Chung-Ho Chen

Economic-statistical design of X ¥ charts for non-normal data by considering quality loss

When the X ¥ control chart is used to monitor a process, three parameters should be determined: the sample size, the sampling interval between successive samples, and the control limits of the chart. Duncan presented a cost model to determine the three parameters for an X ¥ chart. Alexander et al. combined Duncans cost model with the Taguchi loss function to present a loss model for determining the three parameters. In this paper, the Burr distribution is employed to conduct the economic-statistical design of X ¥ charts for non-normal data. Alexanders loss model is used as the objective function, and the cumulative function of the Burr distribution is applied to derive the statistical constraints of the design. An example is presented to illustrate the solution procedure. From the results of the sensitivity analyses, we find that small values of the skewness coefficient have no significant effect on the optimal design; however, a larger value of skewness coefficient leads to a slightly larger sample size and sampling interval, as well as wider control limits. Meanwhile, an increase on the kurtosis coefficient results in an increase on the sample size and wider control limits.

A synthetic double sampling control chart for the process mean

This article proposes a synthetic double sampling chart that integrates the Double Sampling (DS) chart and the conforming run length chart. The proposed procedure offers performance improvements in terms of the zero-state Average Run Length (ARL) and Average Number of Observations to Sample (ANOS). When the size of a mean shift δ (given in terms of the number of standard deviation units) is small (i.e., between 0.4 and 0.6) and the mean sample size n= 5, the proposed procedure reduces the out-of-control ARL and ANOS values by nearly half, compared with both the synthetic and DS charts. In terms of detection ability versus the Exponentially Weighted Moving Average (EWMA) chart, the synthetic DS chart is superior to the synthetic or even the DS chart, as the former outperforms the EWMA chart for a larger range of δ values compared to the latter. The proposed procedure generally outperforms the EWMA chart in the detection of a mean shift when δ is larger than 0.5 and n= 5 or 10. Although the proposed procedure is less sensitive than the EWMA chart when δ is smaller than 0.5, this may not be a setback as it is usually not desirable, from a practical viewpoint, to signal very small shifts in the process to avoid too frequent process interruptions. Instead, under such circumstances, it is better to leave the process undisturbed.

Economic design of X charts for non-normally correlated data

When the X chart is applied to monitor a manufacturing process, three parameters should be determined: sample size, sampling interval between successive samples, and the control limits for the chart. In 1956, Duncan presented the first cost model to determine the three parameters for the X charts, which is called the economic design of X charts. This paper develops the economic design of X charts for non-normally correlated data. An example of juice production process is presented to illustrate the solution procedure. A sensitivity analysis is performed to show the effects of non-normality and correlation coefficient on the optimal design of the chart.

Optimum process mean and manufacturing quantity settings for serial production system under the quality loss and rectifying inspection plan

In 1994, Al-Sultan presented a single sampling plan applied in determining the optimum process mean for two machines in a serial production system. However, Al-Sultan did not consider the quality cost for the product within the specification limits, pointed out that the non-conforming items in the sample of accepted lot is replaced or eliminated from the lot, and proposed an integrated model with production and quality. In this study, the author considers the problem of quality loss for the modified Al-Sultans model with k machines in a serial production system based on a single sampling rectifying inspection plan. Taguchis symmetric quadratic quality loss function is applied in evaluating the product quality. Then, the author further proposes a modified and integrated economic manufacturing quantity (EMQ) model based on the application of the modified Al-Sultans model for obtaining the maximum expected total profit of product per unit of time. The numerical results show that the price of an accepted products sold has the most important effect on both the process means and the expected total profit per unit of time.

Minimum-loss design of x-bar charts for correlated data

Abstract When the x-bar chart is used to monitor a production process, three parameters should be determined: the sample size, the sampling interval between successive samples, and the control limits for the chart. In 1956, Duncan presented a cost model to determine the three parameters, which is called the economic design of x-bar charts. In 1995, Alexander et al. combined Duncan’s cost model with the Taguchi’s quality loss function to present a loss model for determining the three parameters. When designing an x-bar chart, one usually assumes that the measurements within a sample are independent; however, this assumption may not be true for some processes. In this paper, we develop the minimum-loss design of x-bar charts for correlated measurements within a sample by incorporating the Taguchi’s quality loss function. An example of orange juice production process is presented to illustrate the solution procedure. From the results of sensitivity analysis, we find that as the measurements in the sample are positively correlated, highly correlated data result in a smaller sample size and a frequent sampling interval; however, as the measurements in the sample are negatively correlated, highly correlated data yield a smaller sample size and a narrower control limits.

Application of computer simulation to the design of a traffic signal timer

In this article, we obtain a better timer design for a pretimed traffic signal of an intersection located in the urban area of Touliu, Taiwan, by using computer simulation. The objective of this study is to reduce the average waiting time per approaching vehicle during peak hours by redesigning the current signal timer. The validation procedure of a simulation model and the application of orthogonal arrays in experiments are briefly reviewed, and the data collection and output analysis procedure are presented. From the result of this study, a better signal timer design for this intersection is proposed. If the signal timer is appropriately set, the average waiting time per vehicle of this intersection during peak hours is expected to have a reduction of about 20.74%.

THE OPTIMUM SELECTION OF IMPERFECT QUALITY ECONOMIC MANUFACTURING QUANTITY AND PROCESS MEAN BY CONSIDERING QUADRATIC QUALITY LOSS FUNCTION

ABSTRACT In this paper, we present a modified economic manufacturing quantity (EMQ) model under the imperfect product quality. Taguchis quadratic quality loss function is adopted for measuring the product quality. The modified EMQ model denotes the total loss to the society which includes the producers loss and the customers loss. The total inventory cost of the modified EMQ model includes the set-up cost, the holding cost, and the product cost. The perfect and imperfect reworks of product are considered in the modified EMQ model, respectively. By solving the modified EMQ model, we can obtain both the optimum combination of EMQ and process mean in order to have the minimum total loss of society.

Effect of Nonnormality on the Economic Design of Warning Limit Charts

Abstract Control charts are widely applied to monitor manufacturing processes. In 1962, Page presented a modified chart with warning limit, which includes an upper and lower warning band. In 1975, Gordon and Weindling presented a cost model for determining the five parameters of a warning limit chart: the sample size, the sampling interval between successive subgroups, the control limit coefficient, the warning limit coefficient, and the significant run length. When conducting the design of control charts, one usually assumes the measurements are normally distributed. However, this assumption may not be tenable in some specific production processes. Burr developed a general probability distribution to represent a wide range of density functions, including normal and nonnormal ones. In this article, we study the effect of nonnormality on the design of warning limit charts by combining Gordon and Weindlings cost model with the Burr distribution. In this study, it is observed that negative skewness leads to wider control and warning limits. In addition, larger kurtosis results in a longer significant run length and wider control and warning limits.

Economic design of continuous sampling plan under linear inspection cost

The article explores the problem of an economically based type I continuous sampling plan (CSP-1 plan) under linear inspection cost. By assuming that the per unit inspection cost is linearly proportional to the average number of inspections per inspection cycle, and by solving the modified Cassady et al.s model, we not only have the required level of product quality but also obtain the minimum total expected cost per unit produced.

On the present worth of multivariate quality loss

Abstract Quality loss function has been introduced, by Taguchi, to be a quality performance measure for products since the 1980s. In this paper, we extend the work of Teran et al. [The Engineering Economist 42 (1) (1996) 39–52] and incorporate the concept of time value of money into the multivariate loss function. First, the model for the present worth of the expected multivariate quality loss (PWML) is established and its solution procedure is developed. Then, an example is provided to illustrate how the model can be applied. Some sensitivity analyses are conducted to study the effects of planning horizon, customer discount rate and coefficients of parameter drift on the optimal means at production time and the associated quality loss. From the results of analysis, the longer the planning horizon of the product is, the farther the means should be set relative to the targets at production time. Also, as the customer discount rate increases, the mean should be set closer to the target at production time.