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Oosterhuis and Coskun recently proposed a new model for applying the Six Sigma concept to laboratory measurement processes. In criticizing the conventional Six Sigma model, the authors misinterpret the industrial basis for Six Sigma and mixup the Six Sigma “counting methodology” with the “variation methodology”, thus many later attributions, conclusions, and recommendations are also mistaken. Although the authors attempt to justify the new model based on industrial principles, they ignore the fundamental relationship between Six Sigma and the process capability indices. The proposed model, the Sigma Metric is calculated as the ratio CV_{I}/CV_{A}, where CV_{I} is individual biological variation and CV_{A} is the observed analytical imprecision. This new metric does not take bias into account, which is a major limitation for application to laboratory testing processes. Thus, the new model does not provide a valid assessment of method performance, nor a practical methodology for selecting or designing statistical quality control procedures.

Oosterhuis and Coskun recently proposed a new model for applying the Six Sigma concept to laboratory measurement processes (

Although the authors attempt to justify the new model based on industrial principles, they ignore the fundamental relationship between Six Sigma and the process capability indices Cp and Cpk. Such indices were widely used in industry prior to the formalization of Six Sigma in the 1990s and provide the proper framework for understanding the development of Six Sigma (_{u} is the upper tolerance limit, TL_{l} the lower tolerance limit, and SD is the standard deviation for the observed process variation, as illustrated in _{u} = TV + pTE, and TL_{l} = TV – pTE,

Relation of Sigma Metric (SM) to industrial process capability indices (Cp, Cpk) and process control metric (ΔSE_{crit}) for SQC selection and design. ΔSEcrit - critical systematic error. TL - tolerance limit. TV - target value. Μ - observed mean. pTE - permissible total error. Bias - observed trueness. SD - observed imprecision.

Ideally, the process should operate with a Cp of 2.0, which means that ± 6 SDs or a total of 12 SDs of process variation should fit between the tolerance limits. In industry, a minimum Cp of 1.0 is considered essential for routine operation and a Cp of 1.33 is preferred. Knowledge of this relationship led to recommendations in 1990 for changing process acceptance criteria from 2SD < pTE to 4SD < pTE as a minimum and recommending further improvements to 5SD-6SD<pTE for critical medical applications (

A limitation of Cp is that it assumes the process is centered on the TV, therefore it cannot account for any shift that might occur. Another capability index, Cpk, takes “centerness” into account and therefore provides a better metric for assessing performance of a laboratory testing process (

where μ represents the mean observed for the distribution. As shown in

Or

Thus, the conventional calculation of a Sigma Metric is directly related to the traditional industrial process capability index Cpk. The minimum acceptable Cpk of 1.0 is equivalent to SM = 3.0, a Cpk of 1.33 that is recommended to achieve a more controllable process corresponds to SM = 4.0, and the goal for excellent performance is a Cpk of 2.0, which corresponds to SM = 6.0 for world class quality.

Oosterhuis and Coskun state that the “

Another mistake is that the authors mix-up the Six Sigma “counting methodology” with the “variation methodology”. The counting methodology is used when inspecting products to identify defects, whereas the variation methodology is employed when process variation can be measured directly, which is the case for laboratory testing processes where regulation and accreditation guidelines actually require the laboratory to verify the precision and bias of their testing processes. The counting methodology employs a table based on the normal distribution to convert the observed number of defects expressed as DPMO (defects _{crit}, and represents the size of the systematic error that must be detected to maintain the quality of the production process, as shown in _{ed}) for this critical shift and the probability of false rejection (P_{fr}) for stable operating conditions (without this shift). Observe that the upper x-axis in

Quality planning tool for selection/design of SQC procedures having 2 levels of controls. The probability for rejection is plotted on y-axis versus the size of systematic error on bottom x-axis and the sigma-metric on the top x-axis. In the key at the right, the different power curves correspond, top to bottom, to the list of control rules, the probability for false rejection (Pfr), total number of control rules (N), and number of runs (R) over which the rules are applied. This chart was produced by the EZ Rules3 computer program. Vertical line represents examination procedure with observed sigma-metric of 4.0.

or

Therefore, the Sigma-Metric (SM) can provide guidance for the selection and design of SQC procedures, as well as a metric for assessing the quality of performance for a testing process.

In addition to these major mistakes in the development of the new model, they further confuse the Six Sigma performance assessment model with a different goal-setting model for pTE, then combine the two models and make erroneous attributions based on the new model. The result is that the SM is calculated as the ratio CV_{I}/CV_{A}, where CV_{I} is the tolerance limit stated as an imprecision goal based on individual biological variation and CV_{A} is the observed analytical imprecision. This new metric does not take bias into account, which is a major limitation for application to laboratory testing processes. Furthermore, this model ignores other approaches for defining tolerance limits that are commonly employed,

None declared.