Process Capability Analysis via Continuous Ranked Probability Score

Abstract

Process capability analysis is an important aspect of quality control. Various process capability indices are proposed when the distribution is normal. For non-normal cases, percentile and yield-based indices have been introduced. These two methods use partial features of a process distribution, such as key percentiles and the proportion of non-conforming (PNC) to estimate the process capability. However, these local features may not reflect the uniformity of a process appropriately when the distribution is non-normal. In this paper, continuous ranked probability score (CRPS) is introduced to process capability analysis and a CRPS-based approach is proposed. This method can assess the dispersion of process variation across the overall distribution and is applicable to any continuous distribution. An example and simulations show that CRPS-based indices are more stable and accurate indicators of process capability than the existing indices in reflecting the degree of process fluctuation.In the same way, C pl(s) = C pl . Then C pk(s) = min{C pu , C pl } = C pk .

CRPS chart: Simultaneously monitoring location and scale under data‐rich environment

“…Since the CRPS method effectively calculates the distance from a distribution to a certain point, it is now commonly used for many functions beyond forecasting. For example, Shi et al proposed a CRPS‐based approach to analyze the process capability and showed that their method is applicable to both normal and nonnormal cases. Basically, the CRPS statistic is defined as …”

“…Shi et al demonstrated that CRPS can also be expressed as …”

“…Here y is the desired value and t is the observed value; S(F, y) is the CRPS value obtained by computing the integral of the square difference between F and H; Shi et al 21 demonstrated that CRPS can also be expressed as…”

Measuring capability of a Poisson process: Relative goodness of the estimates obtained by different approaches

“…The details about these indices are available in Kane (1986), Kotz and Johnson (1993), English and Taylor (1993), Kotz and Johnson (2002), Vannman (2006), Chen et al (2008), Wu et al (2009), Yum and Kim (2011), Grau (2012) and Chen et al (2017). The generalization of these indices for continuous non-normal variables are suggested by Clements (1989), Pearn and Kotz (1994), Pearn and Chen (1995), Shore (1998), Chen (2000), Goswami and Dutta (2013), Wang et al (2016), Shi et al, (2016), Polhemus (2018) and Chen et al (2019). A good bibliometric analysis for process capability research is available in Ahmad et al (2019).…”

Process Capability Analysis in a Polypropylene Bag Manufacturing Company

“…All processes have inherent statistical variability which can be evaluated by statistical methods. The analyses of manufacturing processes play a vital role in quality control and continuous improvement (Shi et al, 2016). These analyses use indices such as the process capability and potential process capability index as quantitative measures of assessing whether a production process under study is capable of delivering products that meet the required specifications (Dharmasena and Zeephongsekul, 2016).…”