Design Of X-bar Control Chart Research Articles

An Integrated Model of Maintenance Policies and Economic Design of X-bar Control Chart Under Burr XII Shock Model

The combination of different methods of maintenance and economic design of control charts has received much attention from researchers in recent years. These maintenance policies increase the reliability of a system. So far, only a small number of failure distributions, with fixed or increasing hazard rates, have been used as a shock model in the integrated model of maintenance and economic design of X-bar control chart. A proper alternative for this situation may be the Burr distribution, in which the hazard rate has general form. In this paper, for the economic design of the X-bar control chart under the Burr XII shock model, we have presented an integrated model using preventive maintenance and incomplete maintenance. The obtained integrated model has been implemented using a numerical example and its sensitivity analysis has been performed. The results show that, the use of higher maintenance levels causes further reduction of the average cost per unit time of the quality cycle. The results of sensitivity analysis also show that our proposed model is not sensitive to the misspecification of the Burr XII distribution parameters.

Design of X-bar control chart based on Inverse Rayleigh Distribution under repetitive group sampling

The X¯ control chart is usually used in statistical quality control (SQC) to observe the change in procedure mean. In this paper, X¯ control chart for Inverse Rayleigh Distribution (IRD) is designed under repetitive group sampling at lower record values. The width of the X¯ control limits and power is established by using the mean and standard deviation of the Inverse Rayleigh Distribution based upon lower record values. The designed control chart’s Average Run Length (ARL) is determined for different values of the shift, sample size, lower record, and specified ARL. The already existed X¯ control chart is used for the comparison and to propose a new X¯ control chart for Inverse Rayleigh Distribution.

Design of X-Bar Control Chart for Resampling Under Uncertainty Environment

This paper presents the designing of the X-bar control chart using resampling scheme under the uncertainty environment. The necessary measures of the present chart are derived under the neutrosophic system. The neutrosophic average run length (NARL) when the process is in-control and out-of-control are derived under the neutrosophic statistical interval method (NSIM). The neutrosophic control chart coefficients are determined through the algorithm developed under NSIM. The comparative study shows that the proposed chart is better than the existing chart in NARL.

Fuzzy multi-objective economic-statistical design of X-bar control chart

Nowadays manufacturing organisations are aiming towards producing higher quality outputs at lower cost of production to keep stride with the competition. The control charts are the most popular and widely used statistical process control tools that can be used for monitoring the unevenness in quality characteristics of a production process. The economic-statistical design of control chart selects three parameters, namely sample size n, sampling interval h and control limit width k to achieve the lowest cost with desirable statistical properties. However, the cost function and statistical properties are interrelated. Hence, minimising the cost as the only objective is not an efficient method of designing control charts. In this paper, a multi-objective model for the economic-statistical design of X-bar control chart has been proposed with three objectives, i.e., to minimise mean hourly cost, maximise in-control average run length and maximise the power of detecting process shift. A multi-objective evolutionary genetic algorithm is used to obtain the Pareto-optimal solution for this design which is then ranked by fuzzy performance importance index. The performance of the proposed method is compared through a numerical example and observed to be superior to that reported in the literature.

Fuzzy multi-objective economic-statistical design of X-bar control chart

Nowadays manufacturing organisations are aiming towards producing higher quality outputs at lower cost of production to keep stride with the competition. The control charts are the most popular and widely used statistical process control tools that can be used for monitoring the unevenness in quality characteristics of a production process. The economic-statistical design of control chart selects three parameters, namely sample size n, sampling interval h and control limit width k to achieve the lowest cost with desirable statistical properties. However, the cost function and statistical properties are interrelated. Hence, minimising the cost as the only objective is not an efficient method of designing control charts. In this paper, a multi-objective model for the economic-statistical design of X-bar control chart has been proposed with three objectives, i.e., to minimise mean hourly cost, maximise in-control average run length and maximise the power of detecting process shift. A multi-objective evolutionary genetic algorithm is used to obtain the Pareto-optimal solution for this design which is then ranked by fuzzy performance importance index. The performance of the proposed method is compared through a numerical example and observed to be superior to that reported in the literature.

Economic design of x-bar control chart under hybrid maintenance policy

PurposeAccording to the relevance of product quality and machine degradation state, a hybrid maintenance policy is designed. The paper aims to discuss this issue.Design/methodology/approachProduct quality control and machine maintenance are considered simultaneously in this policy. Based on this policy, the economic model of x-bar control chart is proposed using statistical process control and renewal reward theory.FindingsThis model is solved by genetic algorithm and the experimental results validated its feasibility.Originality/valueIn this model, the four corresponding relationship, which is between product quality monitoring result and machine degradation state, is analyzed.

A teaching–learning based optimization approach for economic design of X-bar control chart

Being simple to use X-bar control chart has been most widely used in industry for monitoring and controlling manufacturing processes. Measurements of a quality characteristic in terms of samples are taken from the production process at regular interval and the sample means are plotted on this chart. Design of a control chart involves the selection of three parameters, namely the sample size (n), the sampling interval (h) and the width of control limits (k). In case of economic design, these three control chart parameters are selected in such a manner that the total cost of controlling the process is the least. The effectiveness of this design depends on the accuracy of determination of these three parameters. In this paper, a new efficient and effective optimization technique named as teaching–learning based optimization (TLBO) has been used for the global minimization of a loss cost function expressed as a function of three variables n, h and k in an economic model of X-bar chart based on unified approach. In this work, the TLBO algorithm has been modified to simplify the tuning of teaching factor. A MATLAB computer program has been developed for this purpose. A numerical example has been solved and the results are found to be better than the earlier published results. Further, the sensitivity analysis using fractional factorial design and analysis of variance have been carried out to identify the critical process and cost parameters affecting the economic design.

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

Shewhart charts are the most popular control charts that can be used to monitor variable quality characteristics in a production process. In this paper, a multi-objective model of the economic statistical design of the X-bar control chart is first proposed by incorporating the Taguchi loss function and the intangible external costs. The model minimizes the mean hourly loss cost while minimizing out-of-control average run length and maintaining reasonable in-control average run length. A multi-objective evolutionary algorithm, namely NSGA-II, is then developed and used to obtain the Pareto optimal solution of the model. Some sensitivity analyses are next performed to investigate the effect of parameter estimation on the chart performances. Finally, a comparison study with a traditional economic design model reveals that the proposed multiple objective design of the X-bar control chart offers a better approach and more practical outcomes for the practitioners.

An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.

Economic Design of VSI x-Bar Control Charts for Non Normally Distributed Data under Gamma (λ, 2) Failure Models

This investigation develops the economic design of x-bar control charts with variable sampling interval (VSI) for non normal data under Gamma (λ, 2) shock models. In the past, most of the economic design of control charts follows the Poisson process. However, pragmatically speaking, this process is usually not appropriate. Banerjee and Rahim (1988) presented a cost model which uses variable sampling intervals. This can be contrasted with sampling intervals of fixed length under a process-failure mechanism, which follows a Gamma (λ, 2) model with an increased hazard rate. In a separate study by Al-Oraini and Rahim (2003), an economic statistical design of x-bar control charts with the assumption of the Gamma (λ, 2) failure mechanism was proposed. When the x bar chart is designed to monitor a manufacturing process, three parameters need to be determined via engineers or participators. These parameters are sample size, sampling interval between successive samples, and control limits. However, measurements in the subgroup are assumed to be normally distributed when designing control charts. Said assumption may be untenable. This article employs a numerical example to indicate the solution procedure and to implement sensitivity analysis. Also, the situation of non normal and normal in the Gamma (λ, 2) model was compared. Results in non normal assumption revealed the following: smaller sample size (n) is needed; the initial sampling interval (h 1) can become longer; the sampling interval (h 2) can become shorter; the control limit width (L) can become narrower; and the expected cost per hour (ECT) can likewise be reduced.

Optimal operating policies of X-bar control chart for non-normal variables with generalised Pareto in-control times

In designing the control charts, the choice of control chart parameters like sample size and sampling interval are most important. To determine the optimal design parameters, it is required to consider the model for statistical economic design of control charts with suitable probability distribution for quality characteristic and process in-control times, which are random in nature. In this paper, we consider the economic statistical design of X-bar control chart for non-normal quality characteristic. Here, it is assumed that the sample average of the quality characteristic X-bar has a Johnson distribution and the process in-control times follow generalised Pareto distribution. With suitable cost considerations and modifying the Lorenzen and Vance (1986) cost model, the expected cost per unit time is derived. The optimal sample size and the time interval between samples are obtained by minimising the expected cost per unit time. The sensitivity of the design with respect to the parameters and costs is also studied. This model is much useful for reducing the production cost and to improve product quality in places like, glassware industries, chemicals and films industries, etc.

Economic design of Xbar control charts with continuously variable sampling intervals

AbstractIn the context of economic design, a two‐stage model is proposed that utilizes continuously variable sampling intervals. Specifically, each successive sampling interval is determined by the extremity of the latest sample. Modeling the situation as a Markov chain, the hourly cost is developed for any arbitrary set of design parameters. This proposed approach is found to be more economically desirable, possessing a smaller average out‐of‐control production time, when compared with a standard two‐stage approach where the sampling interval alternates between two fixed values. Copyright © 2009 John Wiley & Sons, Ltd.

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.

AN INTEGRATED ECONOMIC DESIGN MODEL FOR QUALITY CONTROL, REPLACEMENT, AND MAINTENANCE

[This abstract is based on the author's abstract.] An integrated model for joint economic design of X-bar control charts and maintenance schedules is given, and expressions for expected total cost and expected cycle length are developed. Expected to..

Economic design of X-bar control charts for use in monitoring continuous flow processes

SUMMARY This paper develops the economic design of an A'-bar chart for monitoring continuous flow processes such as those encountered in refining, chemical processing and mining. The economic model permits one to optimally select the subgroup size, the sampling interval, and the control limit width based upon an economic criterion. This economic model is then applied to a realistic set of costs from the chemical industry. A sensitivity analysis is performed to illustrate the effects of incorrectly estimating the cost components of the model.

Recent Developments in Control Chart Techniques

In the last three decades several control chart procedures were developed. Prominent among these, are the Cumulative Sum, Economic design of X-bar control charts, Acceptance and Multi-Characteristic charts. This article presents description and analysis..