In industrial, healthcare, and business processes, numerous quality characteristics are matched pairs. These characteristics help to identify anomalies, trends, and patterns that enable better decisions and process optimization. In process monitoring, the control chart is an effective tool for detecting unusual changes in the process parameters. The cumulative sum (CUSUM) and Shewhart charts are considered efficient, respectively, for detecting small and large shifts in the understudy process. The CUSUM and combined Shewhart-CUSUM (CSC) schemes are developed in this study to monitor the location parameter of the differences of paired processes. For the assessment of the proposed CUSUM and CSC charts, the run-length metric is used, which is produced by developing an algorithm in the R language. The conditional and unconditional run length distributions of the proposals are evaluated. The performance of the proposed charts is compared with some well-known existing schemes, and the comparative study shows that the proposed schemes perform uniformly better than their existing counterparts. Moreover, the estimation effect is also evaluated on the performance of the proposed schemes. A practical application related to the continuous stirred-tank reactor (CSTR) process, along with a hypothetical example of the proposed charts, is also provided to implement the proposed designs for the concerns of practitioners.
This paper proposes two new Phase II cumulative sum (CUSUM) control charts for detecting shifts in the location and/or scale parameters of continuous processes. Both charts are constructed using Lepage-type statistics. The first chart utilizes the combination of van der Waerden (VW) and Ansari-Bradley (AB) tests, while the second utilizes the combination of VW and Mood tests. The performance of the proposed charts is evaluated numerically in terms of average run length and compared with two existing competitive charts under four different distributional models. In addition, the statistical design of the proposed charts is examined in detail, with particular attention to the effect of the reference value, and practical empirical guidelines for their implementation are provided. The results indicate that, across all considered distributions, the CUSUM chart based on the VW and Mood tests consistently outperforms its main competitors. Finally, the practical usefulness of the proposed charts is demonstrated through two real-data applications involving a hard-bake manufacturing process and a customer service time process.
Supplier selection is a pivotal element in establishing a robust and reliable supply chain. A supply chain network generally has multiple suppliers for product supply, and different suppliers possess distinct supply capacities, with their production processes accompanied by emissions. In addition, carriers with stochastic capacity are responsible for the goods delivery during which transportation emissions are generated. Consequently, this study includes supply capacity and emissions into a unified assessment framework to construct a comprehensive reliability metric, denoting the probability that the supply chain network can satisfy market demand subject to supply capacity and emission constraints. Accordingly, the optimal supplier selection problem is to find the best suppliers such that supply chain network reliability is maximized. A method that combines network reliability algorithm and the genetic algorithm is designed to address the optimal supplier selection alongside the corresponding maximum network reliability. The algorithm's applicability is confirmed through a case study of a real supply chain network, and sensitivity analysis is carried out to explore the impact of supply capacity, emission and market demand on the optimal supplier selection, providing decision-making support for supply chain management.
In recent years, different monitoring schemes have been developed to simultaneously detect shifts in the mean parameter of the distributions of time between events ($T$T) and the amplitude ($X$X), generally known as time between events and amplitude (TBEA) monitoring schemes or charts. A vast majority of existing research works focus mainly on monitoring the ratio statistic ${Z_2} = X/T$Z2=X/T between variables T and X. Aside from the ratio statistic, two other statistics, constructed as ${Z_1} = X- T$Z1=X-T and ${Z_3} = X+ 1/T$Z3=X+1/T, have also been investigated by researchers for the process monitoring. Instead of focusing only on monitoring the ratio statistic ${Z_2}$Z2, this paper aims at simultaneously detecting shifts in the mean parameter of $X$X and $T$T with statistics ${Z_1}$Z1, ${Z_2}$Z2 and ${Z_3}$Z3 and further proposes several Exponentially Weighted Moving Average (EWMA) TBEA monitoring schemes, aiming at increasing existing TBEA chart's performance for small to moderate mean shifts. To better align with reality, both skewed and normal distributions are considered for modelling the amplitude $X$X. By using the Markov chain method, the run length properties of the proposed EWMA TBEA schemes are derived. Numerical evaluations are extensively conducted to demonstrate the outperformance of the EWMA TBEA schemes in detecting shifts in different scenarios. A detailed comparison is conducted between the proposed EWMA TBEA schemes with statistics ${Z_1}$Z1, ${Z_2}$Z2 and ${Z_3}$Z3. Moreover, a robustness of the distribution mis-specification for modelling the amplitude $X$X is conducted. Extensive simulations demonstrate that the proposed EWMA TBEA schemes are comparable to the CUSUM TBEA schemes and superior to the existing Shewhart TBEA schemes, especially for small mean shifts. Finally, a real data example of France forest fires is presented to show the implementation of the EWMA TBEA schemes.
Performance sharing is widely applied in reliability research of engineering systems owing to its high efficiency and flexibility. Previous studies have mostly focused on a single performance variable, failing to address the multi-dimensional performance requirements of complex systems. Therefore, this paper proposes a hybrid performance system (HPS) with sharing mechanism, adapting to more complex operating environments and achieving better overall performance. The system consists of single-performance units and multi-performance units connected via intra-group buses, while different unit groups are interconnected through inter-group buses. Furthermore, this paper considers the mutual conversion between different performance variables and evaluates the system reliability under both deterministic conversion rate (DCR) and random conversion rate (RCR) using the universal generating function (UGF). Finally, the effectiveness of the proposed model and methods is verified through numerical examples and Monte Carlo simulations.
Profile monitoring is employed to check the stability of the functional relationship between process response variables and explanatory variables. A shift in this functional relationship indicates the presence of assignable causes. Due to the widespread adoption of sensors, manufacturers can now collect extensive data during production, making it feasible to model and monitor the functional relationship using profile monitoring techniques. However, in certain complex manufacturing processes, due to cost and technical limitations of sensors, some critical process information remains unmeasurable. To address this challenge, this study adopts a functional state-space model (FSSM) for process modeling, where the state equation describes the internal dynamic evolution of the system, while the observation equation characterizes the functional relationship between response and explanatory variables. In Phase I, a B-spline-based Expectation-Maximization algorithm is used to estimate the FSSM. For Phase II monitoring, an Exponentially Weighted Moving Average (EWMA)-type monitoring statistic is proposed, and its iterative computation formula is derived to enhance computational efficiency. Simulation results demonstrate that the proposed monitoring scheme delivers superior performance across various scenarios. Finally, the practical implementation of the scheme is validated through a case study on monitoring the machining process of scroll involutes in an air compressor.
Enabled by Industry 4.0 advancements, such as intelligent sensors, the Internet of Things, and artificial intelligence, organizations are now able to efficiently collect process data through virtual metrology and use machine learning models to identify out-of-control processes. While existing research in multivariate process monitoring largely focuses on identifying mean and variance shifts, the growing importance of identifying dependence shifts in Industry 4.0 is evident, as the performance of machine learning-based monitoring critically depends on consistent dependence structures between training and monitored processes. Therefore, this study aims to propose a novel copula-based detection technique capable of identifying dependence shifts by integrating memory sign control charts for monitoring individual multivariate processes. This approach particularly leverages copula models to handle data that does not adhere to the multinormality assumption, making it essential for Industry 4.0, where virtual metrology replaces the physical one, eliminating the need for sampling. A large-scale Monte Carlo simulation study is then conducted to assess the run-length performance of the proposed framework against various dependence shift scenarios. The results demonstrate that the proposed framework outperforms traditional Highest Density Regions and classic Hotelling's ${T<^>2}$T2 in detecting specific dependence shift scenarios, even under the assumption of multinormality.
This paper studies the discrete time component level and system level reliability evaluation by considering a certain protection mechanism that is used to increase reliability. In particular, the discrete time version of the protection mechanism which was previously studied under continuous time setting is considered. An exact matrix-based expression is also obtained for the reliability of the discrete time consecutive k-out-of-n:G system equipped with protection block. The case when the lifetimes have a phase-type distribution is also taken into consideration. The novelty of the paper lies not only in the consideration of the discrete-time version but also in the new formulation of the reliability of the consecutive k-out-of-n:G system having a protection block.
This article examines the transformative impact of Digital Transformation (DX), Artificial Intelligence (AI), and Big Data on modern Quality Management (QM). It explores how traditional frameworks like PDCA and DMAIC are evolving to meet the demands of Industry 4.0, while also acknowledging their limitations in today's fast-paced, data-rich environments. Emerging technologies - including IoT, Machine Learning, and Digital Twins - are enabling real-time monitoring, predictive analytics, and autonomous decision-making. This technological shift is driving the emergence of 'Open Quality', a more dynamic, agile, and integrated paradigm for quality management. To address the shortcomings of conventional methods, new frameworks such as PEARL (Plan, Execute, Assess, Results, Learn) and 3DQIF (Domain, Data, Discovery) are introduced, emphasizing adaptability and data-driven insights. While applications of Industrial Big Data demonstrate significant potential for quality improvements, they also present challenges related to data governance, system integration, and workforce skills. Case studies illustrate how AI and analytics can deliver substantial cost reductions and quality enhancements. Ultimately, this paper advocates for a hybrid approach, integrating timeless quality principles with advanced digital technologies to navigate modern complexities and achieve sustainable quality excellence.
In this article, a reliability acceptance sampling plan (RASP) has been used to determine the acceptability of a lot of products based on their lifetime. We determined the optimal sample size in RASP by using a compound optimal design strategy. To compute the compound optimal design, we have considered two objective functions in the presence of progressive censoring. The extreme value distribution has been used to illustrate the concept. We compute the Fisher information matrix and the asymptotic variance-covariance matrix of the maximum likelihood estimates using a progressively censored sample. This matrix is utilized to determine the compound optimal design by developing a graphical solution approach that facilitates the computation and interpretation of the compound optimal design. A sensitivity analysis has been studied to examine the effects of misspecifying the lifetime model parameters. To demonstrate its practical use, we illustrate the proposed methodology with a real-life example.
In the case of complex products, a large number of observations can be collected for multiple responses. These observations often display diverse curve patterns depending on time or location. In the quality design of functional responses, if the complex relationship between response observations and time or location is not effectively handled, and the non-normality of the responses is not considered, it will affect the predictive accuracy of the model, which in turn will impact the reliability and accuracy of the optimal solution. This paper proposes a new method to tackle the aforementioned quality design problem. Specifically, a semi-parametric mixed-effects modeling strategy is adopted. In the first stage, B-splines are used to fit the relationship between the observations and time or location. In the second stage, the coefficients obtained from the first stage are used as responses to establish a model for their relationship with the input variables. A weighted multivariate quality loss function is then constructed to resolve the optimal parameter settings. Simulation examples and 3D printing examples verify the effectiveness of the proposed method in modeling and optimization.
This paper proposes a novel statistical process control methodology by developing Combined Shewhart-EWMA (CSEWMA) control charts designed for high-dimensional two-sample data. These charts are highly proficient in identifying process variations, meeting the increasing demand for advanced SPC techniques in complex industrial contexts. The suggested methodology includes three unique control charts, DRCSEWMA, BSCSEWMA and SDCSEWMA, which are based on the Dempster (DR), Bai and Saranadasa (BS) and Srivastava-Du (SD) statistics, respectively. These charts are optimized to detect small to moderate process shifts and are evaluated using metrics such as the average and standard deviation of the run length and extra quadratic loss. The effectiveness of the proposed charts is benchmarked against each other and against conventional Shewhart and EWMA-based approaches in high-dimensional scenarios, including multivariate normal, $t$t, and gamma data structures. Practical applicability is demonstrated using wind turbine bearing and daily stock price fluctuation datasets, where real-time responses from high-dimensional data are essential. The DRCSEWMA, BSCSEWMA and SDCSEWMA control charts exhibit exceptional sensitivity and efficient monitoring solutions. By enabling the early detection of process shifts, these charts enhance safety, operational efficiency and decision-making accuracy in environmental engineering processes, highlighting their potential for broader applications in high-dimensional environments.
This paper examines a multi-stage system characterized by different mechanisms at different stages. This system refines the operational processes of traditional systems and is more suitable for systems with stages. Such systems are commonly found in applications including nuclear power plants, offshore drilling platforms, and UAV systems. The degradation of the system is due to the impact of valid shocks. Whenever the state of the system reaches predetermined values, different mechanisms will be triggered to slow down the degradation of the system until the system can no longer support the operation of these mechanisms. To evaluate the reliability of the system, we employ a finite Markov chain imbedding approach along with phase-type distributions. Based on this, a maintenance strategy of the system is proposed and the optimal inspection interval has been found. Finally, we present some numerical examples to demonstrate the practical application and effectiveness of the proposed system.
Minimization of energy consumption and quality of service are two significant aspects of wireless telecommunication systems, which are adequately modeled using discrete-time queueing framework. System's delay can be reduced with the effective use of service and vacation policies. In this article, the modeling and analysis of a discrete-time bulk-service vacation queue with first essential service (FES) and second optional service (SOS) has been carried out. In FES, general bulk-service rule has been incorporated. A part of already served group in FES will join the SOS following binomial distribution. In both the phases, service time distributions are considered to be general distribution with service rates being dependent on batch-size. Here, we derive the bivariate probability generating functions of queue and server size distribution just after FES and SOS completion which are key components of this analysis. We also provide complete joint distribution at arbitrary, vacation completion slots. Various performance indices such as energy saving factor, throughput of the system, mean delay etc. have been sketched. The trade-off between energy consumption and system's throughput has also been depicted which may produce the optimal energy consumption. Numerical illustrations exhibit the implementation of our proposed methodology as well as include an example in which deviation in average power consumption is discussed. Through the graphical representation, sensitivity analysis of key parameters on numerous marginal system's probability and performance metrics have been investigated.
We propose an extended two-dimensional warranty policy that combines a renewing free-replacement warranty with a limited number of repairs during the warranty period. The system is assumed to experience two types of failures: type-I failures, which are repairable through minimal repair, and type-II failures, which are non-repairable or catastrophic and require replacement. In the proposed warranty scheme, type-II failures are covered by a renewing free-replacement policy during the initial warranty period, while type-I failures are subject to an upper limit on the number of allowable occurrences. If the number of type-I failures remains below this threshold, the warranty is extended up to a predetermined time horizon. To identify the optimal warranty strategy, an expected total cost function, incorporating the sale price function, is developed as the model's objective function. Numerical and graphical analyses are conducted under the assumption that the system lifetime follows a Weibull distribution. Finally, the applicability of the proposed policy is demonstrated using two real data sets.
