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Licensed Unlicensed Requires Authentication Published by De Gruyter October 17, 2017

Validation of the Six Sigma Z-score for the quality assessment of clinical laboratory timeliness

  • Cristiano Ialongo EMAIL logo and Sergio Bernardini



The International Federation of Clinical Chemistry and Laboratory Medicine has introduced in recent times the turnaround time (TAT) as mandatory quality indicator for the postanalytical phase. Classic TAT indicators, namely, average, median, 90th percentile and proportion of acceptable test (PAT), are in use since almost 40 years and to date represent the mainstay for gauging the laboratory timeliness. In this study, we investigated the performance of the Six Sigma Z-score, which was previously introduced as a device for the quantitative assessment of timeliness.


A numerical simulation was obtained modeling the actual TAT data set using the log-logistic probability density function. Five thousand replicates for each size of the artificial TAT random sample (n=20, 50, 250 and 1000) were generated, and different laboratory conditions were simulated manipulating the PDF in order to generate more or less variable data. The Z-score and the classic TAT indicators were assessed for precision (%CV), robustness toward right-tailing (precision at different sample variability), sensitivity and specificity.


Z-score showed sensitivity and specificity comparable to PAT (≈80% with n≥250), but superior precision that ranged within 20% by moderately small sized samples (n≥50); furthermore, Z-score was less affected by the value of the cutoff used for setting the acceptable TAT, as well as by the sample variability that reflected into the magnitude of right-tailing.


The Z-score was a valid indicator of laboratory timeliness and a suitable device to improve as well as to maintain the achieved quality level.

Corresponding author: Dr. Med. Cristiano Ialongo, PhD, Department of Physiology and Pharmacology, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome (RM), Italy, Phone: +3906-4991-2987

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Employment or leadership: None declared.

  4. Honorarium: None declared.

  5. Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication.


If x is the continuous random variable representing the TAT:


Eq. (1) is the generalized log-logistic PDF with scale α, shape β, and threshold γ.


1. Lippi G, Plebani M, Graber ML. Building a bridge to safe diagnosis in health care. The role of the clinical laboratory. Clin Chem Lab Med 2016;54:1–3.10.1515/cclm-2015-1135Search in Google Scholar PubMed

2. Valenstein P. Laboratory turnaround time. Am J Clin Pathol 1996;105:676–88.10.1093/ajcp/105.6.676Search in Google Scholar PubMed

3. Howanitz JH, Howanitz PJ. Laboratory results. Timeliness as a quality attribute and strategy. Am J Clin Pathol 2001;116:311–5.10.1309/H0DY-6VTW-NB36-U3L6Search in Google Scholar PubMed

4. Plebani M, Sciacovelli L, Marinova M, Marcuccitti J, Chiozza ML. Quality indicators in laboratory medicine: a fundamental tool for quality and patient safety. Clin Biochem 2013;46:1170–4.10.1016/j.clinbiochem.2012.11.028Search in Google Scholar PubMed

5. Hilborne LH, Oye RK, McArdle JE, Repinski JA, Rodgerson DO. Use of specimen turnaround time as a component of laboratory quality. A comparison of clinician expectations with laboratory performance. Am J Clin Pathol 1989;92:613–8.10.1093/ajcp/92.5.613Search in Google Scholar PubMed

6. Hilborne LH, Oye RK, McArdle JE, Repinski JA, Rodgerson DO. Evaluation of stat and routine turnaround times as a component of laboratory quality. Am J Clin Pathol 1989;91:331–5.10.1093/ajcp/91.3.331Search in Google Scholar PubMed

7. Steindel SJ. Timeliness of clinical laboratory tests. A discussion based on five College of American Pathologists Q-Probe studies. Arch Pathol Lab Med 1995;119:918–23.Search in Google Scholar

8. Howanitz PJ, Steindel SJ. Intralaboratory performance and laboratorians’ expectations for stat turnaround times. A College of American Pathologists Q-Probes study of four cerebrospinal fluid determinations. Arch Pathol Lab Med 1991;115:977–83.Search in Google Scholar

9. Valenstein PN, Emancipator K. Sensitivity, specificity, and reproducibility of four measures of laboratory turnaround time. Am J Clin Pathol 1989;91:452–7.10.1093/ajcp/91.4.452Search in Google Scholar PubMed

10. Armbruster DA, Overcash DR, Reyes J. Clinical chemistry laboratory automation in the 21st century – amat victoria curam (victory loves careful preparation). Clin Biochem Rev 2014;35:143–53.Search in Google Scholar

11. Nevalainen D, Berte L, Kraft C, Leigh E, Picaso L, Morgan T. Evaluating laboratory performance on quality indicators with the Six Sigma scale. Arch Pathol Lab Med 2000;124:516–9.10.5858/2000-124-0516-ELPOQISearch in Google Scholar PubMed

12. Palmer K, Tsui K-L. A review and interpretations of process capability indices. Ann Oper Res 1999;87:31–47.10.1023/A:1018993221702Search in Google Scholar

13. Kovarik M, Sarga L. Process capability indices for non-normal data. WSEAS Trans Bus Econ 2014;11:419–29.Search in Google Scholar

14. Ialongo C, Bernardini S. Timeliness “at a glance”: assessing the turnaround time through the Six Sigma metrics. Biochem Med (Zagreb) 2016;26:98–102.10.11613/BM.2016.010Search in Google Scholar

15. Ialongo C, Porzio O, Giambini I, Bernardini S. Total automation for the core laboratory: improving the turnaround time helps to reduce the volume of ordered STAT tests. J Lab Autom 2016;21:451–8.10.1177/2211068215581488Search in Google Scholar PubMed

16. Clark DE, El-Taha M. Some useful properties of log-logistic random variables fro health care simulations. Int J Stat Med Res 2015;4:79–86.10.6000/1929-6029.2015.04.01.9Search in Google Scholar

17. Vollmer RT. Analysis of turnaround times in pathology: an approach using failure time analysis. Am J Clin Pathol 2006;126:215–20.10.1309/YTEKD0CNUBKJVFTWSearch in Google Scholar

18. Kantam RR, Srinivasa Rao G, Sriram B. An economic reliability test plan: log-logistic distribution. J Appl Stat 2006;33:291–6.10.1080/02664760500445681Search in Google Scholar

19. Al-Shomrani AA, Shawky AI, Arif OH, Aslam M. Log-logistic distribution for survival data analysis using MCMC. Springerplus 2016;5:1774.10.1186/s40064-016-3476-7Search in Google Scholar PubMed PubMed Central

20. Yu C. Resampling methods: concepts, applications, and justification. Pract Assess Res Eval 2003;8:1–16.Search in Google Scholar

21. Holland LL, Smith LL, Blick KE. Total laboratory automation can help eliminate the laboratory as a factor in emergency department length of stay. Am J Clin Pathol 2006;125:765–70.10.1309/3J5P9VJRUP4U5RU5Search in Google Scholar

22. Singh VP. Three-parameter log-logistic distribution. Entropy-based parameter estimation in hydrology. Dordrecht: Springer Netherlands, 1998:297–311.10.1007/978-94-017-1431-0_18Search in Google Scholar

Supplemental Material:

The online version of this article offers supplementary material (

Received: 2017-7-21
Accepted: 2017-9-13
Published Online: 2017-10-17
Published in Print: 2018-3-28

©2018 Walter de Gruyter GmbH, Berlin/Boston

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