Run Rules median control charts for monitoring process mean in manufacturing

Recent studies show that Shewhart median ( ) chart is simpler than the Shewhart chart and it is robust against outliers, but it is often rather inefficient in detecting small or moderate process shifts. The statistical sensitivity of a Shewhart control chart can be improved by using supplementary Run Rules. In this paper, we propose the Phase II median Run Rules type control charts. A Markov chain methodology is used to evaluate the statistical performance of these charts. Moreover, the performance of proposed charts is investigated in the presence of a measurement errors and modelled by a linear covariate error model. An extensive numerical analysis with several tables and figures to show the statistical performance of the investigated charts is provided for both cases of measurement errors and no measurement errors. An example illustrates the use of these charts.     

A general model for the economic-statistical design of adaptive control charts for processes subject to multiple assignable causes

Fully adaptive control charts are efficient statistical process control means to monitor a quality characteristic affecting the outcome of a manufacturing process. Usually, the performance of these adaptive charts is investigated in processes characterised by the possibility of the occurrence of a single assignable cause. 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. In this paper, we investigate the economic-statistical design of a variable-parameter (Vp) Shewhart control chart monitoring the process mean in the presence of multiple assignable causes. We develop a Markov chain that models the occurrence of several assignable causes leading to progressive process deterioration and calling for different corrective actions. A benchmark of examples has been generated to compare the performance of the Vp control chart with other adaptive control charts and the fixed-parameter control chart. The obtained results reveal the economic superiority of the Vp control chart.     

On developing sensitive nonparametric mixed control charts with application to manufacturing industry

Control charts are designed under the normality assumption of the quality characteristic of the process. However, the normality assumption rarely holds in practice. In non-normal conditions, parametric charts tend to display more false alarm rates and invalid out-of-control comparisons. The exponentially weighted moving average chart is a frequently used memory-type control chart for monitoring the process target that only performs effectively under the smoothing parameter's small choices. This study proposes a nonparametric mixed exponentially weighted moving average-progressive mean chart based on sign statistic (NPMEP_SN) under simple and ranked set sampling schemes to address this said drawback. Normal and non-normal distributions are included in this study to observe the proposed chart's in-control behavior and out-of-control efficacy. The prominent feature of the proposed schemes is that it works efficiently in detecting small and persistent shifts in the process location corresponding to the given values of the smoothing parameter. The proposed scheme is also tested under the ranked set sampling scheme to enhance the NPMEP_SN chart's performance (hereafter named “NPMEP_RSN”). The performance of the proposed charts is investigated through simulations using run-length profiles. The proposed schemes were seen to outperform other alternatives, specifically under the ranked set sampling scheme. A real data-set related to the diameter of a piston ring is included as a demonstration of the proposal.     

Construction of double sampling s‐control charts for agile manufacturing

Double sampling (DS) ‐control charts are designed to allow quick detection of a small shift of process mean and provides a quick response in an agile manufacturing environment. However, the DS ‐control charts assume that the process standard deviation remains unchanged throughout the entire course of the statistical process control. Therefore, a complementary DS chart that can be used to monitor the process variation caused by changes in process standard deviation should be developed. In this paper, the development of the DS s‐charts for quickly detecting small shift in process standard deviation for agile manufacturing is presented. The construction of the DS s‐charts is based on the same concepts in constructing the DS ‐charts and is formulated as an optimization problem and solved with a genetic algorithm. The efficiency of the DS s‐control chart is compared with that of the traditional s‐control chart. The results show that the DS s‐control charts can be a more economically preferable alternative in detecting small shifts than traditional s‐control charts. Copyright © 2002 John Wiley & Sons, Ltd.     

The performance of EWMA median and CUSUM median control charts for a normal process with measurement errors

Measurement error is often occurred in statistical process control. The effect of a linearly covariate error model on the exponentially weighted moving average (EWMA) median and cumulative sum (CUSUM) median charts is investigated. The results indicate that the EWMA median and CUSUM median charts are significantly affected in the presence of measurement errors. We compared the performance of the EWMA median and CUSUM median charts by using Markov chain method in the average run length and the standard deviation of the run length. We concluded that the CUSUM median chart for small shifts and the EWMA median chart for larger shifts are recommended. Two examples are provided to illustrate the application of the EWMA and CUSUM median charts with measurement errors.     

Production and quality control policies for deteriorating manufacturing system

In this paper, a novel model for a deteriorating manufacturing system is analysed, considering repairs and overhauls of random durations. The machine manufactures one product and the model is further complicated because the quality of the parts’ produced deteriorates according to the wear of the machine and human interventions. When a breakdown occurs, either a repair or an overhaul is performed. The machine is restored to as-good-as-new conditions if the overhaul is selected, and conversely, its condition deteriorates following repairs. Multiple operational states are considered to define an ageing process. The decision variables of the model are the production rate and the repair/overhaul switching strategy. This paper provides new insights to this research area by considering the simultaneous production and repair/overhaul control policy under the effect of deteriorations. The optimal decision policy minimises the total incurred cost comprising the inventory, backlog, repair and overhaul costs over an infinite planning horizon. Our paper differs from other research projects in its consideration of the machine’s history, defined by the number of repairs and multiple operational states. A numerical example is given to illustrate the proposed approach and a sensitivity analysis has been conducted to confirm the structure of the obtained control policies.     

Markov chain‐based cost‐optimal control charts for health care data

Control charts have traditionally been used in industrial statistics but are constantly seeing new areas of application, especially in the age of Industry 4.0. This paper introduces a new method, which is suitable for applications in the health care sector, especially for monitoring the health characteristic of a patient. We adopt a Markov chain‐based approach and develop a method in which not only the shift size (ie, the degradation of the patient's health) can be random, but the effect of the repair (ie, treatment) and time between samplings (ie, visits) too. This means that we do not use many often‐present assumptions that are usually not applicable for medical treatments. The average cost of the protocol, which is determined by the time between samplings and the control limit, can be estimated using the stationary distribution of the Markov chain. Furthermore, we incorporate the standard deviation of the cost into the optimisation procedure, which is often very important from a process control viewpoint. The sensitivity of the optimal parameters and the resulting average cost and cost standard deviation on different parameter values is investigated. We demonstrate the usefulness of the approach for real‐life data of patients treated in Hungary, namely the monitoring of cholesterol level of patients with cardiovascular event risk. The results showed that the optimal parameters from our approach can be somewhat different from the original medical parameters.     

Design of control charts with m‐of‐m runs rules

This paper investigates economic–statistical properties of the X? charts supplemented with m‐of‐m runs rules. An out‐of‐control condition for the chart is either a point beyond a control limit or a run of m‐of‐m successive points beyond a warning limit. The sampling process is modeled by a Markov chain with 2m states. The steady‐state probability for each state and the average run length (ARL) from each state of the Markov chain are derived in explicit formulas. Then the stationary average run length (SALR) is derived so as to develop an economic–statistical model. Using this model, the design parameters are optimized by minimizing the cost function with constraints on the average time to signal (ATS). The X? chart supplemented with m‐of‐m runs rules is compared with the Shewhart X? chart in terms of the SARL and the cost function. Sensitivity of the design parameters with respect to the cost function is also analyzed. General guidelines for implementing the X? chart with m‐of‐m runs rules are presented from those observations. It should be emphasized that supplementing run rules may provide feasible and efficient solutions even if the sample size is limited, while the Shewhart X? chart may not. Copyright © 2009 John Wiley & Sons, Ltd.     

面向质量目标的Q控制图设计

针对大批量生产开始阶段的过程监控,提出了一种基于预定质量目标的Q控制图监控方法.其基本思路是利用面向质量目标的统计公差技术与Q控制图相结合应用,以实现大批量过程开始阶段均值和方差未知时面向质量目标的过程监控.基于质量目标建立统计公差(CP*,k*),并将该统计公差转化为基于给定置信概率的对CP和k的估计值的判定条件.通过案例分析,面向质量目标的Q控制图能够在过程保持受控状态的前提下以一定置信概率保证质量目标.     

On the performance of coefficient of variation charts in the presence of measurement errors

In the literature, coefficient of variation control charts have been introduced under the assumption of no measurement errors. However, measurement errors always exist in practice, and they do affect the performance of control charts in the detection of an out‐of‐control situation. In this paper, we therefore study the performance of a coefficient of variation Shewhart‐type control chart (Shewhart‐CV chart) and also one‐sided coefficient of variation exponentially weighted moving average–type control charts (EWMA‐γ² charts) using a model with linear covariates. Moreover, we propose and study the performance of a two‐sided EWMA‐γ² chart using a model with linear covariates. Several figures and tables are provided and analyzed to evaluate the statistical performance of these control charts for different sources of measurement errors. The obtained results show that the precision and accuracy errors significantly affect the performance of both the Shewhart‐CV and EWMA‐γ² control charts. An example illustrating the use of this study is finally presented.     

Production and subcontracting control for an unreliable manufacturing system with setups

This paper deals with the problem of joint production, setup and subcontracting control of unreliable manufacturing systems producing two product types. The production requires setups each time it switches from one product type to another. Subcontracting is an integral part of the decision-making process due to limited production capacity in existing facility. The objective is to propose an effective control policy for the considered system which simultaneously manages production, setup and subcontracting activities. The complexity of the problem lies in the interaction between internal manufacturing decisions and subcontracting that outsource a part of the production, in a dynamic and stochastic environment. An experimental optimisation approach is adopted to determine the optimal control parameters which minimise the average total cost. Extensive sensitivity analyses are performed to illustrate the robustness and the usefulness of the adopted approach. An in-depth study comparing five control policies across a wide range of system parameters is also conducted. Extended cases closer to reality are also investigated considering elements such as the preventive maintenance and the production of non-conforming products. The best control policy in terms of economic performance is then obtained. Valuable insights providing a better understanding of interactions involving production, setup, and subcontracting are discussed.     

Optimisation for multi-part flow-line configuration of reconfigurable manufacturing system using GA

To facilitate the configuration selection of reconfigurable manufacturing systems (RMS) at the beginning of every demand period, it needs to generate K (predefined number) best configurations as candidates. This paper presents a GA-based approach for optimising multi-part flow-line (MPFL) configurations of RMS for a part family. The parameters of the MPFL configuration comprise the number of workstations, the number of paralleling machines and machine type as well as assigned operation setups (OSs) for each workstation. Input requirements include an operation precedence graph for each part, relationships between operations and OSs as well as machine options for each OS. The objective is to minimise the capital cost of MPFL configurations. A 0-1 nonlinear programming model is developed to handle sharing machine utilisation over consecutive OSs for each part which is ignored in the existing approach. Then a novel GA-based approach is proposed to identify K economical solutions within a refined solution space comprising the optimal configurations associated with all feasible OS assignments. A case study shows that the best solution found by GA is better than the optimum obtained by the existing approach. The solution comparisons between the proposed GA and a particle swarm optimisation algorithm further illustrate the effectiveness and efficiency of the proposed GA approach.     

Two-level hedging point control of a manufacturing system with multiple product-types and uncertain demands

This research is motivated by the co-operative production process of networked manufacturing systems (NMS). Manufacturing resource sharing and flexible production scheduling are two features of NMS. For an individual manufacturing system in an NMS, ‘flexible production scheduling’ means that it can produce multiple product-types and the switching of products is quick enough to respond to the demand fluctuation. ‘Manufacturing resource sharing’ means the utilisation of extra production capacity from other manufacturing systems in the NMS. Of course, that will bring extra cost. This paper focuses on the optimal production control problem of such a situation: one manufacturing system, multiple product-types, and uncertain demands. Here, it is assumed that there are two demand-levels for each product-type: the lower one and the higher one. The total normal production capacity is larger than the total lower demands and smaller than the total higher demands. If the total demands cannot be satisfied and the work-in-process (WIP) of all product-types decrease to a certain level, e.g. zero WIP, the extra production capacity may be utilised. For such a system, a new two-level hedging point policy is proposed, in which two hedging points (a higher one and a lower one) are given for each product-type. Different from the prioritised hedging point (PHP) policy which is usually applied to one-machine and multiple part-type systems, our control policy considers all part-types at the same prioritised level and keeps the work-in-process states of all product-types on a straight line in the state space. Thus, the total costs for WIP inventory and the occupation of extra capacity can be obtained in a closed form, which is a function with respect to the hedging points. Then the method for optimising the hedging points is proposed and the special structure of the optimal hedging point is obtained. Numerical experiments verify the optimality and the special structure of the hedging point obtained by our method.     

Scheduling of deadlock and failure-prone automated manufacturing systems via hybrid heuristic search

This work focuses on the scheduling problem of deadlock and failure-prone automated manufacturing systems, and presents a new scheduling method by combining a robust supervisory control policy and hybrid heuristic search. It aims to minimise makespan, i.e. the completion time of the last part. Based on the extended reach ability graph of the system, it establishes a new heuristic function and two dispatching rules to guide the search process for a schedule. By embedding a robust supervisory control policy into the search process, it develops a polynomial robust dynamic window search algorithm. Failure and repair events of unreliable resources may occur during the execution of a schedule obtained by the proposed algorithm and may make the schedule infeasible. To reduce the influence caused by them and ensure all parts to be finished, this work proposes two event-driven strategies. The first one suspends the execution of the parts requiring failed resources and those to be started until all failed resources are repaired and permits only those parts that have already been processed on working machines to be completed. The second one invokes the proposed algorithm to obtain a new schedule at the vertex generated after a resource failure or repair event and executes the new schedule. Both strategies are effective while the latter performs better at the expense of more computation.     

LRProb control chart based on logistic regression for monitoring mean shifts of auto-correlated manufacturing processes

With the growth of automation in manufacturing, process quality characteristics are being measured at higher rates and data is more likely to be auto-correlated. Traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries because process parameters are highly auto-correlated. Several attempts such as some time series based control charts have been made in the previous years to extend traditional SPC techniques. However, these extensions pose some serious limitations for monitoring the process mean shifts. These charts require that a suitable model has been identified for the time series of process observations before residuals can be obtained. In this paper, a logistic regression (LR)-based process monitoring model is proposed for enhancing the monitoring of processes. It is capable of providing a comprehensible and quantitative assessment value for the current process state, which is achieved by the event occurrence probability calculation of LR. Based on these probability values over the time series, a novel chart: LRProb chart, is developed for monitoring and visualising process changes. The aim of this research is to analyse the performance of the LRProb chart under the assumption that only a small number of predictable abnormal patterns are available. To such aim, the performance of the LRProb chart is evaluated on two real-world industrial cases and simulated processes. Given the simplicity, visualisation and quantification of the proposed LRProb chart, this approach is proved from the experiments to be a feasible alternative for quality monitoring in the case of auto-correlated process data.     

Approximate design and performance of the robust control charts for monitoring dispersion in Phase I

This article designs and studies the approximate performance of robust dispersion charts, namely, MAD chart, S_n chart, and Q_n chart, in Phase I analysis (recently developed in the literature). The proposed limits are based on false alarm probability for monitoring the dispersion of a process in Phase I analysis. The charting constants are determined to achieve the required nominal FAP (FAP₀). The performance of these structures is evaluated in (i) the attained false alarm rate and (ii) the probability of signals for out‐of‐control situations. The analysis shows that the proposed design of Phase I robust dispersion charts correctly controls the FAP and shows a good performance in detecting the shifts in the process variation. An illustrative example is used to explain the practical implementation of these limits.     

CUSUM control charts with variable sampling interval for monitoring the ratio of two normal variables

In many industrial manufacturing processes, the ratio between two normal random variables plays a key role in ensuring quality of products. Thus,  monitoring this ratio is an important task that is well worth considering. In this paper, we combine a variable sampling interval (VSI) strategy with a cumulative sum (CUSUM) scheme to create a new type of control chart for purpose of tracking the ratio between two normal variables. The average time to signal (ATS) and the expected average time to signal (EATS) criteria are used to evaluate the performance of the new VSI CUSUM RZ control chart. The  numerical results show that the proposed control chart has much more attractive performance in comparison with the standard CUSUM-RZ control chart and the VSI EWMA-RZ control chart.     

Use of the manufacturing system design decomposition for comparative analysis and effective design of production systems

The focus of this paper is on the use of the Manufacturing System Design Decomposition (MSDD) to make effective cost and production system design decisions. A comparative study is conducted to illustrate how and why the total cost is reduced when the functional requirements defined by the MSDD are achieved. The ultimate goal of this research was to advance manufacturing and production system development to being guided by engineering science and design rather than the common practice of duplicating another person’s or entity’s notion of the best physical implementation.     

A systematic approach to determine the optimal maintenance policy for an automated manufacturing system

We propose a systematic approach to determine the optimal maintenance policy for an automated manufacturing system which includes a flexible manufacturing cell (FMC) and several automated machine shops. The systematic approach combines simulation, fractional factorial design, noise or outer array of Taguchi design, regression metamodelling, and classical queueing analysis. A useful expression of the fractional utilization of the manufacturing system is derived and incorporated into formulating and solving the corresponding decision problem. The systematic approach provides an effective implementation procedure to handle practical maintenance problems found in a complex manufacturing environment. © 1997 John Wiley & Sons, Ltd.