• 품질경영학회지
• /
• 제31권1호
• /
• pp.109-122
• /
• 2003

This paper presents a robust process capability index(PCI) based on the expected loss derived from the empirical distribution function(EDF). We propose the EDF expected loss in order to develop a PCI that does not depends on the underlying process distribution. The EDF expected loss depends only on the sample data, so the PCI based on it is robust and it does nor require complex calculations. The inverted normal loss function(INLF) is employed in order to overcome the drawback of the quadratic loss which may Increase unboundedly outside the specification limits. A comprehensive simulation study was performed under various process distributions, in order to compare the accuracy and the precision of the proposed PCI with those of the PCI based on the expected loss derived from the normal distribution. The proposed PCI turned out to be more accurate than the normal PCI in most cases, especially when the process distribution has high kurtosis or skewness. It is expected that the proposed PCI can be utilized In real processes where the true distribution family may not be known.

• 산업경영시스템학회지
• /
• 제20권41호
• /
• pp.213-220
• /
• 1997

Process capability Indices compare the actual performance of manufacturing process to the desired performance. The relationship between the capability index Cpm and the expected squared error loss provides an intuitive interpretation of Cpm. By putting the loss in relative terms a user needs only to specify the target and the distance from the target at which the product would have zero worth, or alternatively, the loss at the specification limits. Confidence limits for the expected relative loss are discussed, and numerical illustration is given.

• 산업경영시스템학회지
• /
• 제28권4호
• /
• pp.116-123
• /
• 2005

The traditional process capability indices Cp, Cpk, Cpm, $Cpm^+$ have been used to characterize process performance on the basis of univariate quality characteristics. Cp, Cpk consider the process variation, Cpm considers both the process variation and the process deviation from target and Cpm+ considers economic loss for the process deviation from target. In manufacturing industry, there is growing interest in quantitative measures of process variation under multivariate duality characteristics. The multivariate process capability index incorporates both the process variation and the process deviation from target or considers expected loss caused by the process deviation from target. This paper proposes multivariate capability index based on the expected loss derived from multivariate normal distribution.

• Asia Marketing Journal
• /
• 제18권3호
• /
• pp.47-63
• /
• 2016

Rational choice theory holds that the alternative with largest expected utility in the choice set should always be chosen. However, it is often observed that an alternative with the largest expected utility is not always chosen while the choice task itself being avoided. Such a choice phenomenon cannot be explained by the traditional expected utility maximization principle. The current study posits shows that such a phenomenon can be attributed to the gap between the expected perceived gain (or loss) and the expected perceived value. This study mathematically analyses the relationship between the expectation of an alternative's gains or losses over the reference point and its expected value, when the perceived gains or losses follow continuous probability distributions. The proposed expected value (EV) function can explain the effects of loss aversion and uncertainty on the evaluation of an alternative based on the prospect theory value function. The proposed function reveals why the expected gain of an alternative should exceed some positive threshold in order for the alternative to be chosen. The model also explains why none of the two equally or similarly attractive options is chosen when they are presented together, but either of them is chosen when presented alone. The EV function and EG-EV curve can extract and visualize the core tenets of the prospect theory more clearly than the value function itself.

• 품질경영학회지
• /
• 제31권4호
• /
• pp.164-175
• /
• 2003

This paper investigates bootstrap confidence intervals of the process capability index(PCI) based on the expected loss derived from the empirical distribution function(EDF). The PCI based on the expected loss is too complex to derive its confidence interval analytically, so the bootstrap method is a good alternative. We propose three types of the bootstrap confidence interval; the standard bootstrap(SB), the percentile bootstrap(PB), and the acceleration biased­corrected percentile bootstrap(ABC). We also perform a comprehensive simulation study under various process distributions, in order to compare the accuracy of the coverage probability of the bootstrap confidence intervals. In most cases, the coverage probabilities of the bootstrap confidence intervals from the EDF PCI turned out to be more accurate than those from the PCI based on the normal distribution. It is expected that the bootstrap confidence intervals from the EDF PCI can be utilized in real processes where the true distribution family may not be known.

• Earthquakes and Structures
• /
• 제10권2호
• /
• pp.429-450
• /
• 2016

An attempt has been made to incorporate the concept of collapse safety margin into the procedures proposed in the performance-based earthquake engineering (PBEE) framework for direct earthquake loss estimation, in which the collapse probability curve obtained from incremental dynamic analysis (IDA) is mathematically characterized with the S-type fitting model. The regressive collapse probability curve is then used to identify non-collapse cases and collapse cases. With the assumed lognormal probability distribution for non-collapse damage indexes, the expected direct earthquake loss ratio is calculated from the weighted average over several damage states for non-collapse cases. Collapse safety margin is shown to be strongly related with sustained damage endurance of structures. Such endurance exhibits a strong link with expected direct earthquake loss. The results from the case study on three concrete frames indicate that increase in cross section cannot always achieve a more desirable output of collapse safety margin and less direct earthquake loss. It is a more effective way to acquire wider collapse safety margin and less direct earthquake loss through proper enhancement of reinforcement in structural components. Interestingly, total expected direct earthquake loss ratio seems to be insensitive a change in cross section. It has demonstrated a consistent correlation with collapse safety margin. The results also indicates that, if direct economic loss is seriously concerned, it is of much significance to reduce the probability of occurrence of moderate and even severe damage, as well as the probability of structural collapse.

• 대한전기학회논문지:전력기술부문A
• /
• 제50권7호
• /
• pp.333-339
• /
• 2001

The transmission networks are not perfect conductors and a percentage of the power generated is therefore lost before it reaches the loads. This network loss effects to the cost of suppling power to consumers, and must be considered if the most efficient dispatch and location of generators and loads is to be achieved. In this paper, we propose an approximate calculation of marginal loss factors to analyze characteristics of transmission loss of KEPCO power system. These static marginal loss factors are approximately calculated based on the KEPCO's expected summer peak load data of year 2000.

• 산업경영시스템학회지
• /
• 제36권4호
• /
• pp.109-115
• /
• 2013

Process Capability Index (PCI) is useful Statistical Process Control (SPC) tool that is measure of process diagnostic and assessment tools widely use in industrial field. It has advantage of easy to calculate and easy to use in the field. $C_p$ and $C_{pk}$ are traditional PCIs. These are only considers of process variation. These are not given information about the characteristic value does not match the target value of the process. Studies of this process capability index by many scholars actively for supplement of its disadvantage. These studies to evaluate the capability of situation of various field has presented a new process capability index. $C_{pm}$ is considers both the process variation and the process deviation from target value. And $C_{pm}{^+}$ is considers economic loss for the process deviation from target value. In this paper development of new process capability index that is Taguchi's quadratic loss function by applying the expected loss. And check the correlation between existing traditional process capability index ($C_{pk}$) and new one. Finally, we propose the criteria for classification about developed process capability index.

• 한국지구과학회지
• /
• 제31권5호
• /
• pp.437-447
• /
• 2010

Spatial estimation of environmental variables has been regarded as an important preliminary procedure for decision-making. A minimum variance criterion, which has often been adopted in traditional kriging algorithms, does not always guarantee the optimal estimates for subsequent decision-making processes. In this paper, a geostatistical framework is illustrated that consists of uncertainty modeling via stochastic simulation and risk modeling based on loss functions for the selection of optimal estimates. Loss functions that quantify the impact of choosing any estimate different from the unknown true value are linked to geostatistical simulation. A hybrid loss function is especially presented to account for the different impact of over- and underestimation of different land-use types. The loss function-specific estimates that minimize the expected loss are chosen as optimal estimates. The applicability of the geostatistical framework is demonstrated and discussed through a case study of copper mapping.

• Communications for Statistical Applications and Methods
• /
• 제17권4호
• /
• pp.575-589
• /
• 2010

Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.