Abstract

In many industrial and non-industrial processes, the quality of a product or a process are described by a functional relationship between a response variable and one or more independent variables, known as profile. On the other hand, the process capability indices provide numerical measures of the process ability. Few researches have been done to evaluate the process capability of profiles; especially for linear profiles. In the present article, we calculate the $S_{\text{pmk}}$ index to measure the process capability for gamma regression profiles and we also construct an approximate confidence interval using the bootstrap method. The performance of the proposed method is assessed through a simulation study. Moreover, we show that the $S_{\text{pmk}}$ index is very robust when the true distribution of data is a lognormal or a Weibull. Finally, the applicability of the proposed index is illustrated using two real examples.

摘要

在许多工业和非工业过程中，产品或过程的质量由响应变量和一个或多个自变量之间的函数关系（称为概况）来描述。另一方面，过程能力指数提供了过程能力的数值度量。很少有研究评估型材的加工能力；特别是对于线性轮廓。在本文中，我们计算${\mathrm{小号}}_{\text{pmk}}$指数来衡量伽玛回归曲线的过程能力，我们还使用引导方法构建了一个近似置信区间。通过模拟研究评估了所提出方法的性能。此外，我们证明了${\mathrm{小号}}_{\text{pmk}}$当数据的真实分布是对数正态或 Weibull 时，索引非常稳健。最后，通过两个实例说明了所提指标的适用性。