A Theoretical Foundation for the Development of Process Capability Indices and Process Parameters Optimization under Truncated and Censoring Schemes

Process capability indices (PCIs) provide a measure of the output of an in-control process that conforms to a set of specification limits. These measures, which assume that process output is approximately normally distributed, are intended for measuring process capability for manufacturing systems. After implementing inspections, however, non-conforming products are typically scrapped when units fail to meet the specification limits; hence, after inspections, the actual resulting distribution of shipped products that customers perceive is truncated. In this research, a set of customer-perceived PCIs is developed focused on the truncated normal distribution, as an extension of traditional manufacturer-based indices. Comparative studies and numerical examples reveal considerable differences among the traditional PCIs and the proposed PCIs. The comparison results suggest using the proposed PCIs for capability analyses when non-conforming products are scrapped prior to shipping to customers. The confidence interval approximations for the proposed PCIs are also developed. A simulation technique is implemented to compare the proposed PCIs with its traditional counterparts across multiple performance scenarios. The robust parameter design (RPD), as a systematic method for determining the optimum operating conditions that achieve the quality improvement goals, is also studied within the realm of censored data. Data censoring occurs in time-oriented observations when some data is unmeasurable outside a predetermined study period. The underlying conceptual basis of the current RPD studies is the random sampling from a normal distribution, assuming that all the data points are uncensored. However, censoring schemes are widely implemented in lifetime testing, survival analysis, and reliability studies. As such, this study develops the detailed guidelines for a new RPD method with the consideration of type I-right censoring concepts. The response functions are developed using nonparametric methods, including the Kaplan-Meier estimator, Greenwood\u27s formula, and the Cox proportional hazards regression method. Various response-surface-based robust parameter design optimization models are proposed and are demonstrated through a numerical example. Further, the process capability index for type I-right censored data using the nonparametric methods is also developed for assessing the performance of a product based on its lifetime