This paper describes the adaptive optimal control of the inventory production system with Weibull-distributed deterioration items. First of all, the dynamic model of the system is presented with all possible disturbances and uncertainties. Then, it is controlled using an adaptive and optimal controller. In this method, by having numerical data from the output of the system without using its dynamic equations, an LQR controller is estimated for it. This is important and practical because in physical systems under significant disturbances and fundamental uncertainties, the dynamic equations of the system will not have the former reliability; And it is possible to change the equations of motion by adding any non-linearity so that the conventional controllers will suffer an error. Finally, it is shown that due to the nature of the system and existing uncertainties, the used method has a clear advantage over other optimal control methods and their application in optimizing the inventory production system in the supply chain.

This study examines the impact of indentations on the strength of float glass. Using the Vickers indentation method with loads of 1N and 10N, we created defects at varying distances from the point of contact. Biaxial flexure tests revealed that indentations with 1N at 18mm decreased the strength, while those with 10N and shorter distances from the point of contact increased the strength. Weibull distribution analyses showed a correlation between the load, distance, and the Weibull modulus, highlighting the influence of defect size on the probability of rupture.

In this paper, the focus is on mechanical systems that, like a ship or a submarine, perform risky missions and that must remain operating for the whole mission time. Missions take place far from the operational base and so, in case of failures, although repairs are possible, spares parts cannot be resupplied. Hence, given space constraints, the problem is to define the optimal set of spare parts that should be taken aboard, to maximize the probability to complete the mission. To solve this problem, we propose a constructive algorithm that generates the Pareto Optimal Frontier of all the non-dominated solutions, in terms of the system’s reliability and of required space. At first, the algorithm is formulated in a generic way; next, it is contextualized to the common case of Weibull distributed failure times. In this condition, the underlying equations of the model cannot be solved in closed form and an approximated procedure is proposed and validated through extensive numerical simulation.

The new method to chart the Hodges-Lehmann estimator control chart is proposed in this study. The evaluation of the three nonparametric control charts - the Sign test (ST), Mann-Whitney (MW), and the Hodges-Lehmann estimator (HL), for the known process distribution using normal and Weibull data represent the symmetric and asymmetric shapes of the process based on the original method through the 10000 run lengths simulation. The result illustrates that the average run length performance of the ST and MW correspond to their respective test statistics but for HL’s performance, the result indicates that the average run length is much greater than that derived from Wilcoxon signed rank statistics. The Hodges-Lehmann estimator control chart by the new approach for the known process distribution will be the alternative method for the process that needs to robust outliers’ properties from this statistics. In addition, the simulation demonstrates that the performances of the Sign test (ST) from mean and median processes are varied in the skewed distribution, and moreover, the Sign test (ST) from the median process represents more accurate performance. Meanwhile, for the control groups, MW generated within control limits or without restriction shows slightly different performance. The performance of dual scheme for the above-mentioned variable parameters control charts also produce the weighted average values that effect from the tight control scheme to the regular control scheme.

In this paper, an attempt is made to develop two inventory models for deteriorating items with variable demand dependent on the selling price and frequency of advertisement of items. In the first model, shortages are not allowed whereas in the second, these are allowed and partially backlogged with a variable rate dependent on the duration of waiting time up to the arrival of next lot. In both models, the deterioration rate follows three-parameter Weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. This cost is dependent on the lot-size as well as the distance from the source to the destination. The corresponding models have been formulated and solved. Two numerical examples have been considered to illustrate the results and the significant features of the results are discussed. Finally, based on these examples, the effects of different parameters on the initial stock level, shortage level (in case of second model only), cycle length along with the optimal profit have been studied by sensitivity analyses taking one parameter at a time keeping the other parameters as same.

Railroad maintenance engineering plays an important role on availability of roads and reducing the cost of railroad incidents. Rail is of the most important parts of railroad industry, which needs regular maintenance since it covers a significant part of total maintenance cost. Any attempt on optimizing total cost of maintenance could substantially reduce the cost of railroad system and it can reduce total cost of the industry. The paper presents a new method to estimate the cost of rail failure using different cost components such as cost of inspection and cost of risk associated with possible accidents. The proposed model of this paper is used for a real-world case study of railroad transportation of Tehran region and the results have been analyzed.