Occurrence Of Assignable Cause Research Articles

Robust Optimization of an Imperfect Process when the Mean and Variance are Jointly Monitored under Dependent Multiple Assignable Causes

Abstract Imperfect processes experience fault productions over time due to specific causes. Integrating the statistical process control, maintenance policy, and economic production quantity has led to more favorable results for the imperfect processes in literature. When monitoring a process, multiple assignable causes (ACs) may shift it to an out-of-control state. As indicated recently, if the interdependency of ACs is neglected, the total cost will be underestimated. Moreover, the mean and variance can simultaneously be affected by the occurrence of ACs. A non-central chi-square (NCS) chart was suggested for its decent performance against X-R chart in detecting the process disturbances and lowering quality loss cost. Besides, the increased occurrence rate of ACs over time leads to higher quality and maintenance costs. Employing a non-uniform sampling (NUS) scheme can significantly reduce costs. In the literature of modeling for imperfect processes under multiple ACs, all input parameters have always been fixed. The effectiveness of the models depends somewhat on the accurate estimates of these parameters. In reality, the estimation of parameters may be associated with uncertainty. For the first time, a robust design approach is proposed for designing NCS chart by considering the interval estimation of uncertain parameters. A particle swarm optimization (PSO) algorithm is used to present solutions. The proposed model is investigated through a real numerical example.

An economic-statistical production quantity model under quality-maintenance policy for imperfect manufacturing systems with interaction effect among assignable causes

This study integrates production and maintenance planning with statistical process monitoring in the presence of dependent multiple assignable causes. To adapt the model to the reality, two assumptions are considered: (1) the assignable causes (ACs) are dependent, and (2) the occurrence of ACs can affect both process mean and variability. Given the second assumption, a non-central chi-square (NCS) chart is used to monitor the process. Since the occurrence rate of ACs increases over time, a non-uniform sampling scheme is presented to reduce the out-of-control time period. A sensitivity analysis is presented to explore how the number of AC types influences the cost terms. The results indicate that the more AC types, the higher quality loss and maintenance costs are imposed on the manufacturer. Moreover, three comparative studies are conducted for confirming the effectiveness of the model. The first comparative study shows that the total cost will be less than its real value when the interdependency among the ACs is ignored. The second comparison shows that the NCS chart outperforms the in detecting the process disturbances and leads to a less quality loss cost. Eventually, the last one represents that employing the non-uniform sampling strategy leads to a significant cost savings.

A FRAMEWORK FOR ENHANCING THE RESPONSIVENESS TO DEFECTS VIA SPC AND WORKER EMPOWERMENT

The ultimate goal of the online quality control initiatives is to prevent the occurrence of defects or rather to detect the occurrence of defects as fast as possible in order to interfere with corrective actions. Generally, Statistical Process Control (SPC) tools such as control charts can be effectively applied to monitor the production processes and can be used as an indicator for the occurrence of assignable causes in the process which are mainly responsible for the occurrence of defects. Typically, the out of control signals resulted from control charts or other signs of developing defective items that are observed directly through visual inspection necessitate a rapid response from the shop floor operators. Meanwhile, the lack of worker empowerment and poor communication between shop floor workers and engineers as well as managers are mainly responsible for the late decisions and actions which lead to increased defect rates. This paper presents a framework that integrates SPC approaches with worker empowerment practices to enhance the responsiveness toward detected defects as well as preventing the occurrence of more ones. Besides, a case study concerned with the manufacturing of Unplasticized Polyvinyl Chloride (UPVC) pipes has been conducted to demonstrate the application of the proposed framework.

Robust design of a VP-NCS chart for joint monitoring mean and variability in series systems under maintenance policy

Abstract Statistical process monitoring and maintenance policy are two important tools to improve system reliability and products quality. To simplify mathematical modeling, most existing papers in the literature suffer from four major drawbacks: (1) designing the control charts under maintenance action for the single-unit systems, in spite of the fact that most real manufacturing processes include multiple units; (2) using control charts with fixed parameters that are slow in detecting small and moderate shifts; (3) this assumption that the occurrence of assignable cause only changes the process mean, which means it doesn’t have any effect on variance of quality characteristic, and (4) emplying the point estimates of input parameters while the precise estimation of them are unavailable in the real industrial situations due to the existence of uncertainty. To overcome the mentioned disadvantages, this study integrates the economic-statistical design of an adaptive non-central chi-square chart with maintenance policy for joint monitoring mean and variability of two-unit series systems. In addition, a robust optimization method is presented to minimize model costs under uncertain parameters. Finally, a case study is applied to indicate the model efficiency. The results confirm that the suggested control chart has better performance in cost-saving in comparison with the other control charts. Furthermore, the results demonstrate that when the number of uncertain parameters increases, the model cost increases obviously.

와이블분포하에서의 최소값 및 최대값 관리도의 설계

Department of Information and Statistics, Chungnam National UniversityStatistical process control techniques have been greatly implemented in industries for improving product quality and saving production costs. As a primary tool among these techniques, control charts are widely used to detect the occurrence of assignable causes. In most works on the control charts it considered the problem of monitoring the mean and variance, and the quality characteristic of interest is normally distributed. In some situations moni-toring of the minimum and maximum values is more important and the quality characteristic of interest is the Weibull distribution rather than a normal distribution. In this paper, we consider the statistical design of mini-mum and maximum control charts when the distribution of the quality characteristic of interest is Weibull. The proposed minimum and maximum control charts are applied to the wind data. The results of the application show that the proposed method is more effective than traditional methods.

A new sampling strategy to reduce the effect of autocorrelation on a control chart

On-line monitoring of quality characteristics is essential to limit scrap and rework costs due to bad quality in a manufacturing process. In several manufacturing environments, during production process data can be massively collected with high sampling rates and tight sampling frequencies. As a consequence, natural autocorrelation may arise among consecutive measures within a sample. Autocorrelation significantly inflates the average run length of a control chart and deteriorates its sensitivity to the occurrence of assignable causes. In this paper, we propose a new mixed sampling strategy for the Shewhart chart monitoring the sample mean in a process where temporal autocorrelation between two consecutive observations can be represented by means of a first order autoregressive model AR(1). With this strategy, the sample mean at each inspection time is computed by merging measures of a generic quality characteristic from two consecutive samples taken h hours apart. The statistical properties of a Shewhart control chart implementing the proposed strategy are compared to those implementing a skipping strategy recently proposed in literature. A numerical analysis shows that the mixed sampling outperforms the skipping sampling strategy for high levels of autocorrelation.

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.

Control Charts for Controlling Variability of Non-Normal Processes

Control charts represent a very effective tool used for reducing process variability by early detection of the occurrence of assignable causes of variation. -charts are applied to detect changes in process mean whereas S-charts are used to detect the same in process variability. Both charts are generally based on the normality assumption. The S-chart utilizes an unbiased estimator of the population standard deviation . However, it is highly affected by any violation of the normality assumption. In this paper, we propose some alternatives of S-charts based on some robust estimate of scale parameters. We will also illustrate the performance of the proposed control chart.

Economic design of variable sampling intervals [formula omitted] charts with A&L switching rule using genetic algorithms

The major function of control chart is to detect the occurrence of assignable causes so that the necessary corrective action can be taken before a large quantity of nonconforming product is manufactured. The control chart for averages (or the X ¯ chart) dominates the use of any other control chart technique if quality is measured on a continuous scale. The control chart with variable sampling intervals (VSI) scheme has been shown to give substantially faster detection of most process shifts than the conventional control charts. In 1991, Amin and Letsinger [Amin, R. W., & Letsinger, W. C. (1991). Improved switching rules in-control procedures using variable sampling intervals. Communications in Statistics – Simulation and Computation, 20, 205–230] improved the operation of VSI X ¯ chart by applying a switching rule, which is denoted by A&L switching rule, to reduce the number of switches and consequently to enhance the convenience of the chart. In the present paper, we develop the economic design of VSI X ¯ chart with A&L switching rule to determine the values of the seven test and switching parameters of the chart (i.e., the sample size, the long and short sampling intervals, the warning- and control-limit coefficients, and two switching parameters) such that the expected total cost is minimized. An illustrative example is provided and the genetic algorithm is employed to search for the solution of the economic design. A sensitivity analysis is carried out to study the effects of cost and model parameters on the solution of the economic design.

The effect of Phase I sample size on the run length performance of control charts for autocorrelated data

Traditional control charts assume independence of observations obtained from the monitored process. However, if the observations are autocorrelated, these charts often do not perform as intended by the design requirements. Recently, several control charts have been proposed to deal with autocorrelated observations. The residual chart, modified Shewhart chart, EWMAST chart, and ARMA chart are such charts widely used for monitoring the occurrence of assignable causes in a process when the process exhibits inherent autocorrelation. Besides autocorrelation, one other issue is the unknown values of true process parameters to be used in the control chart design, which are often estimated from a reference sample of in-control observations. Performances of the above-mentioned control charts for autocorrelated processes are significantly affected by the sample size used in a Phase I study to estimate the control chart parameters. In this study, we investigate the effect of Phase I sample size on the run length performance of these four charts for monitoring the changes in the mean of an autocorrelated process, namely an AR(1) process. A discussion of the practical implications of the results and suggestions on the sample size requirements for effective process monitoring are provided.

The economically designed two-sided Bayesian [formula omitted] control chart

This paper studies a model for the economic design of an adaptive X ¯ chart for short production runs that are subject to the occurrence of assignable causes, which may either increase or decrease the mean of the quality characteristic. At each sampling instance, the probabilities that the process operates under the effect of an assignable cause are updated using Bayes’ theorem. All three chart parameters, i.e., the time until the next sampling instance, the sample size and the control limit are adaptive and depend on these probabilities. We derive properties that facilitate the cost computation and eventually the optimization of the proposed scheme. Then, we evaluate the effectiveness of this chart by comparing its cost against the expected cost of (a) a fixed-parameter Shewhart chart optimized for short runs and (b) a variable-parameter Shewhart chart, optimized for an infinite process. The numerical results indicate that the potential savings from using the Bayesian scheme are significant.

Monitoring capability study and genetic economic design of X-bar control chart

Employing automatic gauges is one of the fundamental steps in advanced manufacturing system not only for assuring product quality, but also monitoring process stability. Statistical process control (SPC), therefore, is developed to detect the occurrence of assignable causes so that unnecessary quality costs can be avoided. However, it is necessary to provide a practical way to evaluate the monitoring capability of an automatic gauge for its application. That is, the monitoring capability study should be conducted before applying any automatic gauge on SPC application. The economic SPC chart then can be properly designed. Rather than conventionally considering the relationship between both manufacturing cappability and control limits, gauge capability is further and concurrently considered to analyze the monitoring error of an automatic gauge in this paper. After interpreting the effect of manufacturing capability, gauge capability, and control limits to construct the monitoring error model, furthermore, the engineer can then distinctly evaluate monitoring capability by the expected cost incurred in the SPC process. Also, genetic algorithm is successfully applied to determine the economic design of X-bar control chart with the realistic monitoring error model embedded.

Economic Design of Moving Average Control Charts

ABSTRACT The economic design of a control chart can reduce the cost of process control and promote the competitive capability of an enterprise. Many authors have studied the design of x¯, x¯ − R, x¯ − S, CUSUM, or EWMA charts from an economical viewpoint since Duncan proposed an economic design of x¯ control chart in 1956. Few studies, however, have attempted to focus on the economic design of a moving average (MA) control chart. Montgomery (2001) pointed out that an MA control chart is more effective than a Shewhart control chart in detecting small process shifts and is considered by some to be simpler to implement than the CUSUM. This paper provides a construction of an economic model to determine the optimal parameters of an MA control chart. A numerical example shows that the loss cost of the economic design of an MA control chart is lower than a conventional MA chart. The sensitivity analysis shows that magnitude of shift, the rate of occurrence of assignable causes and increasing cost when the process is out of control have a more significant effect on the loss cost.

Monitoring Process Mean and Process Variance Using Collani's Statistic

In this paper the use of Collani's statistic for monitoring simultaneously process mean and process variance is investigated by a comparison with the more popular chart and chart, respectively. The comparison is performed by means of an economic design of the charts assuming two different situations with respect to the occurrence of assignable cause. The criteria used for the comparison are the average total cost (ATC) and the average run lengths (ARLs), where the latter make sense only for equal sample sizes. Various cases with respect to the economic parameters and the distribution parameters are considered omitting the case of constant process variance, because in such a case a simple -chart is in any case superior. It turns out that a chart based on Collani's statistic is by far superior than the two popular charts. In order to have the superiority documented the numerical results are displayed in numerous tables.

Determination of Optimal Design Parameters of Moving Average Control Charts

The economic design of a control chart can reduce the cost of process control and promote the competitiveness of an enterprise. This type of design has been studied for over four decades since Duncan's pioneering work in 1956. Few studies, however, have focused attention on the economic design of a moving average (MA) control chart. Montgomery pointed out that an MA control chart is more effective than a Shewhart control chart for detecting small process shifts and is considered by some to be simpler to implement than the CUSUM. This study proposes an economic model of an MA control chart with multiple assignable causes. This economic model is then applied to a realistic case from the chemical industry, and sensitivity analysis shows that the magnitude of shift, rate of occurrence of assignable causes and penalty cost, when the process is out of control, should be more carefully estimated when conducting an economic analysis.

Economic Design of a Moving Average Control Chart with Multiple Assignable Causes when Two Failures Occur

The economic design of control charts has been researched for over four decades since Duncan proposed the concept in 1956. Few studies, however, have focused attention on the economic design of a moving average (MA) control chart. An MA control chart is more effective than the Shewhart chart in detecting small process shifts. This paper provides an economic model for determining the optimal parameters of an MA control chart with multiple assignable causes and two failures in the production process. These parameters consist of the sample size, the spread of the control limit and the sampling interval. A numerical example is shown and the sensititivy analysis shows that the magnitude of shift, rate of occurrence of assignable causes and increasing cost when the process is out of control have a more significant effect on the loss cost, meaning that one should more carefully estimate these values when conducting an economic analysis.