Image data plays an important role in manufacturing and service industries because each image can provide a huge set of data points in just few seconds with relatively low cost. Enhancement of machine vision systems during the time has led to higher quality images, and the use of statistical methods can help to analyze the data extracted from such images efficiently. It is not efficient from time and cost point of views to use every single pixel in an image to monitor a process or product performance effectively. In recent years, some methods are proposed to deal with image data. These methods are mainly applied for separation of nonconforming items from conforming ones, and they are rarely applied to monitor process capability or performance. In this paper, a nonparametric regression method using wavelet basis function is developed to extract features from gray scale image data. The extracted features are monitored over time to detect process out‐of‐control conditions using a generalized likelihood ratio control chart. The proposed approach can also be applied to find change point and fault location simultaneously. Several numerical examples are used to evaluate performance of the proposed method. Results indicate suitable performance of the proposed method in detecting out‐of‐control conditions and providing precise diagnostic information. Results also illustrate suitable performance of our proposed method in comparison with a competitive approach.

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One of the most important and yet complex decision-making problems in the area of transportation programming issues is vehicle routing problem. There are various exact, heuristic, and metaheuristic methods presented for solving different vehicle routing problems. In this manuscript, a mathematical model and a new heuristic solution method are proposed for solving multi-depot vehicle routing problem with time windows and different types of vehicles. In this problem, depots must serve customers between their fuzzy time windows with vehicles having different capacities, velocities, and costs. For this purpose, the mathematical model for multi-depot routing problem is developed to consider the mentioned circumstances. The objectives of this model is travel distance reduction and customers' service level increscent which leads to cost and service time reduction. For complexity of this problem and much computational time of exact solutions of developed model, a heuristic approach is proposed. This systematic approach has some steps as: customer clustering, routing, vehicle type determination, scheduling, and routes improvement using simulated annealing and customer service level improvement. The efficiency of the proposed method is analyzed by a case study in ISACO Co. Results show that the method is efficient and applicable in industries.

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