Estimating Non-Conformance Using the Modified Tolerance Region Method and the Target Distance Method

  • Authors

    • Shirley J. Tanjong
    • Raafat N. Ibrahim
    • Mali Abdollahian
    • Magdalene Andrew-Munot
    2018-08-02
    https://doi.org/10.14419/ijet.v7i3.18.16677
  • Multivariate quality control, Correlated characteristics, Tolerance region, Proportion of non-conformance, Mahalanobis Distance

  • In many cases, the quality of a manufactured product is determined by more than one characteristic and often, these quality characteristics are correlated. A number of methods for dealing with quality evaluation of multivariate processes have been proposed in the literature. However, some of these studies do not consider correlation among quality characteristics. In this paper, two new approaches for estimating the proportion of non-conformance for correlated multivariate quality characteristics with nominal specifications are proposed: (i) the modified tolerance region approach and (ii) the target distance approach. In the first approach, the p number of correlated variables are analysed based on the projected shadow of the p-dimensional hyper ellipsoid so that the ability to visualise the tolerance region and the process region for  is preserved. In the second approach, the correlated variables are combined and a new variable called the target distance is introduced. The proportion of non-conformance results estimated using both methods were used to compute the multivariate capability index and the total expected quality cost. This study also suggest modification to the NMCp index as proposed in Pan and Lee (2010) such that the process capability for  can be measured correctly. The application of both approaches is demonstrated using two examples and it is shown that both methods i.e. the modified tolerance region and the target distance methods are capable of estimating the capability of multivariate processes.

     

     

  • References

    1. [1] Montgomery DC (2005), Introduction to Statistical Quality Control. Wiley, New York.

      [2] Taguchi G (1984), Quality evaluation for Quality Assurance. American Supplier Institute, Romulus, MI.

      [3] Raiman L (1991), The Development and Implementation of Multivariate Cost of Poor Quality Loss Functions. PhD Thesis, Oklahoma State University.

      [4] Artiles-León N (1996), A pragmatic approach to multiple-response problems using loss functions. Quality Engineering 9(2), 213-220.

      [5] Ames AE, Mattucci N, MacDonald S, Szonyi G, Hawkins DM (1997), Quality loss functions for optimization across multiple response surfaces. Journal of Quality Technology 29(3), 339-346.

      [6] Pignatiello JJ (1993), Strategies for robust multiresponse quality engineering. IIE Transactions 25(3), 5-15.

      [7] Kapur KC, Cho BR (1996), Economic design of the specification region for multiple quality characteristics. IIE Transactions 28(3), 237-248.

      [8] Chan WM, Ibrahim RN (2004), Evaluating the quality level of a product with multiple quality characteristics. The International Journal of Advanced Manufacturing Technology 24(9-10), 738-742.

      [9] Tanjong S J, Ibrahim RN, Abdollahian M (2014), Determining quality risk for correlated bivariate normal characteristics. The International Journal of Advanced Manufacturing Technology 72(1-4), 495-508.

      [10] Wierda S (1993), A multivariate process capability index. Trans ASQC Qual Congress, 342-348.

      [11] Polansky AM (2001), A smooth nonparametric approach to multivariate process capability. Technometrics 43(2), 199-211.

      [12] Castagliola P, Castellanos JVG (2005), Capability Indices dedicated to the two quality characteristics case. Quality Technology & Quantitative Management 2(2), 201-220.

      [13] Jalili M, Bashiri M, Amiri A (2012), A new multivariate process capability index under both unilateral and bilateral quality characteristics. Quality and Reliability Engineering International 28(8), 925-941.

      [14] Wang F-K, Hubele NF (1999), Quality evaluation using geometric distance approach. International Journal of Reliability, Quality and Safety Engineering 06(02), 139-153.

      [15] Wang FK (2006), Quality evaluation of a manufactured product with multiple characteristics. Quality and Reliability Engineering International 22(2), 225-236.

      [16] Ahmad S, Abdollahian M, Zeephongsekul P, Abbasi B (2009), Multivariate nonnormal process capability analysis. The International Journal of Advanced Manufacturing Technology 44(7-8), 757-765.

      [17] Taam W, Subbaiah P, Liddy JW (1993), A note on multivariate capability indices. Journal of Applied Statistics 20(3), 339-351.

      [18] Shahriari H, Hubele NF, Lawrence FP (1995), A multivariate process capability vector. Proceeding of the 4th Industrial Engineering Research Conference.

      [19] Shahriari H, Abdollahzadeh M (2009), A new multivariate process capability vector. Quality Engineering 21(3), 290-299.

      [20] Pan JN, Chen SC (2012), A new approach for assessing the correlated risk. Industrial Management & Data Systems 112(9), 1348-1365.

      [21] Pan JN, Lee CY (2010), New capability indices for evaluating the performance of multivariate manufacturing processes. Quality and Reliability Engineering International 26(1), 3-15.

      [22] Pal S (1999), Performance evaluation of a bivariate normal process. Quality Engineering 11(3), 379-386.

      [23] Tano I, Vännman K (2012), Comparing confidence intervals for multivariate process capability indices. Quality and Reliability Engineering International 28(4), 481-495.

  • Downloads

  • How to Cite

    J. Tanjong, S., N. Ibrahim, R., Abdollahian, M., & Andrew-Munot, M. (2018). Estimating Non-Conformance Using the Modified Tolerance Region Method and the Target Distance Method. International Journal of Engineering & Technology, 7(3.18), 68-74. https://doi.org/10.14419/ijet.v7i3.18.16677