Design of EWMA and Mixed EWMA-CUSUM Control Charts under Failure-Censored Lifetime Test Based on Simulation Approach

Document Type : Original Article

Authors

1 Master Student, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

2 Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

3 Ph.D. Student, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

10.48308/jimp.15.1.257

Abstract

Introduction and Objectives: In reliability theory, one of the most important characteristics that is evaluated is the lifetime of products. Lifetime is an important quality characteristic that is considered in various fields, especially engineering sciences, to express the expected survival time and to describe the performance of a manufactured product. Nowadays, one of the concerns of manufacturers and commercial companies is to increase product quality, and in industries where lifetime is considered a quality characteristic, improving product quality is achieved by increasing its lifetime. Therefore, industry experts monitor product lifetimes to ensure the quality of manufactured products. In the present era, with advances in manufacturing knowledge and technology, products have high reliability. Therefore, monitoring the health of a product until the moment of failure under normal conditions is very time-consuming and costly. As a result, engineers use lifetime tests to save time and cost in obtaining product lifetimes.
Methods: In recent years, control charts have been used to monitor the number and time of product failures. Statistical Process Control (SPC) is a set of powerful tools used in manufacturing and service industries to monitor process behavior. Control charts are the most important and effective SPC tools for monitoring the quality characteristics of products through detecting and controlling changes.
Findings: Lifetime data are generally not symmetric and follow non-negative distributions. Therefore, the design of control charts under lifetime testing should consider the probability distribution of failure data. Traditional Shewhart control charts are efficient in detecting large changes in the monitored process but do not have sufficient sensitivity in detecting small changes. Therefore, to identify small changes that occur in the process, memory-type control charts are used. In this study, it is assumed that the quality characteristic of interest is product lifetime. The lifetimes of products follow a Weibull distribution with a fixed shape parameter and a variable scale parameter. Therefore, monitoring the mean of the Weibull distribution is done through monitoring its scale parameter.
In this study, the goal is to monitor the average product lifetime, which is in fact monitoring and evaluating the scale parameter of the Weibull distribution. If the product lifetime is greater than the average or a certain predefined value, the product is considered compliant and healthy, and if it is less than that value, the product is considered non-compliant and defective. The more the product lifetime exceeds the target average or the predefined value, the higher its quality, and vice versa. In this study, EWMA and Mixed EWMA-CUSUM control charts under failure-censored lifetime tests are designed to monitor product lifetimes. The control limits and the average out-of-control run lengths of the proposed control charts will be calculated using the Monte Carlo simulation algorithm.
Conclusion: The performance evaluation criterion of the proposed control charts is the average run length in the out-of-control state. Since the Mixed EWMA-CUSUM control chart is a combination of the two EWMA and CUSUM control charts, a comparison between the performance of the EWMA and Mixed EWMA-CUSUM charts is made. The results show that the Mixed EWMA-CUSUM control chart has better performance than the EWMA control chart in detecting small changes in the scale parameter.

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