Profile control chart based on maximum entropy

TL;DR

This paper introduces a novel process monitoring method using maximum entropy to track profile coefficients, comparing it with linear regression, and demonstrates its effectiveness through simulations and real-world examples in manufacturing.

Contribution

The paper proposes a maximum entropy-based profile control chart for monitoring process profiles, offering an alternative to traditional linear regression methods.

Findings

Maximum entropy method effectively detects process changes in pharmaceutical data.

Both methods perform similarly in semiconductor data.

Maximum entropy better identifies differences in certain real-world scenarios.

Abstract

Monitoring a process over time is so important in manufacturing processes to reduce the waste of money and time. Some charts as Shewhart, CUSUM, and EWMA are common to monitor a process with a single intended attribute which is used in different kinds of processes with various ranges of shifts. In some cases, the process quality is characterized by different types of profiles. The purpose of this article is to monitor profile coefficients instead of a process mean. In this paper, two methods are proposed for monitoring the intercept and slope of the simple linear profile, simultaneously. In this regard, two methods are compared here. The first one is the linear regression, and the one is the maximum entropy principle. The T2 Hotelling statistics is used to transfer two coefficients to a scalar. A simulation study is applied to compare the two methods in terms of the second type of error and average run length. Finally, two real examples are presented to demonstrate the applicability of the proposed chart. The first one is about semiconductors, and the second one is about pharmaceutical production processes. The performance of the methods is relatively similar. The maximum entropy plays an important role in correctly identifying differences in the pharmaceutical example, while linear regression did not correctly detect these changes.