Economic Design of Short-Run CSP-1 Plan Under Linear Inspection Cost

Chung-Ho Chen; Chao-Yu  Chou

doi:10.6180/jase.2006.9.1.02

Economic Design of Short-Run CSP-1 Plan Under Linear Inspection Cost

Computer Science and Information Engineering

Chung-Ho Chen This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Chao-Yu Chou²

¹Department of Industrial Management, Southern Taiwan University of Technology, Yungkang, Taiwan 710, R.O.C.
²Department of Industrial Engineering and Management, National Yunlin University of Science and Technology, Touliu, Taiwan 640, R.O.C.

Received: September 23, 2004
Accepted: December 2, 2004
Publication Date: March 1, 2006

Download Citation: ||https://doi.org/10.6180/jase.2006.9.1.02

ABSTRACT

In general, the unit cost of inspection is assumed to be constant. However, it can be argued that the unit cost of inspection is seldom constant. In 1943, Dodge proposed the type I continuous sampling plan (CSP-1 plan) and indicated how to calculate its average outgoing quality (AOQ) and average fraction inspected (AFI). In this paper, we further propose the problem concerning the economic design of short-run CSP-1 plan under linear inspection cost. A solution procedure is developed to find the unique combination (i^*, f^*) that will meet the average outgoing quality limit (AOQL) requirement, while also minimizing the total expected cost per unit produced for the short-run CSP-1 plan when the process average p (> AOQL) and production run length R are known. A numerical example is illustrated and the sensitivity analysis of parameters is provided.

Keywords: Type I Continuous Sampling Plan (CSP-1 Plan), Average Fraction Inspected (AFI), Average Outgoing Quality (AOQ), Average Outgoing Quality Limit (AOQL), Short-Run Production

REFERENCES

[1] Dodge, H. F., “A Sampling Inspection Plan for Continuous Production,” Annals of Mathematical and Statistics, Vol. 14, pp. 264279 (1943).
[2] Blackwell, M. T. R., “The Effect of Short Production Runs on CSP-1,” Technometrics, Vol. 19, pp. 259263 (1977).
[3] Yang, G. L., “A Renewal-process Approach to Continuous Sampling Plans,” Technometrics, Vol. 25, pp. 5967 (1983).
[4] McShane, L. M. and Turnbull, B. W., “Probability Limits on Outgoing Quality for Continuous Sampling Plans,” Technometrics, Vol. 33, pp. 393404 (1991).
[5] McShane, L. M. and Turnbull, B. W., “New Performance Measures for Continuous Sampling Plans Applied to Finite Production Runs,” Journal of Quality Technology, Vol. 24, pp. 153161 (1992).
[6] Liu, M. C. and Aldag L., “Computerized Continuous Sampling Plans with Finite Production,”Computers and Industrial Engineering, Vol. 25, pp. 445448 (1993).
[7] Wang, R. C. and Chen, C. H., “Minimum Average Fraction Inspected for Short-run CSP-1 Plan,” Journal of Applied Statistics, Vol. 25, pp. 733738 (1998).
[8] Liu, M.-C., “Multiple Criteria Optimization of an Economically-based Continuous Sampling Plan,” Unpublished Ph.D. Dissertation, Arizona State University, U.S.A., p. 45 (1987).
[9] Chen, C.-H. and Chou, C.-Y. “Economic Design of Continuous Sampling Plan Under Linear Inspection Cost,” Journal of Applied Statistics, Vol. 29, pp. 1003 1009 (2002).
[10] Cassady, C. R., Maillart, L. M., Rehmert, I. J., and Nachlas, J. A., “Demonstrating Deming’s kp Rule Using an Economic Model of the CSP-1,” Quality Engineering, Vol. 12, pp. 327334 (2000).