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AbstractIn this work, the authors propose the application of type I continuous sampling plan (CSP-1 plan) with expected inspection cost, expected replacement cost, expected warranty cost, expected quality loss for conforming product, and expected quality loss for nonconforming product per item. The quality characteristics of product is considered as the normal distribution with smaller-the-better characteristics. The quality loss function of product addresses the quadratic quality loss function.The CSP-1 plan is applied in the process control. The optimal combination of parameters is obtained from the minimum expected total cost per item produced under the specified average outgoing quality limit (AOQL) protection. One needs to have the optimal clearance number, sampling frequency, and specification limit coefficient.

AbstractIn this work, the authors propose the integrated application of CSP-1 plan and Dodge-Romig rectifying inspection plan with expected inspection cost, expected replacement cost, expected warranty cost, expected quality loss for conforming product, and expected quality loss for non-conforming product per item. The quality characteristics of product is considered as the normal distribution with nominal-the-best and symmetric quadratic quality loss function.The CSP-1 plan is firstly applied in the process control. The optimal combination of parameters is obtained from the minimum expected total cost per item produced under the specified average outgoing quality limit (AOQL) protection. One needs to have the optimal clearance number, sampling frequency, and specification limit coefficient. Then Dodge-Romig rectifying inspection plan is applied in the product improvement. The optimal sample size, clearance number, and quality investment are obtained by minimizing the expected total cost per lot under the specified consumer’s risk.

AbstractIn this paper, the optimal clearance number and sampling frequency of type I continuous sampling plan (CSP-1 plan) and specification limit coefficient of product are determined with the minimum expected total cost per item under the specified average outgoing quality limit (AOQL) protection. The expected total cost per item includes the expected inspection cost, the expected replacement cost, the expected warranty cost, the expected quality loss for conforming product, and the expected quality loss for non-conforming product per item. The quality characteristic of product is considered as the normal distribution with larger-the-better characteristics. The quality loss function of product addresses the quadratic quality loss function. The sensitivity analysis of numerical example will be provided for illustration.

AbstractIn this work, the authors propose the asymmetric specification limit and quality investment settings for the Dodge-Romig rectifying inspection plan with quality loss and product cost. This method can be used for product improvement. The optimal combination of parameters of Dodge-Romig plan with the specified consumer’s risk protection, the asymmetric specification limit coefficients of product, and quality investment are obtained by minimizing the expected total cost per unit.

AbstractIn this article, the authors propose the integrated application of type I continuous sampling plan (CSP-1 plan) and Dodge-Romig rectifying inspection plan with quality loss and product cost. The normal quality characteristic, nominal-the-best, and asymmetric quadratic quality loss function of product are considered.The CSP-1 plan is firstly applied in the process control. Then Dodge-Romig rectifying inspection plan is applied in the product improvement. The optimal combination of parameters of CSP-1 plan and asymmetric specification limit coefficients are obtained under the specified average outgoing quality limit (AOQL) protection. The optimal combination of parameters of Dodge-Romig rectifying inspection plan and quality investment are determined under the specified consumer’s risk. Finally, the sensitivity analysis of numerical example will be provided for illustration.

AbstractIn this work, the authors proposes the modified Banu and Mondal’s model for obtaining the optimal process mean, quality investment, replenishment cycle time, and trade credit period. Assume that the product quality is normally distributed with unknown process mean and known standard deviation. The product is considered under the larger-the-better characteristic. The declining exponential reduction of process standard deviation is the function of quality investment. Numerical results show that (1) the production cost per item and the parameter of quality investment function for the process standard deviation have the effect on the process mean; (2) the production cost per item, the non-conforming cost per item, the parameter of quality investment function for the process standard deviation and the known process standard deviation have the major effect on the quality investment; (3) the production cost per item has the effect on the retailer’s replenishment cycle time; (4) the production cost per item has the major effect on the expected total profit including the manufacturer and the retailer per unit time.

AbstractIn this paper, the author proposes the modified Banu and Mondal’s model without product warranty for obtaining the optimal quality investment, retailer’s replenishment cycle time, and customer’s trade credit period. Assume that the product quality is normally distributed with known process mean, known standard deviation, and nominal-the-best characteristic. The declining exponential reduction of process mean and standard deviation is the function of quality investment. Numerical example and sensitivity analysis of some parameters will be provided for illustration.

AbstractBanu and Mondal proposed an integrated inventory model with/without manufacturer’s product warranty and customer’s trade credit. Their model needs to obtain the optimal product warranty, retailer’s cycle length, and customer’s credit period with the maximum of the expected total profit per unit time. Their model can be further applied in the process control. In this paper, the author presents a modified Banu and Mondal’s model with product warranty for obtaining the optimal process mean, warranty period, retailer’s replenishment cycle time, and customer’s trade credit period. Consider that the product quality is normally distributed with unknown process mean, known standard deviation, and larger-the-better characteristic. Numerical example and sensitivity analysis of some parameters will be provided for illustration.

AbstractThe optimal setting of process mean is an important issue in operations management and a variable sampling inspection plan is an acceptance sampling technique for quality assurance. In the present study, the newsvendor problem (i.e., the mixed procurement system) is modified by applying a variable sampling inspection plan with specified average outgoing quality limit (AOQL) with maximization of the expected total profit including the manufacturer and the retailer. The optimal retailer’s order quantity and manufacturer’s process mean and the parameters of sampling plan are jointly determined by maximizing the expected total profit. In the model, the single sampling rectifying inspection plan is adopted to determine the quality of lot product and the used cost of customer for product is measured by Taguchi’s quadratic loss function. A numerical example is given and the sensitivity analysis of model parameters are provided for illustration. Based on the results of sensitivity analysis, it may be seen that a higher processing cost per unit generally leads to a lower expected profit. In the meantime, a higher retailer’s selling price always results in a higher expected profit.

AbstractBanu and Mondal (2018) proposed an integrated inventory model with/without manufacturer’s product warranty and customer’s trade credit. Their model needs to obtain the optimal product warranty, retailer’s cycle length, and customer’s credit period with the maximum of the expected total profit per unit time. Their model can be further applied in the process control. In this paper, the authors present a modified Banu and Mondal’s model without product warranty for obtaining the optimal process mean, retailer’s replenishment cycle time, and customer’s trade credit period. Assume that the product quality is normally distributed with unknown process mean, known standard deviation, and larger-the-better characteristic. Numerical example and sensitivity analysis of some parameters will be provided for illustration.

AbstractA variables sampling plan is an acceptance sampling technique, where the process/ quality characteristics are measured in a continuous scale, and usually requires a smaller sample size than an attributes sampling plan. In the rectifying sampling plan, 100% inspection is performed to find the defectives in the rejected lot and then to replace those non-conforming items by conforming ones, which is able to provide the assurance of product quality level. In the present study, a newsvendor problem (pure procurement system) with application of a rectifying sampling plan under the constraint of the specified consumer’s risk is formulated to maximize the expected total profit, including both the producer and the retailer. The retailer’s order quantity and producer’s process mean, and the parameters of sampling plan are decision variables in our model and are jointly determined by maximizing the expected total profit. The solution procedure of this model is proposed and a numerical example is given. Based on the sensitivity analysis, it is obvious that producer’s processing cost and retailer’s selling price significantly affect the expected profit. Particularly, a lower processing cost always leads to a larger sample size, a larger order quantity and a higher expected profit. In addition, a lower retailer’s selling price generally results in a lower expected profit.

AbstractStatistical process control (SPC) is a preventive method for quality control and improvement. It can be applied in the manufacturing and service industry. Optimal process mean and economic specification limits settings are two important topics for SPC. In 2018, Banu and Mondal proposed an integrated inventory model with/without manufacturer’s product warranty and customer’s trade credit. Their model needs to obtain the optimal product warranty, retailer’s cycle length, and customer’s credit period with the maximum of the expected total profit per unit time. In this paper, the author addresses a modified Banu and Mondal’s model without product warranty for obtaining the optimal process mean, specification limits, retailer’s replenishment cycle time, and customer’s trade credit period under the specified process capability index Cpmvalue. Assume that the product quality is normally distributed with unknown process mean, known standard deviation, and nominal-the-best characteristic. Finally, a numerical example and sensitivity analysis of some parameters will be provided for illustration.

AbstractIn 2018, Chen and Chou proposed 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 Cpmor Cpmkvalue. This integrated model is a generalization of economic manufacturing quantity (EMQ) model with statistical quality control chart. In this study, the author presents the practical application of Chen and Chou’s model for the manufacturer. The manufacturer can apply these parameters in the design of a variable single rectifying inspection plan for the output product before shipping to the customer and the determination of the stock quantity for shipment to the customer in the newsvendor problem.

AbstractIn this paper, the author proposes a modified Chen’s model for determining the optimal process mean with sampling inspection and process capability. The maximization of expected total profit per unit for the lot is the objective function. The specified producer’s risk, consumer’s risk, and process capability index are the constraints. Assume that the normal quality characteristic of product has the one-sided lower specification limit and the rectifying sampling inspection plan is adopted for the rejected lot. The numerical example and sensitivity analysis are provided for illustration.

AbstractIn this work, the author proposes a optimal process mean setting for product with quality loss and process adjustment cost. Assume that the quality characteristic is exponentially distributed with parameter (l). The product quality loss is measured by adopting the asymmetric line quality loss function. The adjustment cost of process mean is assumed to be proportional to μ2and the adjustment cost of process variance is assumed to be proportional to 1/σ2. One can obtain the optimal process mean by minimizing the expected total cost of product including the product quality loss and process adjustment cost. Finally, the numerical example and sensitivity analysis of some parameters are provided for illustration.

ABSTRACTSampling 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.

ABSTRACTIn the present paper, the model in Abdul-Kader et al is modified by incorporating the capability index Cpmto 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.

AbstractIn this study, the author presents the economic selection of process mean with the quality loss and process adjustment cost. Assume that the quality characteristic is exponentially distributed with parameter (λ). The product quality loss is measured by adopting the asymmetric quadratic quality loss function. The adjustment cost of process mean is assumed to be proportional to μ2and the adjustment cost of process variance is assumed to be proportional to 1/σ2. The objective is to obtain the optimal process mean under the minimization of the expected total cost of product including the process adjustment cost and product quality loss. The numerical example and sensitivity analysis of some parameters are provided for illustration.

AbstractIn this study, the author considers the problem about economic process mean selection of product with the quality loss and process adjustment cost. Assume that the quality characteristic is normally distributed with process mean (μ) and variance (σ2). The product quality loss is measured by adopting the asymmetric quadratic and line quality loss function. The adjustment cost of process mean is assumed to be proportional to μ2and the adjustment cost of process variance is assumed to be proportional to 1/σ2. One can obtain the optimal process mean by minimizing the expected total cost of product including the product quality loss and process adjustment cost. Finally, the numerical example and sensitivity analysis of parameters are provided for illustration.

AbstractIn 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.

The control charts with exponentially weighted moving average (EWMA) had been shown to be effective for detecting small shifts in the mean of the process characteristic. When the data depart from normality or have the presence of outliers, the sample median might be used to provide a fairer representation of centrality of the data. In the present paper, the performances of the EWMA median control charts are evaluated under several distributions. The average run length (ARL) is applied to evaluate the performance of control charts, and the method for calculating ARL of the EWMA median chart is developed using the integral equation approach. Based on our study, the EWMA median chart with a small value of smoothing constant has a low false alarm rate. But as the shift of process mean is large, to maintain the detection ability of the chart, the value of smoothing constant should be increased. In addition, if the data follow a heavy-tailed distribution, it can be shown that the EWMA median chart is always more efficient than the EWMA average chart in detecting the shift of process mean.

In Chen and Liu's optimum profit model with a traditional production system, they did not consider the effect of product quality on the customer's demand order quantity, and also ignored the used cost of customers for product. In fact, the customer's demand quantity is always seriously related to product quality. Hence, in the present paper, we modify Chen and Liu's model to address the determination of the optimal process parameters by employing the idea of quality loss and single sampling rectifying inspection plan. Assuming that the quality characteristic of the product is normally distributed, Taguchi's symmetric quadratic quality loss function is applied in evaluating the product quality. Three decision variables, i.e., the mean of the process characteristic, the production run length of the product and the retailer's order quantity, are jointly determined in our modified model to maximize the expected total profit of society, which includes both the manufacturer and the retailer. A heuristic solution procedure is developed for this optimization problem, and a numerical example is provided for illustration. From the numerical results, it can be seen that both the sale price per unit and the intercept of the mean demand of the customer are two major (or significant) parameters in the model and should be more accurately estimated in practice. Finally, the quality investment policy is provided to compare its effect on the optimum profit model with quality improvement.

AbstractThe moving range control chart is usually established to monitor the variability of the process characteristic for situations where the individuals control chart is applied. In the design of a control chart, the average run length (ARL) of the chart is usually used as an important indicator for evaluating control chart performance. In the present paper, the out-of-control ARL of the moving range chart is investigated using computer simulation. Three types of data are generated for study: normal and independent data, non-normal data, and autocorrelated data, such that the effects of non-normality and autocorrelation on the detection ability of the chart can be investigated. From the simulation results, we find that positive skewness coefficient present in the underlying distribution would produce a shorter out-of-control ARL than the normal data. Also, if we are able to know that the data are positively highly autocorrelated, then “span two” should be used for the operation of the moving range chart to keep the chart's detection ability.

The control chart with variable sampling intervals (VSIs) scheme has been shown to give substantially faster detection of most process shifts than the conventional control charts. In 2002, Bai and Lee (2002) improved the operation of VSI

This paper provides a theoretical development and an empirical study on determining price, warranty length and production rate in the dynamic sales market, where word of mouth is important. For the theoretical development, we present a decision model of determining the optimal price, warranty length and production rate of a product such that the present value of the product profit may be maximised. The empirical study aims at choosing among the alternative model specifications and assessing the shapes of the sales rate function. The sales rate functions are estimated by non-linear regression, and then are tested by using automobile sales data in Taiwan as input while price, warranty length and production rate as outputs. The results of the empirical study are consistent with the corresponding theoretical predictions and consequently show the applicability of decision model.

A decision model is presented for producers to determine the optimal price, warranty length and production rate of a product in the dynamic sales market to maximize profits based on the pre-determined life cycle. The free renewal warranty policy is considered under which failed items are renewed before the end of the warranty length at no cost to consumers. The expected number of renewals based on the warranty length is derived for a Weibull lifetime distributed product. The cost function involves production cost, warranty cost and inventory cost. A solution approach using the maximum principle is described and is applied to two specific types ofmarkets. The first type of market considers a multiplicative effect of dynamic sale rates function on diffusion, and the second type of market considers market potential of dynamic sale rates function. Effects of the inventory volume, unit cost of the product and market effects on the optimal solution are investigated, and finally some conclusions are drawn based on the analysis.

AbstractRecently developed adaptive charts have been shown to give substantially faster detection of most process shifts than the fixed parameters charts. The “sampling at fixed times” idea can be implemented in the adaptive control charts, and from the practical viewpoint, the adaptive charts with sampling at fixed times are considered to be more convenient to administer than the traditional adaptive charts. The usual assumption for designing the 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 the present paper, the Burr distribution is employed to evaluate the adaptive charts with sampling at fixed times for non-normal populations. Base on the study, it is shown that the variable sampling interval with fixed times (VSIFT) chart and variable sampling rate with fixed times (VSRFT) chart are very sensitive to non-normality; however, the variable parameters with fixed times (VPFT) chart is relatively robust against non-normality. Under consideration of false alarm rate and the ability to detect mean shifts, the VPFT chart is a more appropriate tool for non-normal populations.

AbstractThe capability index is a simple and quantitative way to describe process capability. The index Cpmis an indicator, involving specifications, target value, process mean and standard deviation, for evaluating the capability of a process. When Cpmis applied to evaluate a process, estimating the confidence interval of Cpmis important for statistical inference on the process. Calculating the confidence interval for a process index usually needs the assumption about the underlying distribution. Bootstrapping is a nonparametric, but computer intensive, estimation method. Several types of bootstrap confidence intervals have been developed over the years. In the present paper we report the results of a simulation study on the behavior of the 95% bias-corrected and accelerated (BCa) percentile bootstrap confidence interval for estimating Cpmwhen the data are correlated and follow a Burr distribution, which is used to represent various population distributions. Effects of sample size, process capability, population distribution and correlation on the BCabootstrap interval of Cpmare simultaneously studied. A detailed discussion of the simulation results is presented and some conclusions are provided.

AbstractRecent studies have demonstrated the variable parameters (VP, i.e., variable sample sizes, sampling intervals, and/or action limit coefficients) charts have better performance than standard Shewhart(SS) control chart by statistical and economic criteria. 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 economic design for the adaptive chart is developed when the process data follow a skewed distribution. An example is presented to illustrate the solution procedure. Based on the study, it is shown that the VP chart is more effective than the other adaptive control charts. The sensitivity analysis on the input parameters and various population distributions are illustrated through a numerical example.

AbstractProcess capability indices have been used in manufacturing industries to provide a quantitative measure of process performance. In this paper, we proposed a multiple-stream yield index , and developed a procedure to provide practitioners an efficient tool for interval estimation and hypothesis testing on the yield index . Numerical examples are presented to illustrate how we may apply the procedure to actual data collected in the factory. The procedure is easy to use, and should be expected for in-plant applications.

AbstractTheoretical studies demonstrated that the variable sampling interval(VSI) charts give substantially faster detection of most process mean shifts than traditional charts. The standard VSI chart allows the long and short sampling intervals to be interchangeably used in the practical operation of the chart based on the information of the last sample mean. However, frequent switching between the long and short sampling intervals can be a complicating factor in the application of control charts. Some switching rules have been presented and studied in the literature to improve the situation of frequent switching. In the present paper, a switching rule based on moving average(MA) is proposed for the VSI chart. The advantages of moving average are not only to involve the recent several sample means, but also to consider the magnitude of deviation of these sample means from the centerline, which is not included by the switching rules in the literature. A computer simulation approach is applied to evaluate the performance of the proposed VSI chart with MA rule. From the simulation results, it can be seen that for a small process mean shift, the VSI chart with MA rule is always superior to the other types of VSI charts.

ABSTRACTThe present paper provides a theoretical development and empirical study on determining price, warranty length and production rate in the static sales market, where word of mouth is not important. For the theoretical development, we present the decision model of determining the optimal price, warranty length and production rate of a product such that the present value of the product profit may be maximized. The empirical study aims at choosing among the alternative model specifications and assessing the shapes of the sales rate function. The sales rate functions are estimated by nonlinear regression, and then are tested by using battery sales data as input while price, warranty length and production rate as outputs. Results of the empirical study are consistent with the corresponding theoretical predictions and consequently show the applicability of the decision model.

Process capability plots with single stream process have earlier been discussed by Deleryd and Vännman (1999); however multiple streams process often exists in practice. In the present paper, we introduce a new control chart, called the multiple streams process capability analysis(MSPCA) chart, using the multiple streamsyield index proposed by Wang et al. (2008). The MSPCA chart displays all the stream capability index values on one chart, and indicates the stream yield based on the Spkcontours. Using the chart, engineers can effectively monitor and control the performance of all streams process simultaneously. In addition, the MSPCA chart also provides a clear direction on the streams that should be targeted for quality/reliability improvement. We demonstrate the use of MSPCA chart by presenting a case study of an IC assembly process auto-molding system.

AbstractThe capability index is a simple and quantitative way to describe process capability. The index Cpkis an indicator, involving specifications, process mean and standard deviation, for evaluating the capability of a process. When Cpkis applied to evaluate a process, estimating the confidence interval of Cpkis important for statistical inference on the process. Calculating the confidence interval for a process index usually needs the assumption about the underlying distribution. Bootstrapping is a nonparametric, but computer intensive, estimation method. Several types of bootstrap confidence intervals have been developed over the years. In the present paper we report the results of a simulation study on the behavior of the 95% biased-corrected and accelerated (BCa) percentile bootstrap confidence interval for estimating Cpkwhen the data are correlated and follow a Burr distribution, which is used to represent various probability distributions. Effects of sample size, process capability, non-normality and correlation on the BCabootstrap interval of Cpkare simultaneously studied. A detailed discussion of the simulation results is presented and some conclusions are provided.

In this work we consider an optimization method to image file compression based on fuzzy logic. This optimization is realized thanks to wavelet transform in a pre-compression phase. Thanks to this approach in the pre-processing phase the wavelet transform is used to fix some relevant parameters like as the best compression box and other tolerance parameter (locally defined). With respect to the traditional approach by using wavelet this method is better from time consuming point of view. While with respect to a standard fuzzy logic approach the presented method has the advantage to perform compression with different ratio on different box optimized with respect to each subimage.

AbstractThe signal-to-noise ratio is an indicator, introduced by Taguchi, for evaluating the experimental data in robust design. Constructing 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 distribution. Bootstrapping is a nonparametric, but computer intensive, estimation method. In this paper 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 larger-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.

ABSTRACTPhillips and Cho [17] addressed a method for setting the optimum process mean when the quality characteristic is a beta distribution. They adopted the truncated quadratic loss function to measure the quality loss for a given truncated beta distribution. In this paper, we further propose the modified Phillips and Cho's [17] model with the linear quality loss for determining the optimum process mean. A numerical example is provided and the sensitivity analysis is conducted for illustration.

ABSTRACTKapur and Wang [2] have presented that the inspection in an on-line quality control system conducts as a short term approach to reduce variance of the items shipped to the customers. However, they have neglected to consider the inspection error in the model. In this article, we further propose the modified Kapur and Wang's [2] model with inspection error for determining the economic specification limits. Finally, the sensitivity analysis of the parameters is provided.

ABSTRACTWhen the [xbar] chart is applied to monitor a production process, three parameters should be determined: the sample size, the sampling interval between successive subgroups, and the control limits for the chart. In 1956, Duncan [5] presented the first cost model to determine the three parameters for the Xcharts, which is called the economic design of [xbar] charts. Alexander et al. [1] combined Duncan's cost model with the Taguchi loss function to present a loss model for determining the three parameters. Traditionally, when conducting the design of control charts, one usually assumes the measurements within a subgroup are independently and normally distributed. However, this assumption may not be tenable. In this paper, we develop the minimum-loss design of [xbar] charts for non-normally correlated data, where Alexander's loss model is used as the objective function. An example is provided to illustrate the solution procedure. A sensitivity analysis is performed to investigate the effects of non-normality and correlation coefficient on the optimal design of the chart.

In this paper we further extend Chen and Wang's study concerning a CSP-1 plan applied to the economic manufacturing quantity (EMQ) model with imperfect quality. Adopting the backorder assumption for shortages, the modified total inventory cost includes the setup cost, the holding cost, the backordering cost, the inspection cost, and the internal and external failure cost. By solving the modified EMQ model, we not only obtain the required level of product quality but also determine the minimum of the total inventory cost.

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.

Quality loss function has been used as a quality performance measure for products since the 1980s. In this paper, we extend the work of Teran et al. (1996) and incorporate the concept of time value of money into the bivariate loss function. First of all, the model of the present worth of the expected bivariate quality loss (PWBL) is established and its solution procedure is developed. Then, an example is given to illustrate how the model can be applied. Some sensitivity analyses are conducted to study the effects of planning horizon, customer's discount rate and coefficients of parameter drift on optimal means/biases at production time and the associated quality loss. From the results of analysis, the longer the planning horizon of product is, the more deviations from targets should be set for optimal biases at production time. Also, as the customer's discount rate increases, fewer deviations from the targets should be set for optimal biases at production time.

AbstractControl charting is an important technique in statistical process control. When a control chart is applied to monitor a process, three design parameters (i.e., sample size, sampling interval, and control limit) should be determined. In this article, we present a loss model of bivariate T2control charts by incorporating the bivariate loss function (which considers the customers' potential cost) into the cost model given in Montgomery and Klatt [17]. The purpose of this loss model is to determine the three design parameters such that the average total loss (ATL) per unit of product is minimized. Some sensitivity analyses are conducted to study the effects of the model parameters on the optimal solution of the loss model.

摘要自從1930年以來，統計方法在工業製程管制的應用就備受重視。而在這期間，管制圖扮演著極重要的角色。當處理一個計量值的品質特性時，一般都是用全距管制圖（Rchart)來監控製程的變異水準，並以平均數管制圖來監控製程的平均水準。而在這二種管制圖裏，通常均使用三倍標準差爲管制上下界限。傳統上，一般都假設測量值的母體分配爲常態。這個假設的真實性，則視測量值的偏態和峰態而定。由中央極限定理可知，只要抽樣數夠大，則樣本平均數的抽樣分配趨近常態分配；然而，即使母體呈常態分配，全距(range)的抽樣分配亦非對稱，且測量值往往也不服從常態分配。因此，在母體不爲常態的情況下，使用三倍標準差爲管制上下界限之全距管制圖，其偵錯之機率可能會變大。本文嘗試利用Burr所發展之Burr分配，在非常態資料下，選定全距管制圖的管制上下界限，並比較其與傳統常態假設下之全距管制圖之差異。

摘要自從1980年代以來，田口式直交表實驗計算法被廣泛應用於產品與製程設計以提昇產品之品質。本文應用田口式直交表實驗，配合統計分析與模擬方法，對批量再訂購點存貨模式的決策參數進行穩健設計，以求達到降低存货成本的目的。爲了提昇批量再訂購點摸式的功能，本文首先構建改良型的批量再訂購點模式（具有四個決策參數）；然而，一般存貨模式的數理解法不易求得這個新模式的參數，所以本文應用田口式實驗計畫法來決定改良型批量再訂購點摸式的決策參数。因爲田口式參數設計的過程已經考慮了影響存貨系統運作的雜訊效應，所以設計得到的結果具有穩健性，使系統能夠抵抗外界商場環境的衝擊，讓輸出更穩定（變異最小），從而降低存貨成本。文中舉一範例說明田口式參數設計之實驗及求解過程。在此範例中，對因子間的交互作用進行分析後，克服了確認實驗失敗（再現性不佳）所造成的困擾，使田口方法在確認實驗失敗後仍能找到理想的參數水準組合以降低存貨成本。

Since the 1930s statistical methods applied to industrial process control have received much attention. Many techniques of statistical process control, such as control chart and process capability analysis, require knowledge of process standard deviation. Therefore, estimation of the process standard deviation plays an important role in statistical process control. In this article, we reviewed four widely used estimators of standard deviation and derived the efficiency of each estimator. Then, these four estimators of standard deviation were compared based on their efficiencies. From the comparative studies, we suggest that if the sample size is greater than or equal to 6, the second, third and fourth estimators may be used to estimate process standard deviation. However, if the sample size is less than or equal to 5, then the third and fourth estimators should be preferred.

AbstractThe 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.