In the literature of six sigma, one can see that an organization is classified as either 'world-class' or 'industry average' or 'non-competitive' based on the sigma level -the milestoneit achieves at a given point of time. It is well known that, in an organization, many critical processes exist. When an organization is termed as a 'six sigma organization', there exists a question whether all critical processes are at six-sigma level. If all such processes are not at six sigma level then how an overall sigma level is obtained needs further study. Hence, it is attempted to assign weights to all critical processes based on their importance and this information is used along with the defects per million (dpm) units produced by the respective process to determine the overall sigma level, called as 'weight-based sigma level' of an organization at a given point of time. As weights are assigned to the dpm's of the respective critical processes, the resulting dpm's are considered equally likely. The approach is described in detail and studied numerically to illustrate the effectiveness of the approach using various arbitrary values of weights and sigma levels.

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Whenever specification is provided for a measureable quality characteristic, under normality assumption, the defects per million opportunities (DPMO) can be computed by taking into account both the tail probabilities. This implies that a unit of a product is declared defective if a measurement on quality characteristic falls either below the specified lower limit or above the upper limit. However, there are practical situations, where a unit is said to be defective if the measurement either falls below the lower limit (higher-the-better) or falls above the upper limit (lowerthe-better). Under this circumstance, the DPMO needs to be computed taking into account the appropriate tail probabilities (left or right). In this paper, the aspects of Six Sigma are used to decide the upper and lower sigma quality limits for these two cases. Followed by this, the DPMO is estimated accordingly. Probabilities of far good units, that is, extremely good parts per million opportunities (EGPMO), of the quality characteristic are also determined. It is discussed about how DPMO and EGPMO help in evaluating the overall quality level of the process/product of interest. The procedure is illustrated with numerical examples.

PurposeThe purpose of this paper is to propose a new approach in which cost‐based process weights are used to determine a unique weighted‐defects per million opportunity (DPMO) and its corresponding overall sigma level in order to classify an organization as either “world‐class,” “industry average” or “non‐competitive.”Design/methodology/approachIn order to achieve this objective, the proposed approach uses both internal and external performances of the products and processes in terms of costs involved to determine cost‐based process weights. These weights are then incorporated into the respective DPMOs for computing weighted‐DPMOs. Finally, a unique weighted‐DPMO and its corresponding sigma level are found.FindingsThe proposed method is a new one and it involves various costs for determining process weights. The findings reveal that the weight‐based overall sigma level is more realistic than the one that is calculated without weights. Further, the results of this study could provide interesting feedback to six‐sigma practitioners, as they are particular about DPMOs and return on investments in project implementations.Research limitations/implicationsThe results of this paper are based on the weights of respective processes and their products that are calculated using various cost aspects. Determining such weights by means of any other process and product factors incorporating the effects of various marketing activities, if any, could extend its generality and fulfil the gap.Practical implicationsThe proposed method is simple to implement and the required data can be collected without any additional commitments. Also, it is more generic so that it can be adapted by organizations of any nature. This paper recommends change in the practice from simply using the DPMOs with equal importance to using the weight‐based DPMOs for evaluating overall sigma level (performance) of an organization.Originality/valueThe proposed approach would have a high value among six‐sigma quality practitioners and researchers as it provides a new and more realistic measure for overall performance of an organization during the evaluation process.

The accuracy of computer numerical control machine tools can be improved by identifying error sources affecting the overall position error and orientation errors. Because of their inevitable nature, the position errors cannot be entirely eliminated from the machinery, but they can be identified, measured and compensated during the manufacturing process of the components by developing and using a mathematical model. In this present work, different mathematical models have been developed for the errors measured by laser interferometer at different nominal positions of X, Y and Z axes both in forward and reverse direction movement as per VDI 3441 Germany standard. Using Akaike information criterion, the best model is selected for each axis and later the best model’s coefficients have been optimized by considering both minimizing sum square errors and maximizing R2 values using teaching–learning-based optimization algorithm. Technique for Order Preference by Similarity to the Ideal Solution method has been adopted to convert the dual objectives into a single objective. An improvement of 1%–71% in R2 values was reported to prove the effectiveness of the proposed optimization algorithm, Teaching–Learning-Based Optimization algorithm, with the same sum square error values.