Machine condition recognition via hidden semi-Markov model

https://doi.org/10.1016/j.cie.2021.107430Get rights and content

Abstract

In intelligent manufacturing systems, machines are subject to condition deterioration.Identifying machine condition is crucial for making practical decisions in production management. This paper studies the machine condition recognition problem in wafer fabrication. A sequence of processing times collected from past production is used to train a hidden semi-Markov model (HSMM). To improve the precision of the HSMM in the application of wafer fabrication, state duration dependency is considered. Experimental analyses based on real data demonstrate the effectiveness of the HSMM and reveal some managerial insights.

Introduction

In intelligent manufacturing systems, machines condition recognition palys an improtant role in many decision-making processes,such as production scheduling, maintenance policy optimization, etc. In reality, machine processing conditions keep changing due to several reasons such as loose linkage, wear and fatigue of parts, or misalignment of tighteners, etc (Lee, Lapira, Bagheri, & Kao, 2013; Ahmadzadeh and Lundberg, 2013). Time-changing effects thus occur, which mainly refers that the actual processing time of a job is affected (Strusevich & Rustogi, 2017). Various types of time-changing effects have been studied (Gawiejnowicz, 2008). All these studies mathematically formulate the time-changing effects by assuming that the actual processing time of a job is a function of its normal processing time and some features of production (i.e., the position of the job in a schedule, the start time of the job in a schedule, etc.). However, the practical application of these mathematical formulations is very limited due to their ideal nature. And deriving real correlation between machine condition and job processing times is a topic that is largely unexamined in current literature. In this paper, a Hidden Semi-Markov Model (HSMM) is applied to recognize machine condition, based on which a more precise processing time estimation becomes possible.

The above motivation of this paper concurs with the production challenge by a wafer fabrication work center in a semiconductor manufacturing corporation. Due to the high capital-intensive characteristics of the machines in this industry, high level of machine utilization is necessary to promise profit. However, fluctuation of job processing times in upstream machines incurs unexpected changeover and adjustment for downstream machines. How to recognize machine condition, thus to make production scheduling more practical is a major challenge for the work center. Instead of using sensor data from multiple sources which requires data fusion technique, the HSMM in our paper is trained by a sequence of processing times collected from past production. The trained HSMM can thus be used to estimate the deviation of processing time of future jobs.

The paper is organized as follows. Section 2 reviews the related literature. In Section 3, a HSMM is introduced. An online machine condition recognition approach is proposed in Section 4. Experimental results are analyzed in Section 5. Conclusions and perspectives are provided in Section 6.

Section snippets

Literature review

In this section, work on machine condition recognition is firstly reviewed. Then, different time-changing effects of processing times are discussed. They are followed by the contributions of our paper.

Summary and our contributions

Most existing studies assume that machine condition follows a given stochastic distributions and the deterioration effects can be formulated by static mathematical functions. However, these functions are either difficult to derive in reality or unrealistic for making practical production decision. Therefore, although these studies form a solid theoretical background, their practical applications are very limited. In our study, the observed processing time is used as the input data sequence to

Definition of the HSMM

Suppose that the machine addressed in this study has N states (s1, (…), si, (…), sN), each of which is associated with a certain degree of deterioration. Each state lasts for processing a certain number of jobs, which is denoted as the state duration. The duration of each state is characterized by a duration probability density, which is assumed to follow Gaussian distribution. For each state si,pi(di) denotes the probability of state si having duration di. State duration is also an indicator

Deriving the HSMM

In this section, forward and backward algorithms are firstly developed to infer the relationship of the parameters of the HSMM, i.e., initial state distribution π, duration-dependent state transition probability matrix A, and emission probability matrix B. Then the Baum-Welch algorithm is applied to re-estimate the model parameters. The Baum-Welch algorithm was introduced by Baum et al. (1966) to find the maximum estimation value of the parameters in finite state Markov chains by employing the

Machine condition recognition

In this section, the effectiveness of the HSMM to recognize machine condition is demonstrated by real data obtained from the wafer fabrication work center. All the experiments were performed on a personal computer with an Intel ® CoreTM i7-7700HQ(2.8GHZ) CPU and 8 GB RAM memory under Windows 10 operating system. The algorithms were coded with MATLAB.

Job processing time prediction

In this section, we apply the HSMM to predict job processing time. In the addressed work center, fluctuation of job processing times often incurs unexpected changeover and adjustment for downstream machines. A precise job processing time can lead to an improved utilization of the machines in the work shop.

In the work center, the deviation of job processing time is observed to have a strong dependency on machine state. For example, the processing times of the 256 jobs on one of the machines are

Conclusion

In this study, we have addressed a machine condition recognition problem derived from a wafer fabrication work center. A HSMM is proposed to recognize machine condition with job processing times as the input sequence. The HSMM is adapted to the situation of consecutive production process, where there is time dependency of state duration on the dummy age of the machine. The modified forward algorithm and backward algorithm are designed to establish the relationship of the parameters of the HSMM.

Acknowledgement

This work was supported by National Natural Science Foundation of China (Project number:51775347). We thank the referees for their valuable comments.

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