Employing fuzzy hypothesis testing to improve modified p charts for monitoring the process fraction nonconforming

Although 3σ control limits of p control charts are quite common in practical applications, they are not appropriate when the process mean is wandering with some degree of consistency. For this reason, we firstly present modified control limits for the binomial p chart based on interval-valued hypothesis testing to allow the process fraction nonconforming to vary over a specified interval without appreciably affecting the overall performance of the process. This modified p chart is able to support extreme quality levels, but it neglects to consider economy in production of units between both these extremes, i.e., gradual deterioration or gradual improvement of the product quality with respect to the average quality. With the aim of achieving a reasonable balance between both these extremes, we additionally introduce a modified p chart based on fuzzy-valued hypothesis testing. The fuzzy modified p chart is not only able to adequately meet the trade-off between the common and the modified p chart, but also enables to incorporate economic aspects of producing better/worse acceptable quality. To demonstrate the benefits of the proposed fuzzy modified p chart, we conduct a comprehensive case study on monitoring of medical insurance claims.