Modified Cp and Cpk Indices Based on Left-Truncated Data

The process capability indices Cp and Cpk are commonly used in industry to evaluate process capability, but they usually require that quality data follow a normal distribution. However, in the actual supply–demand relationship, some suppliers artificially eliminate products that do not meet the inspection requirements in order to make buyers accept their products, and these truncated sample data have a more significant impact on process capability evaluation. Based on the left-truncated sample, two modified process capability indices, CpT and CpkT, are proposed, and bootstrap confidence interval estimation methods are established for each of them. Extensive simulation experiments are conducted on the modified indices by varying the sample size and truncation location parameters, and the results are compared with those of traditional methods. The comparison reveals that the new methods outperform the traditional ones across a range of sample sizes and truncation locations. Finally, a real example is used to validate the usefulness of the new method in guiding production management.