Estimating Process Capability with Truncated Samples

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Process capability has long been viewed as a critical performance measure to indicate how well a process meet the specifications and customer requirements. Several indices, including $C_p$ and $C_{pk}$, have been proposed and widely implemented to quantify the process capability. However, these indices have been obtained without regard to inspection or screening procedures through which finished products will be truncated at the specifications. Consequently, only a fraction of outgoing products within the specifications will be passed into the customers. From the customer's point of view, it will thus be meaningful to assess the process capability with truncated samples. This article investigates how to estimate the process capability when only incomplete truncated data are available. On the basis of parameter estimation for truncated samples, the proposed methodology may be helpful to evaluate the process capability by examining a sample of items from the lots submitted.