Design and Performance Investigation of Some Advanced Quality Control Charts

高級質量控制圖的設計與性能研究

Student thesis: Doctoral Thesis

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Award date29 Oct 2020

Abstract

As a statistical monitoring tool, control chart was initially designed for monitoring the quality of products in manufacturing industries and it has been proved to be effective in manufacturing processes. A large number of control charts have been constructed based on different statistical methods and they have been studied for different scenarios.

Control charts for monitoring the exponential type-II censoring samples are significant to investigate since such data are very common in many practical inspection scenarios in reliability context when items are replaced in groups after a period of time. The average time to signal (ATS), which involves both the number and the time of samples inspected until a signal occurs, is a good criterion to evaluate the performance of control charts. Chapter 2 proposes an ATS-unbiased control chart with known parameter and compares the proposed method with the traditional ones. The results indicate the proposed control chart is more sensitive to system deterioration. Then the effects of parameter estimation on the proposed control charts are evaluated. Since the control limits with estimated parameters result in more false alarms, an adjusted control chart with estimated parameters is proposed and the self-starting control chart based on sequential sampling scheme is adopted to solve the phase I problem. Finally, two examples are given to illustrate the implementation of the proposed approach.

Two-parameter (shifted) exponential distribution is widely applied in many areas such as reliability modeling and analysis where time to failure is protected by a guaranty period that induces an origin parameter in the exponential model. Despite a large volume of works on inferential aspects of two-parameter exponential distribution, only few studies are done from the perspective of process monitoring. In the modern production process, where items come with a warranty, we often encounter shifted-exponential time between events from consumers’ perspective and therefore, in Chapter 3, we propose two CUSUM schemes for joint monitoring of the origin and scale parameters based on the Maximum Likelihood estimators. We study the in-control (IC) behavior of the proposed procedures via Markov chain approach as well as applying Monte-Carlo. We provide detailed implementation strategies of the two schemes along with the follow-up procedures to identify the source of shifts when an out-of-control (OOC) signal is obtained. We examine the performance properties of CUSUM schemes and find that the two proposed schemes offer performance advantages over the Shewhart-type schemes especially for monitoring small to moderate shifts. Further, we provide some guidance for choosing the appropriate schemes and study the effect of reference parameter k of the CUSUM schemes. We also investigate the optimal design of reference values both in known and unknown shift cases. Finally, two examples are given to illustrate the implementation of the proposed approach.

Simultaneous monitoring of the time between events (TBEs) and event magnitude, such as, the time between successive manufacturing plant accidents and the magnitude of damage in an industry, for example, coal mines, has evolved as a popular research topic in industrial engineering. Most of the existing methods assume that the TBEs and magnitude are mutually independent, which is difficult to justify in practice. Several researchers consider some bivariate parametric models to take into account the dependence between the TBEs and magnitude, and construct joint monitoring schemes. In practice, such parametric methods are often unrealistic in absence of prior knowledge about the underlying distribution of a process. To this end, Chapter 4 used two distribution-free statistic to design two exponentially weighted moving average schemes, abbreviated as EWMA-JKBWS and EWMA-Mathur. We offer detailed implementation strategies for these two schemes and provide simplified computational algorithm for determination of control limits. Moreover, we investigate both the IC and OOC performances in a comprehensive comparison study. The results indicate that in general, EWMA-JKBWS scheme performs significantly better than EWMA-Mathur scheme in large number of situations. Finally, we provide two real examples to illustrate the application of the proposed approach.

Joint design of SPM (Statistical Process Monitoring) and maintenance strategies has evolved as a popular research topic in industrial engineering. Most existing works only consider location shifts of a process but neglect the effects of scale shifts. Besides, traditional SPM schemes are usually employed based on single-sampling, which might be insensitive to detect quality shifts and perform uneconomically from the cost-saving perspective. To overcome the drawbacks mentioned above, Chapter 5 proposes a double-sampling SPM scheme for simultaneously monitoring of location and scale shifts, and then develop a more realistic and effective model for the joint design of SPM and maintenance strategies. First, we propose a new SPM scheme with double-sampling for simultaneously monitoring location and scale shifts. The comparison results indicate that our proposed DS (double-sampling) scheme has a faster detection speed than the single-sampling one for different combination of shifts. Therefore, we combine our proposed SPM scheme with two widely used maintenance strategies: corrective maintenance and prevent maintenance, and then construct a new cost model under the constraints of sample size, operation time and ARL (average run length). A real case study is implemented to verify the effectiveness of our proposed method. Results demonstrate that our proposed model is more economical than the traditional method.

This thesis focuses on both theoretical study and practical applications in process monitoring. All the proposed control charts in this thesis have satisfactory performances in detection of quality shifts for typical scenarios or situations. Moreover in Chapter 5, the adaptive monitoring scheme integrating control chart with maintenance planning can not only help guarantee the equipment reliability, but also reduce the total manufacturing cost. The outcomes from this thesis make the control charts for quality monitoring more practical and effective.