Supplier Selection for Multiple Linear Proﬁles with One-Sided Speciﬁcations Fu-Kwun Wang * † When the quality of a process is represented by a relationship between one response variable and one or more independent variables called a multiple linear proﬁle with in statistical control, the process capability analysis is widely used to measure the capability of the process to manufactured item within the required tolerance. In this paper, we propose the difference test statistic to compare two processes for multiple linear proﬁles with one-sided speciﬁcations. The number of proﬁles required for a designated selection power and conﬁdence level is also provided. The performance of the proposed method is assessed using simulation study. The results provide useful information to practitioners. A real data from the logistic service shows that our method performs well in the application. Copyright © 2014 John Wiley & Sons, Ltd. Keywords: process capability analysis; multiple linear proﬁles; one-sided speciﬁcations 1. Introduction S upplier selection has received considerable attention in many industries. Many aspects, including quality, price, delivery, service, technical capabilities, and ﬁnancial strength, are considered in choosing a supplier. In particular, quality that can be measured as conformance to speciﬁcation is the most important criteria. Process capability indices have been used widely as a benchmark for evaluating process conformance to speciﬁcation. When there are two suppliers with quality of a process is characterized by linear proﬁles with one-sided speciﬁcations, the decision maker faces the problem of determining whether two suppliers are equally capable of not how large is the expected magnitude of difference. Proﬁle monitoring is the use of control charts for cases in which the quality of a process can be characterized by a functional relationship between a response variable and one or more independent variables. 1 Woodall 1 provided a review of research topics on monitoring linear proﬁles. A comprehensive review of proﬁle monitoring can be found in Noorossana et al. 2 Assuring the process capability in linear proﬁles to meet the quality requirement is a very important task. Hosseinifard and Abbasi 3 employed the proportion of non-conformance concept to estimate the process capability for linear proﬁles with one-sided speciﬁcations. Wang 4 proposed two new indices C puA and C plA to evaluate the process yield for simple linear proﬁles with one-sided speciﬁcations. For the study of a process with one-sided speciﬁcations, Pearn et al. 5 presented the ratio test statistic to tackle the supplier selection problem with two one-sided processes. Pearn et al. 6 developed a method based on the difference test statistic, which is indeed more powerful than the method proposed by Pearn et al. 5 Hsu et al. 7 applied the Bootstrap method for calculating the lower conﬁdence bounds of the index C T pu and determined the sample size for a speciﬁed estimation accuracy. Pearn et al. 8 derived the approximate distribution of the natural estimator of the index C T pu . Pearn et al. 9 implemented the index C T pu into the product acceptance determination. Yum and Kim 10 provided some reviews for process capability indices . Recent research related to supplier selection problem for a process with one-sided speciﬁcations can be found in the literature. 11–16 However, research for selecting the better process for multiple linear proﬁles with one-sided speciﬁcations is still scarce. The rest of the paper is organized as follows. In Section 2, we review the capability indices for multiple linear proﬁles with one- sided speciﬁcations and provide the conﬁdence intervals of the indices based on the asymptotic distribution of the indices. Additionally, we derive a more reliable lower conﬁdence bound based on a simple form in Section 4. Section 5 describes the difference test statistic for two-supplier selection. Some examples are used to illustrate the application of our proposed approach in Section 5. Finally, we offer a conclusion and suggestions for future studies. 2. Process yield indices for multiple linear proﬁles with one-sided speciﬁcations A multiple linear proﬁle is usually deﬁned by a linear regression model. When the process is in statistical control, the relationship between the response variable and the two independent variables is modeled as Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, Taiwan *Correspondence to: Fu-Kwun Wang, Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, 106, Taiwan. † E-mail: fukwun@mail.ntust.edu.tw Copyright © 2014 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2016, 32 257–268. Research Article (wileyonlinelibrary.com) DOI: 10.1002/qre.1746 Published online 27 October 2014 in Wiley Online Library 257