The Food and Drug Administration’s 2011 Process Validation Guidance and International Council for Harmonization Quality Guidelines recommend continued process verification (CPV) as a mandatory requirement for pharmaceutical, biopharmaceutical, and other regulated industries. As a part of product life cycle management, after process characterization in stage 1 and process qualification and validation in stage-2, CPV is performed as stage-3 validation during commercial manufacturing. CPV ensures that the process continues to remain within a validated state. CPV requires the collection and analysis of data related to critical quality attributes, critical material attributes, and critical process parameters on a minimum basis. Data is then used to elucidate process control regarding the capability to meet predefined specifications and stability via statistical process control tools. In statistical process control, control charts and Nelson rules are commonly used throughout the industry to monitor and trend data to ensure that a process remains in control. In the control chart, the mean value is taken as the center line, and 3σ limits are placed on either side of the center line. In CPV, manufactured lots are summarized, trended, and discussed at a cross-functional level at pre-defined intervals (either weekly, bi-weekly, or even monthly) based on the batch run rate. A cross-functional team assesses details regarding 1) violation frequency, 2) statistical strength of the signal, 3) violation magnitude and its impact on process or quality, and 4) any potential root causes for out-of-expectation or out-of-trend signals. The cross-functional team must analyze whether any signal identified by the control chart is reliable and must determine whether corrective action should be taken and justify the decision in the CPV meeting minutes based on statistical strength and reliability of the signal. However, basic control charts are susceptible to false alarms and nuisance alarms. Therefore, it is imperative to understand the assumptions behind control charts and the inherent false alarm rates for different Nelson rules. In this article, the authors have detailed the assumptions behind the usage of control charts, the rate of false alarms for different Nelson rules, the impact of skewness and kurtosis of a data distribution on the false alarm rate, and methods for optimizing control chart design by reducing false alarm rates and nuisance signals.

Supervised land-use/land-cover (LULC) classifications are typically conducted using class assignment rules derived from a set of multiclass training samples. Consequently, classification accuracy varies with the training data set and is thus associated with uncertainty. In this study, we propose a bootstrap resampling and reclassification approach that can be applied for assessing not only the uncertainty in classification results of the bootstrap-training data sets, but also the classification uncertainty of individual pixels in the study area. Two measures of pixel-specific classification uncertainty, namely the maximum class probability and Shannon entropy, were derived from the class probability vector of individual pixels and used for the identification of unclassified pixels. Unclassified pixels that are identified using the traditional chi-square threshold technique represent outliers of individual LULC classes, but they are not necessarily associated with higher classification uncertainty. By contrast, unclassified pixels identified using the equal-likelihood technique are associated with higher classification uncertainty and they mostly occur on or near the borders of different land-cover.