ENG  Vol.9 No.5 , May 2017
Analysis of the Effect of Subgroup Size on the X-Bar Control Chart Using Forensic Science Laboratory Sample Influx Data
Abstract: This paper analyzes the effect of subgroup size on the x-bar chart characteristics using sample influx (SIF) into forensic science laboratory (FSL). The characteristics studied include changes in out-or-control points (OCP), upper control limit UCLx, and zonal demarcations. Multi-rules were used to identify the number of out-of-control-points, Nocp as violations using five control chart rules applied separately. A sensitivity analysis on the Nocp was applied for subgroup size, k, and number of sigma above the mean value to determine the upper control limit, UCLx. A computer code was implemented using a FORTRAN code to create x-bar control-charts and capture OCP and other control-chart characteristics with increasing k from 2 to 25. For each value of k, a complete series of average values, Q(p), of specific length, Nsg, was created from which statistical analysis was conducted and compared to the original SIF data, S(t). The variation of number of out-of-control points or violations, Nocp, for different control-charts rules with increasing k was determined to follow a decaying exponential function, Nocp = Aeα, for which, the goodness of fit was established, and the R2 value approached unity for Rule #4 and #5 only. The goodness of fit was established to be the new criteria for rational subgroup-size range, for Rules #5 and #4 only, which involve a count of 6 consecutive points decreasing and 8 consecutive points above the selected control limit (σ/3 above the grand mean), respectively. Using this criterion, the rational subgroup range was established to be 4 ≤ k ≤ 20 for the two x-bar control chart rules.
Cite this paper: Manyele, S. (2017) Analysis of the Effect of Subgroup Size on the X-Bar Control Chart Using Forensic Science Laboratory Sample Influx Data. Engineering, 9, 434-456. doi: 10.4236/eng.2017.95026.

[1]   Montgomery, D.C. (1980) The Economic Design of Control Charts: A Review and Literature Survey. Journal of Quality Technology, 12, 75-87.

[2]   Wang, R.-C. and Chen, C.-H. (1995) Economic Statistical np-Control Chart Designs Based on Fuzzy Optimization. International Journal of Quality & Reliability Management, 12, 82-92.

[3]   Shaban, A., Shalaby, M. Abdelhafiez, E. and Youssef, A.S. (2010) Automated Identification of Basic Control Charts Patterns Using Neural Networks. Journal of Software Engineering and Applications, 3, 208-220.

[4]   Seliaman1, M.E. and Duffuaa, S.O. (2012) The Principle of Mathematical Induction Applied to the Generalized Model for the Economic Design of X-Control Charts. Open Journal of Applied Sciences, 2, 236-240.

[5]   Westgard, J.O., Barry P.L. and Hunt, M.R. (1981) A Multi-Rule Shewhart Chart for Quality Control in Clinical Chemistry. Clinical Chemistry, 27, 493-501.

[6]   Swift, J. A. and Mize, J.H. (1995) Out-of-Control Pattern Recognition and Analysis for Quality Control Charts Using Lisp-Based Systems. Computers and Industrial Engineering, 28, 81-91.

[7]   Guh, R.-S., Zorriassatine, F. Tannock, J.D.T. and O’Brien, C. (1999) On-Line Control Chart Pattern Detection and Discrimination: A Neural Network Approach. Artificial Intelligence in Engineering, 13, 413-425.

[8]   Chen, Z., Lu, S. and Lam, S. (2007) A Hybrid System for SPC Concurrent Pattern Recognition. Advanced Engineering Informatics, 21, 303-310.

[9]   Rahim, M.A. and Banerjee, P.K. (1993) A Generalized Model for the Economic Design of X-Control Charts for Production Systems with Increasing Failure Rate and Early Replacement. Naval Research Logistics, 40, 787-809.<787::AID-NAV3220400605>3.0.CO;2-4

[10]   Smith, A.E. (1994) X-Bar and R Control Chart Interpretation Using Neural Computing. International Journal of Production Research, 32, 309-320.

[11]   Manyele, S. and Rioba, N. (2016) Monitoring Saccharification Process in the Brewery Industry Using Quality Control Charts. Engineering, 8, 481-498.

[12]   Montgomery, D.C. (1996) Introduction to Statistical Quality Control. 3rd Edition, Wiley, New York.

[13]   Holmes, D.S. and Mergen, A.E. (2007) Proper Subgroup Size for Statistical Process Control. Quality and Reliability Engineering International, 4, 339-345.

[14]   Nelson, L.S. (1984) The Shewhart Control Chart: Tests for Special Causes. Journal of Quality Technology, 16, 237-239.

[15]   Tabim, P.M. and Ferreira, M.L.R. (2015) Productivity Monitoring of Land Pipelines Welding via Control Chart Using the Monte Carlo Simulation. Journal of Software Engineering and Applications, 8, 539-548.

[16]   Razmy, A.M. (2016) Effect of Sample Size on the Control Limits of Exponentially Weighted Moving Average Distance Square Scheme. Open Access Library Journal, 3, 1-7.

[17]   Ahmed, E., Elkettun, Y. and Kasem, A. (2016) Application of Statistical Methods of Time-Series for Estimating and Forecasting the Wheat Series in Yemen (Production and Import). American Journal of Applied Mathematics, 4, 124-131.