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首页> 外文期刊>Journal of applied statistics >Measuring Process Performance Based on Expected Loss with Asymmetric Tolerances
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Measuring Process Performance Based on Expected Loss with Asymmetric Tolerances

机译：基于具有不对称公差的预期损失来测量过程性能

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摘要

By approaching capability from the point of view of process loss similar to C_(pm), Johnson (1992) provided the expected relative loss L_e to consider the proximity of the target value. 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 to quantify the process loss. Tsui (1997) expressed the index L_e as L_e = L_(ot) + L_(pe), which provides an uncontaminated separation between information concerning the process relative off-target loss (L_(ot)) and the process relative inconsistency loss (L_(pe)). Unfortunately, the index L_e inconsistently measures process capability in many cases, particularly for processes with asymmetric tolerances, and thus reflects process potential and performance inaccurately. In this paper, we consider a generalization, which we refer to as L"_e, to deal with processes with asymmetric tolerances. The generalization is shown to be superior to the original index L_e. In the cases of symmetric tolerances, the new generalization of process loss indices L"_e, L"_(ot) and L"_(pe) reduces to the original index L_e, L_(ot), and L_(pe), respectively. We investigate the statistical properties of a natural estimator of L"_e L"_(ot) and L"_(pe) when the underlying process is normally distributed. We obtained the rth moment, expected value, and the variance of the natural estimator L"_e, L"_(ot), and L"_(pe). We also analyzed the bias and the mean squared error in each case. The new generalization L"_e measures process loss more accurately than the original index L_e.
机译：通过从类似于C_（pm）的过程损失的角度来接近能力，Johnson（1992）提供了预期的相对损失L_e来考虑目标值的接近性。用相对的术语来表示损耗，用户只需要指定目标和距目标的距离，产品在该目标处的价值为零即可量化过程损耗。 Tsui（1997）将索引L_e表示为L_e = L_（ot）+ L_（pe），这提供了有关过程相对偏离目标损失（L_（ot））和过程相对不一致损失（L_ （pe））。不幸的是，索引L_e在许多情况下（尤其是对于具有非对称公差的过程）不一致地测量过程能力，因此无法准确反映过程潜力和性能。在本文中，我们考虑一种称为L“ _e的泛化来处理具有非对称公差的过程。该泛化表现出优于原始索引L_e。在对称公差的情况下，过程损耗指数L” _e，L” _（ot）和L” _（pe）分别减小为原始指数L_e，L_（ot）和L_（pe）。当基础过程为正态分布时，我们研究L“ _e L” _（ot）和L“ _（pe）的自然估计量的统计性质。我们获得了自然估计量的第一个矩，期望值和方差L” _e，L” _（ot）和L” _（pe）。我们还分析了每种情况下的偏差和均方误差。新的概括L“ _e比原始索引L_e更准确地测量过程损失。

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