Аccounting for possible displacements of the process adjustment center when determining the performance index

Abstract

The range of natural dispersion of the controlled indicator x contains 99.73% of all possible values and has a width of 3𝜎 from the center of the manufacturing process setting (𝜇) towards the upper allowable value (USL) and 3𝜎 from the average towards the lower allowable value (USL). A traditional approach to ensuring the acceptability of a production process is to maintain a process operability index of at least 1.66. At the same time, the performance index of the production process (𝐶𝑝𝑘) is defined as the minimum of the values of the performance indexes at the lower (𝐶𝑝𝑙) and upper limit (𝐶𝑝𝑢) of the range of permissible values of the controlled quality indicator: 𝐶𝑝𝑘=𝑚𝑖𝑛(𝑈𝑆𝐿−𝜇3𝜎; 𝜇−𝐿𝑆𝐿3𝜎), where μ is the mathematical expectation of the controlled indicator, which is usually taken to be equal to the average value (x ̅) and used as the actual value of the center of adjustment of the process.