Sample Size Determination for the Audit and Validation of an Industrial Process Control Outcome


Authors : David Umolo; Tega Emmanuel Akponoka; Idris Babatunde Adebisi

Volume/Issue : Volume 10 - 2025, Issue 5 - May


Google Scholar : https://tinyurl.com/4nz6az2a

DOI : https://doi.org/10.38124/ijisrt/25may293

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.


Abstract : This study is aimed at determining sample sizes at subgroup level and number of groups utilized in monitoring, evaluating and validating the reliability of an industrial process control output using a set of simulated data underlying the variable and attribute charts scenarios. The methodology adopts sample size estimation procedure using X̅ for the case of a variable control charts and P, NP,& C charts for the case of attribute control charts based on available information provided for the validation of reported quality control results. Findings shows that the possibility of process validation using of diverse provided specific information. A sample subgroup sample size of 3 and sample group number of 20 were estimated provided UCL of 17.5 corresponding to total mean of 227.2 and grand total of 681.6 for an x̅ control chart. Considering the attribute control chart for the proportion defective, a UCL of 0.801 yields an estimated subgroup sample size of 202 attributed to 0.773 overall proportion of defectives. A UCL of 11.08 resulted to an estimated sample size of 7 given a reported overall proportion of defective with attention drawn towards number of defectives all complemented by an estimation plot. However, the result above proves the estimation procedure as best suited in the validation of the reliability industrial process or reports to ascertain inclusively the effectiveness and accuracy of the internal or assigned inspection team.

Keywords : Quality Control, Industrial Process, Validation, Subgroup, Sample Number.

References :

  1. Champ, C. M. and Chou, S. P. (2003). Comparison of Standard and Individual Limits Phase I Shewhart, X, R and S Charts. Quality and Reliability Engineering International, Vol. 19(1), pp. 161-170.
  2. Cochran, W. G. (1977). Sampling Techniques (3rd ed.). John Wiley & Sons.
  3. Del Castillo, E. (2002). Statistical Process Adjustment for Quality Control. John Wiley & Sons, New York.
  4. FDA (2011). Guidance for Industry: Process Validation: General Principles and Practices. U.S. Food and Drug Administration.
  5. ISO (2015). International Standard Organization. Report.
  6. Lind, D. A., Marchal, W. G. and Wathen, S. A. (2013). Statistical Techniques in Business and Economies (16th ed.). McGraw-Hill Education.
  7. Montgomery, C. D. (2009). Introduction to Statistical Quality Control (6th ed.), John Wiley & Sons, Inc.
  8. Smith, J. R. (2016). Application of Stratified Sampling in Industrial Process Audits. Industrial Management Journal, 34(2), 112-119.
  9. Thompson, S. K. (2012). Sampling (3rd ed.). John Wiley & Sons.

This study is aimed at determining sample sizes at subgroup level and number of groups utilized in monitoring, evaluating and validating the reliability of an industrial process control output using a set of simulated data underlying the variable and attribute charts scenarios. The methodology adopts sample size estimation procedure using X̅ for the case of a variable control charts and P, NP,& C charts for the case of attribute control charts based on available information provided for the validation of reported quality control results. Findings shows that the possibility of process validation using of diverse provided specific information. A sample subgroup sample size of 3 and sample group number of 20 were estimated provided UCL of 17.5 corresponding to total mean of 227.2 and grand total of 681.6 for an x̅ control chart. Considering the attribute control chart for the proportion defective, a UCL of 0.801 yields an estimated subgroup sample size of 202 attributed to 0.773 overall proportion of defectives. A UCL of 11.08 resulted to an estimated sample size of 7 given a reported overall proportion of defective with attention drawn towards number of defectives all complemented by an estimation plot. However, the result above proves the estimation procedure as best suited in the validation of the reliability industrial process or reports to ascertain inclusively the effectiveness and accuracy of the internal or assigned inspection team.

Keywords : Quality Control, Industrial Process, Validation, Subgroup, Sample Number.

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