This paper presents a new multivariate process capability index (MPCI) which is based on the principal component analysis (PCA) and is dependent on a parameter which can take on any real number. This MPCI generalises some existing multivariate indices based on PCA proposed by several authors when or . One of the key contributions of this paper is to show that there is a direct correspondence between this MPCI and process yield for a unique value of . This result is used to establish a relationship between the capability status of the process and to show that under some mild conditions, the estimators of this MPCI is consistent and converge to a normal distribution. This is then applied to perform tests of statistical hypotheses and in determining sample sizes. Several numerical examples are presented with the objective of illustrating the procedures and demonstrating how they can be applied to determine the viability and capacity of different manufacturing processes.

Resilience describes the capacity of systems to react to, withstand, adjust to, and recover from disruptive events. Despite numerous metrics proposed to quantify resilience, few studies predict these metrics or the restoration time to nominal performance levels, and these studies often focus on a single domain. This paper introduces three methods to model system performance and resilience metrics, which are applicable to various engineering and social science domains. These models utilize reliability engineering techniques, including bathtub-shaped functions, mixture distributions, and regression analysis incorporating event intensity covariates. Historical U.S. job loss data during recessions are used to evaluate these approaches’ predictive accuracy. This study computes goodness-of-fit measures, confidence intervals, and resilience metrics. The results show that bathtub-shaped functions and mixture distributions accurately predict curves possessing V, U, L, and J shapes but struggle with W and K shapes involving multiple disruptions or sudden performance drops. In contrast, covariate-based models effectively track all curve types, including complex W and K shapes, like the successive shocks in the 1980 U.S. recession and the sharp decline in the 2020 U.S. recession. These models achieve a high predictive accuracy for future performance and resilience metrics, evidenced by the low sum of square errors and high adjusted coefficients of determination.

This paper reports on the Failure To Attend (FTA) rate of appointments as well as patients following the implementation of SMS reminders in a public dental outpatient service. Given the ineffectiveness of the intervention and a highly representative patient’s profile, this paper identifies the demographic characteristics of patients who miss all of their appointments. Data on appointment attendance, patient demographics and dental service type was collected over a time period of 46 consecutive months. Using descriptive and inferential statistics (chi-square, two sample tests and Marascuilo procedure) we found the SMS intervention was ineffective in reducing the FTA rates. Further, patients associated with high rates of non-attendance exhibited one or more of the following characteristics: male; age 26 – 44; non-concession card holders; a person of Indigenous, local, Asian or African descent, and of refugee status, persons living in low socio-economic areas; and appointments in General Care and Student Clinics. Whilst the literature overwhelmingly attributes SMS reminders to improving the attendance rate of patients in outpatient clinics, our contradictory findings suggest a more targeted approach in settings whose patients exhibit strong characteristics associated with non-attendance.

Construction of a confidence interval for process capability index CPM is often based on a normal approximation with fixed sample size. In this article, we describe a different approach in constructing a fixed-width confidence interval for process capability index CPM with a preassigned accuracy by using a combination of bootstrap and sequential sampling schemes. The optimal sample size required to achieve a preassigned confidence level is obtained using both two-stage and modified two-stage sequential procedures. The procedure developed is also validated using an extensive simulation study.