Journal of Quality Engineering and Management

Combining Taguchi loss function and economic design of X ̅ control diagrams in the presence of normal and abnormal data

Document Type : Original Article

Authors

Mohammad Bamenimoghadam 1
Mojtaba Aghajanpour Pasha 2
Shabnam Fani 2

1 Allameh Tabatabaei University

2 Statistics, Mathematics and Statistics, Allameh Tabatabai University, Tehran, Iran

Abstract
Control chart is one of the basic tools of statistical quality control and monitoring during production of production and service processes. The cost of quality in the classical approach to control chart design depends on whether the quality characteristic is inside or outside the control range. Since the integration of the loss function approach into in-production monitoring activities such as control charts, which is derived from Taguchi's concept of social quality loss, in which the cost of quality depends on the amount of deviation of the quality characteristic from the target value, is a more comprehensive evaluation process. It is better guided in the management strategy. This paper combines the Taguchi loss function and the economic design of the X نمودار control chart. In addition, since the output data of the process may not follow the normal distribution or the assumptions of the central limit theorem may not be true of it, it is necessary to study the integrated model in these situations, in addition to the normal distribution mode. In this regard, the economic design parameters of the integrated model will be compared in the presence of normal and abnormal data, in which, due to the extent of incremental failure rate in production systems, from non-uniform sampling design for sample inspection and Weibull shock model for failure mechanism. The process is used. 

Keywords

Generalized Economic Design
Taguchi’s Loss Function
Quality Characteristic Distribution
Process Failure Mechanism
Integrated Hazard over Sampling Intervals
[1] Duncan, J. (1591). The Economic Design of ̅– Charts Used to Maintain Current Control of a Process. J. American Statistical Association, 91, 222-242.
[2] Lorenzen, T. J. & Vance, L. C. (1521). The Economic Design of Control Charts: A Unified Approach. Technometrics, 22, 3-11.
[3] Ross, S. M. (1591). Applied Probability Models with Optimization Applications. San Francisco: Holden-Day.
[4] Banerjee, P. K. & Rahim, M. A. (1522). Economic Design of ̅-Control Charts Under Weibull Shock Models. Technometrics, 31, 419-414.
[5] Rahim, M. A. & Banerjee, P. K. (1553). A Generalized Model for Economic Design of ̅– Control Charts for Production Systems with Increasing Failure Rate and Early Replacement. Naval Research Logistics, 41, 929-215.
[6] Gibra, I. (1599). Recent developments in control charts techniques. Journal of Quality Technology, 9, 123-152.
[7] Montgomery, D. (1521). The economic design of control charts: A review and literature survey. Journal of Quality Technology, 12, 99-29.
[8] Vance, L. (1523). A bibliography of statistical quality control chart techniques. Journal of Quality Technology, 19, 95-12.
[9] Ho, C. & Case, K. E. (1554). Economic design of control charts, a literature review for 1521-1551. Journal of Quality Technology, 21, 35-93.
[10] Taguchi, G. (1521). Introduction to Quality Engineering. Designing Quality into Products and Processes. Asian Productivity Organization.
[11] Taguchi, G. & Wu, Y. (1595). Introduction to Off-Line Quality Control. Tokyo: Central Japan Quality Control Association.
[12] Taguchi, G., Elsayed, E. A. & Hsiang, T. (1525). Quality Engineering in Production Systems. New York: McGraw-Hill.
[13] Alexander, S. M., Dillman, M. A., Usher, J. S. & Damodaran, B. (1559). Economic design of control charts using the Taguchi loss function.Computers and Industrial Engineering, 22, 191- 195.
[14] Duffuaa, S. O. & Ben-Daya, M. (2113). Integration of Taguchi’s loss function approach in the economic design of x –chart. International Journal of Quality & Reliability Management, 21(9), 119-115.
[15] Burr, IW. (1542). Cumulative frequency functions. Annal Math Stat, 13, 219–232.
[16] Johnson, N. L. (1545). Systems of frequency curves generated by methods of translation. Biometrika, 31, 145-191.
[17] Chen, H. & Cheng, Y. (2119). Non-normality effects on the economic-statistical design of ̅ charts with Weibull in-control time. European Journal of Operational Research, 191, 521-552.
[18] Chen, F. L. & Yeh, C. H. (2115). Economic statistical design of non-uniform sampling scheme Xbar control charts under non-normality and Gamma shock using genetic algorithm. Expert Systems with Applications, 31, 5422-5459.
[19] Chen, F. L. & Yeh, C. H. (2111). Economic statistical design for x-bar control charts under nonnormal distributed data with Weibull in-control time. Journal of the Operational Research Society, 12, 991-995.
[20] Rahim, M. A. (1553). Economic design of ̅ control charts assuming Weibull distribution incontrol times. Journal of Quality Technology, 29(4), 251-319.
Journal of Quality Engineering and Management
Volume 6, Issue 1
Spring 2016
Pages 1-8

Home

Editorial Board

Indexing and Abstracting

Guide for Authors

Submit Manuscript

Reviewers

Contact Us