Long story short: an introduction to the short-term and longterm Six Sigma quality and its importance in laboratory medicine for the management of extra-analytical processes

Cristiano Ialongo; Sergio Bernardini

doi:10.1515/cclm-2018-0310

Article

Long story short: an introduction to the short-term and longterm Six Sigma quality and its importance in laboratory medicine for the management of extra-analytical processes

Cristiano Ialongo and Sergio Bernardini

Published/Copyright: June 18, 2018

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From the journal Clinical Chemistry and Laboratory Medicine (CCLM) Volume 56 Issue 11

Abstract

There is a compelling need for quality tools that enable effective control of the extra-analytical phase. In this regard, Six Sigma seems to offer a valid methodological and conceptual opportunity, and in recent times, the International Federation of Clinical Chemistry and Laboratory Medicine has adopted it for indicating the performance requirements for non-analytical laboratory processes. However, the Six Sigma implies a distinction between short-term and long-term quality that is based on the dynamics of the processes. These concepts are still not widespread and applied in the field of laboratory medicine although they are of fundamental importance to exploit the full potential of this methodology. This paper reviews the Six Sigma quality concepts and shows how they originated from Shewhart’s control charts, in respect of which they are not an alternative but a completion. It also discusses the dynamic nature of process and how it arises, concerning particularly the long-term dynamic mean variation, and explains why this leads to the fundamental distinction of quality we previously mentioned.

Keywords: extra-analytical phases; quality control; statistics; total quality management

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

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Employment or leadership: None declared.
Honorarium: None declared.
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.

Appendix A: setting up the control chart with Phase I data

Of course the issue with respect to building a CC is finding the best estimation of the process variability, on which depends σ in Eq. 1.2 and in turn the width of the CLs. To this end, there are several procedures that can be used and rely on the preliminary process analysis (Phase I). A common way is to average the s of some preliminary samples and correct it by an appropriate factor (c4 and A3). Alternatively, it can be computed the average range and correct it by appropriate constants (d2 and A2). Finally, a method is using the pooled variance of the samples if they all have the same size n. Detailed explanations can be found elsewhere in textbooks and research articles [14], [27], [28].

Appendix B: computing control charts performance (ARL) using Excel

It is possible to rewrite Eq. 3.1 in the following form:

(3.1a)P missed alarm=β=P(LCL≤Xi≤UCL)=P(Xi≤UCL)+P(Xi≥LCL)

That could be further rewritten as:

(3.1b)β=P(0≤Xi≤UCL) − P(0≤Xi≤LCL)

According to the equation above, P can be computed as the difference between two unidirectional intervals and calculated by integrating the cumulative distribution function of the normal curve (Φ). In particular, recalling Eq. 1.1, it is possible to rewrite Eq. 3.1b into a standardized form which is more comfortable for calculations:

(3.1c) β=Φ[(UCL–Xi)/SE]−Φ[(UCL–Xi)/SE]

Substituting Eq. 3.1c for Eq. 1.1 and Eq. 1.3 it yields:

(3.1d)β=Φ[((T+Zα/2*SE)–Xi)/(σ/n0.5)]–Φ[((T−Zα/2*SE)−Xi)/(σ/n0.5)]

And substituting Eq. 3.2 for Eq. 3.1d it follows that:

(3.1e)β=Φ[((T+Zα/2*σ/n0.5)–(T+δ*σ))/(σ/n0.5)]–Φ[((T−Zα/2*σ/n0.5) –(T+δ*σ))/(σ/n0.5)]

Rearranging Eq. 3.1e and removing the common terms, Eq. 3.3 is obtained.

In order to compute β, it can be used the NORM.S.DIST function that is available in Microsoft Excel. For calculations, the input corresponding to Eq. 3.3 turns into:

β=NORM.S.DIST(Zα/2−δ*n0.5; true)− NORM.S.DIST(−Zα/2−δ*n0.5; true)

Herein, “true” is a logical value returning the cumulative probability of the standard normal curve.

Appendix C: calculating the ppm inflation by the equivalent most-shifted average method

In order to calculate the long-term ppm inflation due to the LTDMV, it is possible to use a simple procedure whereby the calculation is taken in a sample which was supposed to have the largest average deviation from T, namely, 1.5σ [12]. Because this allows computing the non-conformity in only one tail of the output, the final result must be multiplied by two because the LTDMV was not constrained in a particular direction.

In this instance, let’s consider the most upward-shifted sample, which can be quantified as follows:

(4.1b)μ′=μ+1.5σ

Thus, substituting for Eq. 4.1 yields:

(4.1c)Z′UL=[(+Δ)−(μ+1.5σ)]/σ; Z′LL=[(−Δ)−(μ+1.5σ)]/σ

That can be further rearranged to give:

(4.1d)Z′UL=[(+Δ)−μ]/σ–(1.5σ/σ); Z′LL=[(−Δ)−μ]/σ–(1.5σ/σ)

And finally simplified into:

(4.1e)Z′UL=ZUL– 1.5; Z′LL=ZLL– 1.5

In fact, if σ does not change, the average shift simply translates the former distribution within the interval of conformity, and thus it is equivalent to offset the interval itself. Notably, this makes it possible to subtract or add the shift directly to the Z-score yielding the new value without any further calculation.

With respect to Z_LL=−3 and Z_UL=3, Eq. 4.1d yielded Z′_LL=−4.5 and Z′_UL=1.5 and in turn ~3.4 ppm and ~66,800 ppm, respectively. Thus, multiplying by two, there were ~133,600 ppm that is the sought proportion. Noteworthy, if the long-term μ was not significantly shifted from T and Δ was constant, rearranging Eq. 4.1 and applying Eq. 4.3, it was possible to compute the equivalent inflated σ (σ′):

(4.1e)σ′= |(μ−Δ)/Z′|

The σ′ is the overall variability (inflated), which was expected on the long term due to the LTDMV.

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Received: 2018-03-23

Accepted: 2018-05-25

Published Online: 2018-06-18

Published in Print: 2018-10-25

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Articles in the same Issue

https://doi.org/10.1515/cclm-2018-0310

Keywords for this article

extra-analytical phases; quality control; statistics; total quality management