previous two steps and the gradient of the previous step

Vendor Managed Inventory of a Supply Chain under Stochastic Demands

In this research, an integrated inventory problem is formulated for a single-vendor multiple-retailer supply chain that works according to the vendor managed inventory policy. The model is derived based on the economic order quantity in which shortages with penalty costs at the retailers` level is permitted. As predicting customer demand is the most important problem in inventory systems and there are difficulties to estimate it, a probabilistic demand is considered to model the problem. In addition, all retailers are assumed to share a unique number of replenishments where their demands during lead-time follow a uniform distribution. Moreover, there is a vendor-related budget constraint dedicated to each retailer. The aim is to determine the near optimal or optimal order quantity of the retailers, the order points, and the number of replenishments so that the total inventory cost of the system is minimized. The proposed model is an integer nonlinear programming problem (NILP); hence, a meta-heuristic namely genetic algorithm (GA) is employed to solve it. As there is no benchmark available in the literature to validate the results obtained, another meta-heuristic called firefly algorithm (FA) is used for validation and verification. To achieve better solutions, the parameters of both meta-heuristics are calibrated using the Taguchi method. Several numerical examples are solved at the end to demonstrate the applicability of the proposed methodology and to compare the performance of the solution approaches

Closed-form equations for optimal lot sizing in deterministic EOQ models with exchangeable imperfect ACquality items

In this paper, the optimal lot size for batches with exchangeable imperfect items is derived where the delay time for the exchange process depends on the quantity of imperfect items. This delay in exchange may or may not lead into shortage. The initial received lot is 100% screened. After the screening process, an order to exchange defective products takes place. The imperfect items are held in buyer's warehouse until the arrival of the exchange lot from the supplier for which, after another 100% screening process, imperfect items are sold at a lower price in a single batch. Two possible situations in which 1) there will not be any shortage, and 2) there will be a shortage that is fulfilled before the end of the replenishment cycle, are investigated. Proper mathematical models are developed and closed-form formulae are derived. Numerical examples are provided not only to demonstrate application of the proposed model, but also to analyze and compare the results obtained employing the proposed model and the ones gained using the classical economic order quantity model

A Hybrid Meta-Heuristic Method to Optimize Bi-Objective Single Period Newsboy Problem with Fuzzy Cost and Incremental Discount

In this paper the real-world occurrence of the multiple-product multiple-constraint single period newsboy problem with two objectives, in which there is incremental discounts on the purchasing prices, is investigated. The constraints are the warehouse capacity and the batch forms of the order placements. The first objective of this problem is to find the order quantities such that the expected profit is maximized and the second objective is maximizing the service rate. It is assumed that holding and shortage costs, modeled by a quadratic function, occur at the end of the period, and that the decision variables are integer. A formulation to the problem is presented and shown to be an integer nonlinear programming model. Finally, an efficient hybrid algorithm of harmony search, goal programming, and fuzzy simulation is provided to solve the model. The results are illustrated by a numerical example

Phase-II Monitoring of AR (1) Autocorrelated Polynomial Profiles

In some statistical process control applications, quality of a process or product can be characterized by a relationship between a response and one or more independent variables, which is typically referred to a profile. In this paper, polynomial profiles are considered to monitor processes in which there is a first order autoregressive relation between the error terms in each profile. A remedial measure is first proposed to eliminate the effect of autocorrelation in phase-ІІ monitoring of autocorrelated profiles. Then, three methods are employed to monitor polynomial profiles where their performances are compared using the average run length criterion

Absorbing Markov Chain Models to Determine Optimum Process Target Levels in Production Systems with Rework and Scrapping

In this paper, absorbing Markov chain models are developed to determine the optimum process mean levels for both a single-stage and a serial two-stage production system in which items are inspected for conformity with their specification limits. When the value of the quality characteristic of an item falls below a lower limit, the item is scrapped. If it falls above an upper limit, the item is reworked. Otherwise, the item passes the inspection. This flow of material through the production system can be modeled in an absorbing Markov chain characterizing the uncertainty due to scrapping and reworking. Numerical examples are provided to demonstrate the application of the proposed model

Two-dimensional Warranty Cost Analysis for Second-hand Products

In spite of the recent steady increase of the volume of the second-hand markets, often customers remain in doubt regarding the quality and durability of the secondhand products. Aiming to reduce and share this uncertainty, dealers offer warranty on their products. Offering warranty for second-hand products is a relatively new marketing strategy employed by dealers of used electronic equipment, furniture, automobiles, etc. Usually, for used products, the dealer’s expected warranty cost is a function of product reliability, past age and usage, servicing strategy and conditions and terms of the warranty policy/contract. Sometimes the offered policy is limited by two parameters, typically the product age and usage after the sale. This type of policies is referred to as two-dimensional warranty policies. In this article, we develop statistical models for estimating the dealer’s expected warranty cost for second-hand products sold with two-dimensional free repair/replacement warranty

An Integrated Model of Project Scheduling and Material Ordering: A Hybrid Simulated Annealing and Genetic Algorithm

This study aims to deal with a more realistic combined problem of project scheduling and material ordering. The goal is to minimize the total material holding and ordering costs by determining the starting time of activities along with material ordering schedules subject to some constraints. The problem is first mathematically modelled. Then a hybrid simulated annealing and genetic algorithm is proposed tosolve it. In addition, some experiments are designed and the Taguchi method is employed to both tune the parameters of the proposed algorithm and to evaluate its performance. The results of the performance analysis show the efficiency of the proposed methodology

A Comparative Study of Four Evolutionary Algorithms for Economic and Economic-Statistical Designs of MEWMA Control Charts

The multivariate exponentially weighted moving average (MEWMA) control chart is one of the best statistical control chart that are usually used to detect simultaneous small deviations on the mean of more than one cross-correlated quality characteristics. The economic design of MEWMA control charts involves solving a combinatorial optimization model that is composed of a nonlinear cost function and traditional linear constraints. The cost function in this model is a complex nonlinear function that formulates the cost of implementing the MEWMA chart economically. An economically designed MEWMA chart to possess desired statistical properties requires some additional statistical constraints to be an economic-statistical model. In this paper, the efficiency of some major evolutionary algorithms that are employed in economic and economic-stati stical design of a MEWMA control chart are discussed comparatively and the results are presented. Theinvestigated evolutionary algorithms are simulated annealing (SA), differential evolution (DE), genetic algorithm (GA), and particle swarm optimization (PSO), which are the most well known algorithms to solve complex combinatorial optimization problems. The major metrics to evaluate the algorithms are (i) the quality of the best solution obtained, (ii) the trends of responses in approaching the optimum value, (iii) the average objective-function-value in all trials, and (iv) the computer processing time to achieve the optimum value. The result of the investigation for the economic design shows that while GA is the most powerful algorithm, PSO is the second to the best, and then DE and SA come to the picture. For economic-statistical design, while PSO is the best and GA is the second to the best, DE and SA have similar performances.</p