A joint design of production run length,maintenance policy and control chart with multiple assignable causes

Although economic production quantity, statistical process monitoring and maintenance are three major concepts in process optimization of industrial environments, they have been often investigated separately in literature. Furthermore, in studies that consider these three concepts simultaneously, it is assumed that there is only one assignable cause in the production process. This simplified assumption is unlikely to occur in real production processes due to the usual complexity of manufacturing systems, which may lead to a poor performance in both economic and statistical criteria if the assignable cause originating the shift is different from the one anticipated at the design of the chart. To overcome these drawbacks, this paper develops an integrated model ofeconomic production quantity, statistical process monitoring and maintenance in the presence ofmultiple assignable causes. The particle swarm optimization algorithm is used to minimize the expected total cost per production cycle, subject to statistical quality constraints. Also, a comparative study is performed to illustrate the effect of considering multiple assignable causes on model’s costs. Finally, a sensitivity analysis is conducted on the expected total cost per production cycle and process variable values to extend insights into the matter.     

Economic model of x̄-CHART under non-normality and measurement errors

This paper investigates the effect of non-normality and measurement errors on the economic design of $\text{x}\text{?}\text{-}\text{control}$ charts. The measurable quality characteristic of the product is assumed to be non-normally distributed random variable. The process is subject to a single assignable cause with exponentially distributed occurrence time. This assignable cause shifts the process from in-control state to out-of-control state. Each observation involves some deviation from true value due to measurement error. This deviation, characterized by bias and imprecision, is considered to be a normally distributed random variate. The production cycle for the process model consists of: (1 ) the in-control period, (2) the out-of-control period due to occurrence of the assignable cause, (3) the search period due to false alarm, and (4) the search and correction time due to true alarm. An expected-cost model is formulated which comprises the fixed and variable cost of sampling, the cost of searching for the assignable cause when it does and does not exist, and the adjustment and correction costs. The economic design of $\text{x}\text{-}\text{?}\text{rmchart}$ involves optimal determination of the design parameters; the sample size, the sampling interval and the control limits coefficients so as to minimize the expected total cost. The optimal value of the design parameters are obtained using a computerized search technique. Consequently the effect of non-normality parameters and measurement errors on the design parameters and on the loss-cost function is explained through numerical examples.     

A variable parameter Shewhart control scheme for joint monitoring of process mean and variance

This paper presents a new Statistical Process Control model for the economic optimization of a variable-parameter control chart monitoring a process operation where two assignable causes may occur, one affecting the mean and the other the variance 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. By making the assumption that the occurrence rate of each assignable cause is exponential, a Markov chain approach is utilized to determine the probabilities that the process operates at any of the above possible states. The model uses an economic (or an economic/statistical) optimization criterion for the time to the next sampling instance, the size of the next sample, as well as the control limits of the inspection. That is, all design parameters of the control scheme are selected so as to minimize the total expected quality-related costs. The superiority of the proposed model is estimated by comparing its expected quality control cost vs. the outcome of the Fp (Fixed-parameter) Shewhart control chart, the Variable Sample Size (VSS) control chart, the Variable Sampling Interval (VSI) and the Variable Sample Size and Sampling Interval (VSSI) control chart, for a benchmark of examples. The numerical investigation indicates that the economic improvement of the proposed model may be significant.     

A variable parameter Shewhart control scheme for joint monitoring of process mean and variance

This paper presents a new Statistical Process Control model for the economic optimization of a variable-parameter control chart monitoring a process operation where two assignable causes may occur, one affecting the mean and the other the variance 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. By making the assumption that the occurrence rate of each assignable cause is exponential, a Markov chain approach is utilized to determine the probabilities that the process operates at any of the above possible states. The model uses an economic (or an economic/statistical) optimization criterion for the time to the next sampling instance, the size of the next sample, as well as the control limits of the inspection. That is, all design parameters of the control scheme are selected so as to minimize the total expected quality-related costs. The superiority of the proposed model is estimated by comparing its expected quality control cost vs. the outcome of the Fp (Fixed-parameter) Shewhart control chart, the Variable Sample Size (VSS) control chart, the Variable Sampling Interval (VSI) and the Variable Sample Size and Sampling Interval (VSSI) control chart, for a benchmark of examples. The numerical investigation indicates that the economic improvement of the proposed model may be significant.     

The economic design of control charts with repair cost depending on detection delay

This study extends Duncan's [1] model to two different manufacturing process models in which the processes continue and discontinue in operations during the search for the assignable cause. A more realistic assumption considered in this paper is that the cost of repair and the net hourly out-of-control income are functions of detection delay. In the continuous model, detection delay is defined as the elapsed time from the time when the shift of the process occurs until it is identified by control charts and the assignable cause is eliminated. The discontinuous model defines detection delay as the time interval from the occurrence of the process shift to the completion of testing a set of samples and interpreting the results. An efficient procedure is developed to determine the optimal designs without using any approximation approach. Thus, the proposed procedure can obtain the truly optimal designs rather than those approximate designs determined by Duncan [1] and other subsequent researchers. This paper illustrates several numerical examples and makes some relevant comparisons. The results indicate that this optimal solution procedure is more accurate than that of Panagos et al. [2]. Also, detection delay is sensitive to the economic design of control charts.     

Using Bayesian networks for root cause analysis in statistical process control

Despite their fame and capability in detecting out-of-control conditions, control charts are not effective tools for fault diagnosis. There are other techniques in the literature mainly based on process information and control charts patterns to help control charts for root cause analysis. However these methods are limited in practice due to their dependency on the expertise of practitioners. In this study, we develop a network for capturing the cause and effect relationship among chart patterns, process information and possible root causes/assignable causes. This network is then trained under the framework of Bayesian networks and a suggested data structure using process information and chart patterns. The proposed method provides a real time identification of single and multiple assignable causes of failures as well as false alarms while improving itself performance by learning from mistakes. It also has an acceptable performance on missing data. This is demonstrated by comparing the performance of the proposed method with methods like neural nets and K-Nearest Neighbor under extensive simulation studies.     

一种基于SPC的软件过程质量分析方法

一个项目的开发活动是很多软件过程的集合,不同软件过程之间关联性很强,成功地分析特定软件过程质量的关键是确保软件过程分析的独立性,剔除来自于其他过程的影响。传统Shewhart控制图基于统计假设检验理论,能够区分软件过程中的偶然因素和系统因素,但Shewhart控制图是全控图,无法区分过程之间的影响。为解决这种问题,定义软件过程的总质量和分质量,把系统因素细分为外部系统因素和内部系统因素,并总结软件过程质量诊断表,以使用控制图和选控图来帮助诊断导致软件过程质量异常的偏差源。     

Multi-criteria design of an control chart

Control chart designs are widely studied because control charts are not only costly used but also play an important role in improving firms' quality and productivity. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. In this paper, a possible combination of design parameters is considered as a decision-making unit; it is characterized by three attributes: hourly expected cost, average run length of process being controlled, and detection power of the chart designed with the selected parameters. Accordingly, optimal design of control charts can be formulated as a multiple criteria decision-making (MCDM) problem. To solve the MCDM problem, a solution procedure on the basis of data envelopment analysis is proposed. Finally, an industrial application is presented to illustrate the solution procedure. Also, adjustment to control chart design parameters is suggested when there are process improvements or process deteriorations.     

The quality control chart for monitoring multivariate autocorrelated processes

Previously, quality control and improvement researchers discussed multivariate control charts for independent processes and univariate control charts for autocorrelated processes separately. We combine the two topics and propose vector autoregressive (VAR) control charts for multivariate autocorrelated processes. In addition, we estimate AR(p) models instead of ARMA models for the systematic cause of variation. We discuss the procedures to construct the VAR chart. We examine the effects of parameter shifts and by example present procedures to show the feasibility of VAR control charts. We simulate the average run length to assess the performance of the chart.     

Multi-criteria design of an X̄ control chart

Control chart designs are widely studied because control charts are not only costly used but also play an important role in improving firms' quality and productivity. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. In this paper, a possible combination of design parameters is considered as a decision-making unit; it is characterized by three attributes: hourly expected cost, average run length of process being controlled, and detection power of the chart designed with the selected parameters. Accordingly, optimal design of control charts can be formulated as a multiple criteria decision-making (MCDM) problem. To solve the MCDM problem, a solution procedure on the basis of data envelopment analysis is proposed. Finally, an industrial application is presented to illustrate the solution procedure. Also, adjustment to control chart design parameters is suggested when there are process improvements or process deteriorations.     

Integrating economics into quality control charts

When control of a manufacturing process is needed, the common tool is Statistical Quality control (SQC). In the past, however, economic factors were the results after employing the SQC charts. Design of control charts refers to the specification of the sample size, the sampling frequency and the control limits for the chart. The authors have tested a model that uses economics as an integral part for the design of an X-bar control chart.

Douglas C. Montgomery developed a computer program for the optimal economic design of an X-bar control chart. The program is based on the cost model proposed by A.J. Duncan.

Montgomery's program was modified to select the optimal design parameters from a table of parameter values. Subroutines were developed to enable the user to enter the number of subgroups and the data points for each subgroup. The economically designed control chart is plotted using standard Graphical Kernel System (GKS) subroutines.     

The economic design of cumulative sum charts used to maintain current control of non-normal process means

This paper proposes a method for the economic design of cusum charts to maintain the current control of the non-normal process means. The economic design involves the determination of the design parameters that minimize a relevant cost function. An expression for the expected loss-cost function for the process is defined. An algorithm for near-optimal determination of the design parameters is presented. A computer program is designed for the application of the algorithm, and deriving the values of the design parameters and loss-cost function of an economic design of cusum chart to control non-normal process means. Also a numerical example is provided. Finally, a simplified scheme, which would be appliable at the workshop level is presented.     

Economic design of time-between-events control chart system

This article presents the economic design of the control chart system consisting of several individual control charts based on time-between-events (TBE) data for monitoring multistage manufacturing processes. The design algorithm considers all the TBE charts within a system in an integrative and optimal manner. Numerical studies show that the proposed design algorithm improves the performance characteristics (in terms of profit) considerably. The proposed control chart system is easy to understand and operate, and thus the floor operators can utilize and understand it as easily as for the traditional system.     

A neural network approach to characterize pattern parameters in process control charts

Abnormal patterns on manufacturing process control charts can reveal potential quality problems due to assignable causes at an early stage, helping to prevent defects and improve quality performance. In recent years, neural networks have been applied to the pattern recognition task for control charts. The emphasis has been on pattern detection and identification rather than more detailed pattern parameter information, such as shift magnitude, trend slope, etc., which is vital for effective assignable cause analysis. Moreover, the identification of concurrent patterns (where two or more patterns exist together) which are commonly encountered in practical manufacturing processes has not been reported. This paper proposes a neural network-based approach to recognize typical abnormal patterns and in addition to accurately identify key parameters of the specific patterns involved. Both single and concurrent patterns can be characterized using this approach. A sequential pattern analysis (SPA) design was adopted to tackle complexity and prevent interference between pattern categories. The performance of the model has been evaluated using a simulation approach, and numerical and graphical results are presented which demonstrate that the approach performs effectively in control chart pattern recognition and accurately identifies the key parameters of the recognized pattern(s) in both single and concurrent pattern circumstances.     

An adaptive Bayesian scheme for joint monitoring of process mean and variance

This paper presents a new model for the economic optimization of a process operation where two assignable causes may occur, one affecting the mean and the other the variance. The process may thus operate in statistical control, under the effect of either one of the assignable causes or under the effect of both assignable causes. The model employed uses the Bayes theorem to determine the probabilities of operating under the effect of each assignable cause. Based on these probabilities, and following an economic optimization criterion, decisions are made on the necessary actions (stop the process for investigation or not) as well as on the time of the next sampling instance and the size of the next sample. The superiority of the proposed model is estimated by comparing its economic outcome against the outcome of simpler approaches such as Fp (Fixed-parameter) and adaptive Vp (Variable-parameter) Shewhart charts for a number of cases. The numerical investigation indicates that the economic improvement of the new model may be significant.     

Optimal decision rules for determining the length of the production run

During the production period in some industrial processes, the process mean is shifted owing to the occurrence of an assignable cause. In other situations, simultaneous changes in process mean and process variance are experienced as time passes. When the changes are time dependent, the process mean and the process variance drift steadily as time goes on, and subsequently drive the process into an out-of-control state. Thus, at any point in the, a total change in product quality may result from drift or shift or both. This paper describes how to determine the optimal production run for a process under such conditions. The process is in control at the beginning of the production run and is shut down at the end for resetting. It is assumed that the process is subject to drift and/or shift. A cost function is developed that consists of the cost of resetting the process, the cost of rejected items, the lost product cost due to shutdown and the sampling cost. Optimal production run is determined by minimizing the cost function. A search algorithm as well as a graphical method are employed to locate the optimum solution.     

Stochastic manufacturing system with process deterioration and machine breakdown

This paper presents a realistic manufacturing inventory model with process deterioration and machine breakdown. In economic manufacturing quantity model, process usually starts with ‘in-control’ state and produces items of good quality. After some random point of time, process may deteriorate and shift to ‘out-of-control’ state due to occurrence of assignable cause. From that point, process produces some percentage of non-conforming items. Further process deterioration after machine shift may result in machine breakdown at any random time during the production period. If machine breakdown occurs during the production period, then corrective (emergency) repair is performed immediately otherwise preventive (regular) repair is performed at the end of production period. The proposed model is formulated assuming that the time required for production facility shifting from ‘in-control’ state to ‘out-of-control’ state, time when machine breaks down, corrective and preventive repairing time and demand of items follows probability distribution. We have derived analytically the optimal production time which minimises the total expected production cost annually for machine breakdown and no machine breakdown cases. The solution procedure is illustrated with the help of numerical examples for different probability distributions. Sensitivity of the optimal solution with respect to different parameters are also analysed.     

Design and optimization of EWMA control charts for in-control,indifference, and out-of-control regions

The design of quality control charts is normally carried out considering a process shift size that is considered important to be detected. The EWMA control chart is one of the best available options to use when good performance is needed to detect small process shifts. This paper presents a method for design of EWMA charts for control processes, in which the detection of small shifts is not necessary, and at the same time is effective in detecting important shifts. In such cases the EWMA control chart can also be designed successfully to deal with these requirements. A Markov chain approach is also applied to determine the ARL of the modified EWMA control chart. The implementation and interpretations are provided and numerical examples are used to illustrate the application procedure. We also investigate some basic properties of the proposed scheme. Genetic algorithms have been used to carry out this design.     

Fuzzy logic based assignable cause diagnosis using control chart patterns

Control chart patterns, besides determining the presence of assignable causes, also provide hints on the nature of assignable cause(s) present. Relating the patterns exhibited on the control chart to assignable causes is an ambiguous and vague task especially when multiple patterns co-exist. In this work, a rule based fuzzy inference system is developed for control chart to prioritize the control chart causes based on the accumulated evidence. When a process goes out of control, search for assignable causes can be assisted by the priorities assigned to the causes. For an in-control process, developing patterns can be tracked and preventive action can be taken to prevent the process from going out of control.