Qualitometro, a (Wrong) Method for Service Control Charts

Many quality characteristics of products or services are commonly evaluated on ordinal scales with a finite number of categories. A systematic analysis of categorical variables collected over time may be very useful for a profitable management strategy. In order to measure customer satisfaction or quality improvement in a process, two or more quality characteristics are often conjointly measured and summarized by suitable indexes. A common practice suggests evaluating a synthetic index by mapping each outcome of a multivariate ordinal variable into numbers. This procedure is not always legitimate from the measurement theory point of view. Recently the author read the paper “Synthesis maps for multivariate ordinal variables in manufacturing” and found in it many ideas about Control Charts for Services. We analyse them from a “scientific point of view” to compare the authors findings with ours. The analysis shows the “same (=equivalent)” results for the “linguistic control charts” and different results for the “numeric Control Charts”: the cause is that they do not use correctly the Theory. The Control Limits in the Shewhart CCs are based on the Normal Distribution (Central Limit Theorem, CLT) and are not valid for non-normal distributed data: consequently, the decisions about the “In Control” (IC) and “Out Of Control” (OOC) states of the process are wrong. The Control Limits of the CCs are wrongly computed, due to unsound knowledge of the fundamental concept of Confidence Interval. Minitab and other software e (e.g. JMP, SAS) use the “T Charts”, claimed to be a good method for dealing with “rare events”, but their computed Control Limits of the CCs are wrong. The same happens for the Confidence Limits of the parameters of the distribution involved in the papers (Weibull, Inverse Weibull, Gamma, Binomial, Maxwell).