Journal of Quality Engineering and Management

Stattistical Design of X ̅ Control Chart With Variable Sample Size Under Weibull Shock Model With Non-Uniform Sampling Intervals

Document Type : Original Article

Authors

Bahman Fasihi 1
Reza pourtaheri 2

1 Department of Statistics,Allameh Tabataba'i University, Tehran, Iran.

2 Department of Statistics, Allameh Tabataba, University, Tehran,Iran

https://doi.org/10.48313/jqem.2021.148852
Abstract
This paper for the first time in the statistical design of adaptive control charts, deals with the statistical design of univariate control chart X ̅ under the Weibull shock model. practically, the use of shock models with more flexible risk rate functions in the statistical design of adaptive control charts is closer to reality. This study shows that diagram X ̅-VRS under Weibull shock model with non-uniform sampling intervals and variable sample size, compared to diagram X ̅ under Weibull shock model with non-uniform sampling intervals and fixed sample size (FRS), Detecting average changes is faster and performs better.
In this model, with increasing changes in the mean, the rate of detection of changes in the mean increases and the value of h_1 increases and the ANF decreases. Also relatively large changes (𝛅≥2), lead to a relatively small sample size (n_2≤ 10) and smaller changes (2 ≤ 𝛅 <0.25) lead to a larger optimal sample size (〖"11≤n" 〗_2 "≤14" ).

Keywords

Statistical design
Control chart X ̅
Non-uniform sampling distance
Weibull shock model
1] Burr, I.W. (1969), Control charts for measurements with varying sample sizes. Journal of Quality Technology, 1, 163-167.
[2] Prabhu, S.S., Runger, G.C. and Keats, J.B. (1993), chart with adaptive sample sizes. International Journal of Production Research, 31, 2895-2909.
[3] Costa, A.F.B. (1997), charts with variable sampling size and sampling intervals. Journal of Quality Technology, 29:2, 197-204.
 DOI: 10.1080/00224065.1997.11979750.
[4] Zimmer, L.S., Montgomery, D.C., and Runger, G.C. (1998), Evaluation of a Three-state adaptive sample size control chart. International Journal of Production Research, 36 733-743.
[5] Reynolds Jr, M.R. and Arnold, J.C., (1989). Optimal one-side Shewhart control chart with variable sampling intervals. Sequential Analysis 8, 51–77.
[6] Aparisi, F. (1996), Hotelling's  control chart with adaptive sample sizes, International Journal of Production Research, 34, 2853-2862.
[7] Aparisi, F. and Haro, C.L. (2003), A comparison of control charts with variable sampling schemes as opposed to MEWMA chart. International Journal of Production Research 41, 2169–2182.
[8] Ghanaatiyan, R., Amiri, A., Sogandi, F. (2017). Multi-Objective Economic-Statistical Design of VSSI-MEWMA-DWL Control Chart with Multiple Assignable Causes. Journal of Industrial and Systems Engineering, 10(special issue on Quality Control and Reliability), 34-58.
 [9] بامنی‌مقدم، محمد و رفیعی، سعیدرضا. (1396). طراحی آماری- اقتصادی نمودار کنترلی  برای داده‌های همبسته تحت مدل‌های شوک نمایی تعمیم یافته و وایبول، نشریه علمی پژوهشی مهندسی و مدیریت کیفیت.
[10] naderi, M., Bameni Moghadam, M., Seif, A. (2020). Minimum Loss Design of X Control Chart for Correlated Data Under Weibull In-Control Times with Multiple Assignable Causes. Journal of Computational Statistics and Modeling, 1(1), 99-127.
 [11] Banerjee, P. K., & Rahim, M. A. (1988). Economic design of–control charts under weibull shock models. Technometrics, 30(4), 407-414.
Journal of Quality Engineering and Management
Volume 11, Issue 3
Autumn 2021
Pages 221-241

Home

Editorial Board

Indexing and Abstracting

Guide for Authors

Submit Manuscript

Reviewers

Contact Us