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The synthetic Tukey's control chart (denoted by Syn-TCC) applies a single observation in the process monitoring and is relatively robust to outliers. For a complex process, the probability distribution of quality characteristic must be carefully identified and the loss of quality characteristic, which is defined as the deviation from the target value, must be accurately estimated so that the quality state of the process may be more comprehensively described. However, the literature rarely studied the economic design of the Syn-TCC with Taguchi's loss function under non normality. In the present study, it is assumed that the quality characteristic follows a log-normal distribution and Taguchi's asymmetric linear and quadratic loss functions are involved to develop the economic-statistical design of the Syn-TCC for multiple assignable causes. A case study is presented to illustrate the application of this economic-statistical design of the Syn-TCC to an IC package industry. The sensitivity analysis of this case study reveals that a larger production lot size and larger two coefficients of loss functions generally lead to a higher total expected cost. [ABSTRACT FROM AUTHOR]

Coefficient of variation (CV) control charts are widely used to monitor processes in which the mean of process characteristic varies and its standard deviation changes with the mean. However, such charts are generally insensitive to small shifts. In the present paper, a double-sampling (DS) CV chart is proposed to effectively detect the CV shifts. An optimization model is developed to obtain the values of parameters in the DS CV chart. The performance of the DS CV chart is then compared with those of the variable parameter (VP) and the exponentially weighted moving average (EWMA) CV charts. Based on our study, the DS CV chart outperforms the VP CV chart in detecting all shift sizes. In addition, the EWMA CV chart outperforms the DS CV chart only for very small shifts, but the DS CV chart generally has better detection ability than the EWMA CV chart for small, medium and large shifts. A real example of integrated circuit lead electroplating is provided for illustration of applications and this example confirms that the DS CV chart has superior performance when compared with the other two charts. [ABSTRACT FROM AUTHOR]

In the present paper, the model in Abdul-Kader et al is modified by incorporating the capability index Cpm to assure the capability of production process and to obtain the process mean, economic specification limits, and quality investment level with minimization of the expected total cost per item. Three modified models are presented and discussed, where Model I firstly determines the optimal process mean and economic specification limits, and then by applying this optimal mean and specification limits, the optimal quality investment level is subsequently obtained, Model II firstly determines the optimal process mean and quality investment level and then, by applying this optimal mean and quality investment level, the economic specification limits are obtained afterwards, and Model III simultaneously determines the optimal process mean, economic specification limits and the optimal quality investment level. Solution procedure for each modified model is provided and a numerical example is given for illustration. Based on the results of sensitivity analysis, Model II is generally superior to the other two modified models under consideration of cost. [ABSTRACT FROM AUTHOR]

Sampling inspection is one of preventive quality methods for decreasing waste of time and cost, but should be along with other quality control approaches to effectively enhance product quality. Determination of optimum process mean tends to reduce the bias of the central tendency of process characteristic from its target, and has been an important topic in quality system design. Pulak and Al-Sultan developed a single sampling rectifying inspection model to determine the optimum process mean, based on maximization of the expected total profit per item. Since setting the economic specification limits for process characteristic is considered a short-term approach for quality assurance and, on the other hand, quality investment is a long-term approach for process improvement, in the present paper, a modified product inspection model, which is modified from Pulak and Al-Sultan's work, is firstly presented to simultaneously determine the optimum process mean and economic specification limits, based on maximization of the expected total profit per item. Then, quality investment is integrated into this modified model to obtain the optimum quality investment level. [ABSTRACT FROM AUTHOR]

In 1996, Pulak and Al-Sultan provided a rectifying sampling inspection plan for determining the optimal process mean, by assuming that the quality characteristic is larger-the-better and is normally distributed. In their inspection plan, the 100% rectifying inspection is executed when the quality of the lot is rejected. Pulak and Al-Sultan obtained the optimal process mean by maximizing the expected profit per item. Quality investment setting, e.g., new equipment, new software system, new material and parts, etc., is usually considered a long-term method for reducing the bias and variability of the product characteristic when the process improvement is required. The major objective of the present paper is to involve the effect of quality investment on the expected profit per item, where the original Pulak and Al-Sultan's model is modified. Numerical results show that our modified model yields the higher expected profit per item than the original model. [ABSTRACT FROM AUTHOR]

In this paper, the author presents a jointly design model with manufacturing quantity, specification limits, process mean and the parameters of X-bar control chart based on the specified process capability index value. The quality loss of a product is set to be related to the limits of the control chart. Assume that the quality characteristic of a product is normally distributed with known standard deviation and adjustable mean. The production process may have a shift in the process mean, while the process standard deviation remains constant. The optimal combination of parameters is determined by minimizing the expected total cost of product under the specified value. This integrated model is a generalization of the economic manufacturing quantity (EMQ) model with statistical quality control chart. Finally, the numerical example and sensitivity analysis of parameters will be provided for illustration. [ABSTRACT FROM AUTHOR]

This study proposes a modified economic manufacturing quantity (EMQ) model with deteriorating production process. Assume that the quality characteristic of the product is normally distributed. Consider the unstable production process with positive shift and an age-dependent positive drift while process variance increases. The target value of product characteristic is considered to be equal to its specification center and Taguchi’s symmetric quadratic quality loss function is applied to evaluate the product quality. The specification limits, process mean, and EMQ are jointly determined by minimizing the total expected cost of product per unit time under the specified process capability indexCpmvalue. A solution procedure is devised to find the optimal solution for modified EMQ model and the sensitivity analysis of key parameters is conducted to investigate the effect on the optimal solution. Numerical results show that the expected total cost of product per unit time is significantly influenced by the process capability index, the quality loss coefficient, the production rate, the demand rate, and process standard deviation. [ABSTRACT FROM AUTHOR]

Chung and Hou develop a deteriorating production system with allowable shortage for determining the optimal production run time. The rework cost of the defective products is included in their model. However, they did not consider the quality cost of non-defective products. In this study, the author proposes a modified Chung and Hou’s model for obtaining the optimal production process parameters (process quality level and production run time) under the minimization of the expected total relevant cost of product per unit time. Taguchi’s asymmetric quadratic quality loss function is used for measuring the product quality. [ABSTRACT FROM PUBLISHER]

In 2000, Roan et al. developed an imperfect production system including raw material procurement cost and finished product cost for determining the optimal process mean, production run size, and raw material order quantity, in which the quality cost of conforming products was not included. Taguchi proposed the quadratic quality loss function for measuring the product quality and redefined the product quality as the loss of society when the product is shipped and sold to the customer. In the present paper, the model developed by Roan et al. is modified with quality loss for obtaining the optimal parameters associated with raw material and production process. Numerical results show that our modified model leads to larger process mean, larger raw material order quantity, higher expected total relevant cost of products, smaller production run size, and smaller number of order quantity of the raw material satisfying each production run than those from the original model, which indicates that the original model given in Roan et al. may underestimate the expected total relevant cost of products due to ignoring the quality loss of conforming products. [ABSTRACT FROM PUBLISHER]

In the present paper, we propose a modified Kouikoglou and Phillis's produce-to-stock system with a the specified process capability index Cpm value under the partly loss sales or complete backlogging. The economic specification limits, specified process capability value, output quantity, and incoming order are jointly determined by maximizing the expected total profit of product. Hundred percent inspection is executed before the products are shipped to the customer. The finite output buffer (production quantity) and rejection of incoming order are also considered in our model. Assuming that the target value of product characteristic is equal to its specification center, the Taguchi's asymmetric quadratic quality loss function is applied to evaluate the product quality. From the above numerical examples and sensitivity analysis of parameters, the results suggest that one can adopt the modified Kouikoglou and Phillis's produce-to-stock system under the complete backlogging. If the produce-to-stock system under the partly loss sales, then one should use the original Kouikoglou and Phillis's model for obtaining the larger expected total profit of product than that of modified one. [ABSTRACT FROM AUTHOR]

In this paper, the author proposes a modified Kapur and Wang's model with unequal target value and specification center. The economic specification limits and process mean are determined by minimizing the expected total quality loss per unit product under the specified process capability index value. The process capability indices Cpm and Cpmk correlated with Taguchi's quadratic quality loss function are considered. The 100% inspection is executed before the product shipped to the customer. Taguchi's asymmetric quadratic quality loss function is applied in evaluating the product quality. The numerical results show that the modified model with specified Cpm value has smaller specification tolerance, larger process mean, and smaller expected total cost per unit product than those of the modified model with specified Cpmk value. [ABSTRACT FROM AUTHOR]

In the present paper, a new economic design with variable single sampling inspection plan for determining the optimal process mean is presented. The quality characteristic with the one-sided lower specification limit is assumed to be normally distributed with unknown mean and known standard deviation. The 100% rectifying inspection plan is adopted when the product lot is rejected. The optimum process mean and the parameters of sampling inspection plan are simultaneously determined by maximizing the expected total profit per unit and meeting the requirement of the specified consumer's risk. Two numerical examples and sensitivity analyzes of parameters are provided for illustration. The numerical results show that, among the model parameters, the price of product for accepted lot, the processing cost per unit, and the lower specification limit significantly affect the expected total profit per unit. [ABSTRACT FROM AUTHOR]

Design of sampling plan always plays a key role in statistical quality control. Dodge-Romig provided the rectifying single sampling plans (SSP) for attributing with the protection of lot tolerance percent defective (LTPD) or the average outgoing quality limit. The on-line 100% rectifying inspection can be applied as a short-term method for controlling the product quality, while the quality investment is an available method for improving the process parameters in the long run. In the present paper, the economic selection of quality investment for designing a Dodge-Romig SSP with LTPD protection is proposed. Both the mean and standard deviation of process characteristic are measured as the exponential function of quality investment. The optimal sampling plan and quality investment level are jointly determined by minimizing the expected total cost of product for a specified consumer's risk. The Dodge-Romig LTPD SSP with quality investment under fuzzy environment that satisfies the consumer's risk is also developed. Numerical examples are provided for illustration. Based on the results of analysis, it can be seen that the quality investment level and the expected total cost of product are significantly influenced by the known process standard deviation and the exponential reduction coefficient of process standard deviation for quality improvement. [ABSTRACT FROM AUTHOR]

The process capability index is a simple quantitative way to assess the capability of a process. To measure the overall yield of a multiple-stream process, Wang et al. (2009) proposed a yield index, denoted by , and then provided a point estimator of for practical industrial applications. In addition to point estimation, interval estimation plays an important role in statistical inference on the process index. In the present paper, we consider the problem of constructing the confidence interval for . First, the sampling distribution of is derived by applying Central Limit Theorem and the method of cumulative distribution functions. Then, the confidence intervals for are obtained using numerical integration by coding a MATLAB computer program. Several useful tables are provided for the purpose of constructing the confidence intervals of . A numerical example is presented to show how these tables may be applied for interval estimation of in a real production process. [ABSTRACT FROM AUTHOR]

The exponentially weighted moving average (EWMA) control charts with variable sampling intervals (VSIs) have been shown to be substantially quicker than the fixed sampling intervals (FSI) EWMA control charts in detecting process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true for some processes. In the present paper, the performances of the EWMA and combined X-EWMA control charts with VSIs are evaluated under non-normality. It is shown that adding the VSI feature to the EWMA control charts results in very substantial decreases in the expected time to detect shifts in process mean under both normality and non-normality. However, the combined X-EWMA chart has its false alarm rate and its detection ability is affected if the process data are not normally distributed. [ABSTRACT FROM AUTHOR]

Control charting is a graphical expression and operation of statistical hypothesis testing. In this article, we develop the joint economic design of the variable sampling intervals (VSI) and R charts to determine the values of the seven test parameters of the charts (i.e., the sample size, the long sampling interval, the short sampling interval, the warning limits of the chart, the control limits of the chart, the warning limit of the R chart, and the control limit of the R chart) such that the expected total cost associated with the test procedure is minimized. The genetic algorithm (GA) is employed to search for the optimal values of the seven test parameters of the VSI and R charts, and an example is provided to illustrate the solution procedure. A sensitivity analysis then is carried out to investigate the effects of cost and model parameters on the solution of the joint economic design. [ABSTRACT FROM AUTHOR]

Recent studies demonstrated that the variable sample size (VSS) &Xmacr; chart is quicker than the standard Shewhart (SS) &Xmacr; chart in detecting small process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be tenable in some production processes. The Burr distribution has been used in the literature to represent various non normal distributions. In this article, the Burr distribution will be employed to evaluate the control charts for non normal populations. We first show the VSS and Shewhart &Xmacr; charts are sensitive to non normality. Then we propose a method of varying the sample size and the control limits simultaneously. The variable sample size and control limit (VSSCL) &Xmacr; chart is shown to be quicker than the VSS &Xmacr; chart in detecting small and moderate shifts in the process. Most importantly, the risk of false alarm for the VSSCL &Xmacr; chart can be substantially decreased. In addition, with proper selection of chart parameters, the VSSCL &Xmacr; chart is more robust to non normality than the VSS and Shewhart &Xmacr; charts. [ABSTRACT FROM AUTHOR]

The signal-to-noise ratio is an indicator, introduced by Taguchi, for evaluating the experimental data in robust design. Estimating the confidence interval of the signal-to-noise ratio is an important topic in data analysis of robust design. Calculating the confidence interval for a parameter usually needs the assumption about the underlying distributions. Bootstrapping is a nonparametric, but computer-intensive estimation method. In this article, we present the results of a simulation study on the behavior of three 95% bootstrap confidence intervals (i.e., SB, PB, and BCPB) for estimating the smaller-the-better signal-to-noise ratio when the data are from either a normal distribution or one of the Burr distributions. A detailed discussion of the simulation results is presented and some recommendations are given. [ABSTRACT FROM AUTHOR]

Control charts are one of the most important methods in industrial process control. The acceptance control chart is generally applied in situations when an &Xmacr; chart is used to control the fraction of conforming units produced by the process and where 6-sigma spread of the process is smaller than the spread in the specification limits. Traditionally, when designing control charts, one usually assumes that the data or measurements are normally distributed. However, this assumption may not be true in some processes. In this paper, we use the Burr distribution, which is employed to represent various non-normal distributions, to determine the appropriate control limits or sample size for the acceptance control chart under non-normality. Some numerical examples are given for illustration. From the presented examples, ignoring the effect of non-normality in the data leads to a higher type I or type II error probability. [ABSTRACT FROM AUTHOR]

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 Weindling's 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. [ABSTRACT FROM AUTHOR]

Chen and Chou presented the economic design of type I continuous sampling plan (CSP-1 plan) under the linear inspection cost. However, it can be argued that the production process is seldom independent. In this paper, we further propose the problem concerning the economic design of CSP-1 plan under the dependent production process and linear inspection cost. A solution procedure is developed to find the unique combination (i*, f*) that will meet the average outgoing quality limit (AOQL) requirement while also minimizing the total expected cost per unit produced during one inspection cycle. [ABSTRACT FROM AUTHOR]

This paper explores the problem of minimizing the average total inspection (ATI) of Read & Beattie's variable lot-size sampling plan for continuous production. The solution procedure is developed to find the optimal parameters (n, c) that will meet the average outgoing quality limit (AOQL) requirement, while also minimizing the ATI for this variable lot-size plan. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents the calculation of the average outgoing quality limit (AOQL) for the tightened single-level continuous sampling plan (TCSP-1 plan) based on a numerical method. A solution procedure is developed to find the parameters (i, f, k) that will meet the AOQL requirement, while also minimizing the average fraction inspected (AFI) for the TCSP-1 plan when the process average pmacron(> AOQL) is known. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the problem of the design of integrating Dodge-Romig lot tolerance per cent defective (LTPD) single sampling plans (SSP) for variables and specification limits. Considering that the quality characteristic obeys a normal distribution, we propose a modification of Kapur and Wang's model for obtaining the optimal inspection policy of Dodge-Romig LTPD SSP for variables. [ABSTRACT FROM AUTHOR]

This article explores the problem of designing a CSP-1 plan with the specified average outgoing quality limit (AOQL), the acceptable quality level (AQL), and the limiting quality level (LQL) value. By adopting the regret-balanced criterion under the producer's and consumer's interests of quality, we can design the optimal CSP-1 plan. [ABSTRACT FROM AUTHOR]

The fast-food industry has experienced prosperous growth over the last three decades. In fast-food operations, the term “fast” refers to “quickservice.” The customers coming to a fast-food restaurant do not expect to wait for a long time to receive the food service. The waiting time for customers to receive the food service becomes one of the key quality characteristics in a fast-food restaurant. However, waiting lines always exist in a fast-food restaurant during peak hours. In this article, a simulation model is built to study the queuing system in a fast-food restaurant, which is located in the downtown area of the city of Touliu, Taiwan. From the results of the study, the manager of the restaurant should recruit another server during peak hours such that the customers' waiting time can be reduced. Meanwhile, the validation procedure for a simulation model is also briefly reviewed in this article. [ABSTRACT FROM AUTHOR]