Development and analysis of advanced adaptive statistical process control charts for the joint monitoring of variables central tendency and dispersion

Abstract

Fully adaptive control charts are efficient Statistical Process Control (SPC) means to monitor a quality characteristic affecting the outcome of a manufacturing process. Usually, the performance of these adaptive charts is investigated in processes characterized by a single assignable cause mechanism. However, this assumption is frequently far from reality because a process shift to the out-of-control condition can be the consequence of several assignable causes, which can occur at the same time, or independently, and may affect the process mean, the standard deviation of the process, or both. Furthermore, the logical link between quality control and equipment maintenance and the improvement of the process performance in case of the incorporation of proactive actions to process monitoring techniques necessitated the study of their interaction under a multiplicity of assignable causes. Another complicated issue is the simultaneous monitoring of multiple correlated quality characteristics, which is, undoubtedly, crucial in today’s process applications. The independent monitoring of these multiple quality characteristics, especially in the presence of high correlation between them, may lead to erroneous monitoring policies. In this thesis, Variable-Parameter (VP) Shewhart control schemes, monitoring the location and scale of processes in presence of multiple assignable causes are presented. All the proposed control schemes are both economically and statistically optimized. Furthermore, for each of the proposed control schemes a Markov chain that models the occurrence of several assignable causes leading to progressive process deterioration, and calling for different corrective actions, is developed. The motivation and contribution of this thesis precede a detailed literature review. In the literature review, statistically optimized control schemes utilized for the joint monitoring of location and scale of processes are, firstly, presented. Then, some models both economically and statistically optimized for monitoring the mean and the dispersion of a process are pointed out. Partially adaptive and fully adaptive control charts, that have a better economic and statistical performance compared to their respective static ones, are also presented. Furthermore, studies on control charts for monitoring processes subject to a multiplicity of assignable causes and a detailed review on integrated maintenance and quality control schemes are presented. Finally, multivariate control charts for monitoring processes subject to multiple assignable causes affecting both location and scale can be found in the literature review. The problem setting and the assumptions of the proposed models both for univariate and multivariate processes are also presented in detail. Furthermore, every statistical measure utilized to define the statistical performance of the proposed control schemes is presented. The extension of the models to the realistic cases of imperfect process restoration and downward affection of the process mean increase significantly the applicability of the control schemes, introduced in the thesis. The first proposed SPC model is a new economic-statistically optimized VP control scheme for the optimization of a process operation where two assignable causes may occur, one affecting the mean and the other the standard deviation of the process. Therefore, it is possible for the process to operate in statistical control, when none of the two assignable causes has occurred, or under the effect of one, or both the assignable causes. The superiority of the proposed model is estimated by comparing its expected total quality-related costs vs. the economic outcome of the respective static and partially adaptive control schemes, for a benchmark of numerical examples. The numerical investigation indicates that the economic improvement of the proposed model may be significant. Moreover, the economic-statistical design of a VP control chart monitoring the process mean in presence of multiple assignable causes affecting the location of the process is presented. A benchmark of examples has been generated to compare the performance of the VP control chart with other less-adaptive control charts and the Fixed-Parameter (FP) control chart. The obtained results reveal the economic superiority of the VP control chart. The problem of the possible occurrence of multiple assignable causes that may affect both the location and scale of the monitored process is investigated. Subsequently, the economic-statistical design of a VP Shewhart control scheme for monitoring processes where multiple assignable causes, affecting both the mean and the dispersion of the process, is presented. The assignable causes may lead to progressive process deterioration and their simultaneous occurrence and the different corrective action for each assignable cause makes the proposed model more realistic. An extended numerical investigation is utilized to demonstrate the economic and statistical superiority of the proposed model against simpler approaches. An example from aviation industry illustrates the application of the model. Furthermore, a new VP Shewhart control scheme is presented for the economic-statistical optimization in cases where apart from multiple independent assignable causes, affecting both the mean and dispersion, failures may also occur. Each time the control scheme signals an alarm, preventive maintenance (PM) actions are initiated which are obviously preferable to corrective maintenance (CM) actions, required after a failure. The realistic assumption of imperfect PM actions has been considered. The optimal design parameters of the scheme are selected through a bi-objective optimization problem formulated by the long-run average cost per time unit minimization, and the long-run expected availability maximization, subject to statistical constraints. An extended numerical investigation is utilized to demonstrate the superiority of the proposed model against simpler control schemes. A new fully adaptive multivariate statistical process control (m-SPC) scheme for monitoring processes where multiple assignable causes may occur is studied. The assignable causes are independent and affect both the mean vector and the covariance matrix, which are monitored by a T2 control chart and a multivariate Shewhart control chart based on differential entropy, respectively. A real case example is employed to illustrate the operation of the proposed model and measure its economic and statistical performance for the specific example. Finally, the basic conclusions of this thesis, which are presented in Chapter 10, can be summarized in the following:  The development of the proposed, easy-to-use, monitoring tools allow the simultaneous monitoring of both the location and scale of processes under a multiplicity of assignable causes. Moreover, the effective monitoring of processes where, except for multiple quality shifts, failures are also possible to occur, is now feasible. Finally, the development of a control scheme for the simultaneous monitoring of multiple correlated quality characteristics allow the monitoring of multivariate processes when both the process location and variability are affected by multiple shifts.  All the proposed fully adaptive control schemes have a better economic and statistical performance compared to the respective, less-adaptive ones. Subsequently, the proposed schemes lead to significant cost savings and also enhance the confidence of practitioners to the control procedure.  The incorrect consideration of a single instead of multiple assignable causes imposes a significant cost to the process. This conclusion necessitates the application of the proposed control schemes in modern processes where the assumption of only one possible quality shift is, in most cases, far from reality.