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Commercial Off-The-Shelf (COTS) Electronics Reliability for Space Applications

This presentation describes the accelerating use of Commercial off the Shelf (COTS) parts in space applications. Component reliability and threats in the context of the mission, environment, application, and lifetime. Provides overview of traditional approaches applied to COTS parts in flight applications, and shows challenges and potential paths forward for COTS systems in flight applications it's all about data!

Field Programmable Gate Array (FPGA)↗

Recommendations on Use of Commercial-Off-The-Shelf (COTS) Electrical, Electronic, and Electromechanical (EEE) Parts for NASA Missions

The NASA Electronic Parts & Packaging Program Manager, requested a NASA Engineering and Safety Center independent assessment to summarize Commercial Crew Program and NASA Centers’ current and best practices, and lessons learned, on use of commercial-off-the-shelf (COTS) for all mission risk classifications, and provide recommendations that could lead to future NASA Electronic Parts and Packaging Program and/or Agency guidance on COTS parts. This document contains the outcome of the assessment.

Commercial-Off-The-Shelf↗

Recommendations on the Use of Commercial-Off-The-Shelf (COTS) Electrical, Electronic, and Electromechanical (EEE) Parts for NASA Missions - Phase II

This assessment had two Phases. Phase I captured NASA Centers’ current practices for commercial-off-the-shelf (COTS) Electrical, Electronic, and Electromechanical (EEE) parts 1 used in spaceflight systems and ground support equipment (available at https://ntrs.nasa.gov/citations/20205011579) [ref. 1]. The Phase II report provides guidance for selecting and using COTS parts in NASA missions. The approaches proposed in this report differ from current agency practices. This top-level executive summary touches on these new approaches for using COTS parts but does not provide the detailed information that is critical in understanding the rationale behind these new approaches. Readers will need to read the entire report to gain full understanding and effectively use the recommendations herein. NASA’s historical approach to selecting and applying parts has been to define certain parts, primarily specific classes of military specification (MIL-SPEC) parts, as “standard”, leaving all others, including COTS parts, as nonstandard. Standard parts typically are used without further testing (“use-as-is”). Nonstandard parts are subjected to initial screening and subsequent lot acceptance testing of representative samples from each procured lot per MIL-SPEC or similar requirements. Decades later, top-tier commercial part manufacturers have evolved significant manufacturing, statistical control, and technological improvements that can now provide parts as reliable or more reliable than MIL-SPEC parts, when used within their datasheet limits. Concurrently, the space science and exploration community’s needs demand technological advances unavailable with MIL-SPEC parts. This ongoing change necessitates using COTS parts for space missions. Properly selected COTS parts in appropriate applications can offer performance and supply availability advantages compared to MIL-SPEC parts. Their utility and demonstrated reliability result from large volumes and automated production and testing processes. However, careful review and a thorough understanding of their specifications (i.e., datasheet limitations) is needed, and verifying that manufacturer specifications and reliability meet space hardware application needs are necessary. This report recommends MIL-SPEC screening and non-radiation-related lot acceptance testing be reduced or eliminated in cases where evidence of sufficient quality and reliability exists for COTS parts. The extent of NASA's insight into COTS manufacturers and the amount and nature of the needed evidence will differ by mission and will likely be driven by a mission's resources and associated risk posture. To facilitate this goal, two new terminologies have been defined and described: “Industry Leading Parts Manufacturer (ILPM)” and “Established COTS parts.” An ILPM is a COTS manufacturer that produces high quality and reliable parts. Some parts produced by ILPMs, defined as Established COTS parts, do not need any additional MIL-SPEC or NASA screening and lot acceptance testing to be used in space applications. This report provides guidance for selecting, procuring, and applying COTS parts and for performing part-, board-, and system-level COTS parts verification. The recommendation to select Established COTS parts from ILPMs will assure those COTS parts will have comparable quality to corresponding MIL-SPEC parts. Selecting, applying, and verifying Established COTS parts from ILPMs requires a holistic team approach, engaging parts engineers, circuit designers, quality, reliability, and systems engineers, procurement specialists, radiation specialists, avionics leads, and program/project managers. A mission-specific approach tailored to a project’s Mission, Environment, Applications and Lifetime (MEAL) [ref. 2] requirements should be developed and approved by program/project managers. Any associated risks should be clearly identified, quantified, mitigated, and/or accepted. Different approaches are recommended according to program/project Risk Classes A, B, C, and D [ref. 3] and human-rated missions [ref. 4]: 1. Recommend Classes A and B and human-rated missions consider a “MIL-SPEC parts- based design” approach. ”MIL-SPEC parts-based design” approach is one in which most parts are MIL-SPEC parts and Established COTS parts from ILPMs are used only when an equivalent MIL-SPEC part does not meet functional or size, weight, and power (SWaP) or performance requirements, or is not available. 2. Recommend Classes D and Sub-D missions consider a “System of COTS” approach. “System of COTS” approach is one which most parts are Established COTS parts from ILPMs. 3. Recommend Class C missions determine which approach is the best for their projects; that is, use either a “MIL-SPEC parts-based design” approach, “System of COTS” approach, or a combined approach utilizing elements of both. This report intends to provide guidance in using COTS parts for NASA missions with risk classifications of A through D and human-rated missions; but it does not address the costs of using COTS parts. Costs of using COTS parts in different NASA mission classes can vary significantly even if the same parts are used in different risk postures, due to differing verification levels needed. The guidance does not distinguish between critical or non-critical systems, and a given project will need to apply the appropriate guidance based on their risk posture. The intended audience of this report are NASA personnel and commercial practitioners who support NASA’s spaceflight missions, including spaceflight program or project managers, parts engineers, parts manufacturers, radiation engineers, avionics engineers, system engineers, circuit design engineers, reliability engineers, safety and mission assurance (SMA) personnel, and parts procurement specialists. The NEPP Program will perform a pathfinder study to explore implementing the guidance in this NESC report. An ILPM verification process is not the same as conventional vendor qualification processes performed according to military standards and specifications. This NESC report intends to provide guidance in utilizing available parts data from ILPM manufacturers for parts assurance assessments needed for NASA missions. The report also captured the current practices from DoD and Federal Aviation Administration (FAA) in Section 10. Note each DoD and FAA report was provided by the corresponding agencies regarding their practices, which are independent from the NESC recommendations in the report.

Commercial-Off-The-Shelf↗

Investigating Commercial Off-The-Shelf (COTS) Glovebox and Support Components Compared to Custom Curatorial Laboratories

There is a need envisioned to investigate the application of commercial off-the-shelf (COTS) systems as tools that could be used within commercial preliminary curation as the expected space economy is supported and begins to take flight. NASA is involved with supporting and developing the space economy [1] and therefore it’s feasible that at some point, a commercial space company would bring back materials and either store initially, or permanently, within COTS equipment as a stand-in for custom curation laboratories. While utilizing opportunities to explore this capability at NASA-Johnson Space Center (JSC) during the establishment of other laboratories [2] it was realized that cleanliness and/or other properties could be evaluated for these COTS systems during their installation in advanced research facilities that are not ISO-class rated clean rooms. Several aspects of a COTS-Curation system were explored including various gloves for curation manipulation within a negative pressure glovebox (Fig.1), Balazs organic and inorganic contaminant levels testing prior to glovebox ever being used, mode swapping comparison of recirculation vs. single pass, constant monitoring of oxygen (O2) and moisture (H2O) levels in various conditions, etc. To acquire inorganic and organic compound loads inside the glovebox, Balazs wafer testing and gas sampling were implemented. These are standardized analytical tests provided by Balazs™ NanoAnalysis, a division of Air Liquide USA. Deployment of 8-inch silicon wafer witness plates for 24-hours in an undisturbed environment capture the organic compound load and inorganic trace metal contents which can be obtained by Vapor Phase Decomposition Inductively Coupled Plasma Mass Spectrometry (VPD ICP-MS). Balazs gas sample analysis was also performed for better measurements of volatile organic compounds (VOC) in glovebox air analyzed by Thermal Desorption Gas Chromatography Mass Spectrometry (TD GC-MS). These analytical testings were carried out in a controlled ultra high pure (UHP) gaseous nitrogen (N2)-purged environment where oxygen and moisture contents were continuously monitored at certain temperature and pressure. The preliminary outcomes of these testings are promising. The COTS systems appear to maintain the steady-state controlled environment for days, if not weeks, with uninterrupted gaseous N2-supply which was operated from a standard medium pressure LN2 250L 230L dewar, exchanged as needed. The outgassing load can be maintained by selecting the glove materials that have the least outgassing and particle shedding performances. Further experiments will be considered to validate the preliminary findings. While this project is exploratory, it is not intended as an endorsement by NASA Curation for approved materials or usage for advanced curatorial activities. NASA does not endorse nor promote any one particular product or company. References: [1] McCubbin F. M. et al. (2019) Space Science Reviews 215:A48. [2] Lewis, E.K. et. al (2024) LPSC LV, Abstract #2457.

Curation↗

Surface and subsurface oceanographic features drive forage fish distributions and aggregations: Implications for prey availability to top predators in the US Northeast Shelf ecosystem

Abstract Forage fishes are a critical food web link in marine ecosystems, aggregating in a hierarchical patch structure over multiple spatial and temporal scales. Surface‐level forage fish aggregations (FFAs) represent a concentrated source of prey available to surface‐ and shallow‐foraging marine predators. Existing survey and analysis methods are often imperfect for studying forage fishes at scales appropriate to foraging predators, making it difficult to quantify predator–prey interactions. In many cases, general distributions of forage fish species are known; however, these may not represent surface‐level prey availability to predators. Likewise, we lack an understanding of the oceanographic drivers of spatial patterns of prey aggregation and availability or forage fish community patterns. Specifically, we applied Bayesian joint species distribution models to bottom trawl survey data to assess species‐ and community‐level forage fish distribution patterns across the US Northeast Continental Shelf (NES) ecosystem. Aerial digital surveys gathered data on surface FFAs at two project sites within the NES, which we used in a spatially explicit hierarchical Bayesian model to estimate the abundance and size of surface FFAs. We used these models to examine the oceanographic drivers of forage fish distributions and aggregations. Our results suggest that, in the NES, regions of high community species richness are spatially consistent with regions of high surface FFA abundance. Bathymetric depth drove both patterns, while subsurface features, such as mixed layer depth, primarily influenced aggregation behavior and surface features, such as sea surface temperature, sub‐mesoscale eddies, and fronts influenced forage fish diversity. In combination, these models help quantify the availability of forage fishes to marine predators and represent a novel application of spatial models to aerial digital survey data.

54 ENVIRONMENTAL SCIENCES↗

Projected Seismic Activity at the Tiger Stripe Fractures on Enceladus, Saturn, From an Analog Study of Tidally Modulated Icequakes Within the Ross Ice Shelf, Antarctica

Abstract Dissipation of tidal energy is expected to generate seismicity on icy‐ocean worlds; however, the distribution and timing of this seismic activity throughout an orbital cycle is not known. We used new observations from an icy‐ocean‐world analog environment on Earth to examine the relationship between tidally driven tensile stress and seismic activity within an ice shell. We investigated a pair of rifts within Antarctica's Ross Ice Shelf which are tidally stressed in a manner analogous to the orbital cycle of tidal stress experienced by Enceladus' Tiger Stripe Fractures. We found that seismic activity at the Antarctic rifts is sensitive to both the amplitude and the rate of tensile stress across the rifts. We combined these findings with calculated stress values along Enceladus' Tiger Stripe Fractures to predict seismic‐activity levels expected along the ice‐shell fractures. We predict a peak in seismicity along the four Tiger Stripe Fractures when Enceladus is 90°–120° past pericenter in its orbit around Saturn, at which point tensile stresses would reach ∼2/3 of their maximum value. We also used the magnitude distribution of icequakes along Antarctic rifts to investigate implications for the likely size of stick‐slip rupture patches along icy faults on Enceladus. Our findings predict that the Tiger Stripe Fractures should produce sustained, low‐magnitude seismic events that involve rupture along discrete portions of each fracture's total length. We predict that seismicity would fall to 50% of peak levels when stresses across the Tiger Stripe Fractures are dominantly compressional.

Olsen, Kira G.↗

Carotenoid biomarkers in Namibian shelf sediments: Anoxygenic photosynthesis during sulfide eruptions in the Benguela Upwelling System

Significance Anoxygenic photosynthesis by phototrophic sulfur bacteria is prevalent in microbial mat ecosystems and in restricted, highly stratified aquatic environments. This limited distribution reflects their simultaneous requirements for an anoxic habitat, reduced sulfur to supply electrons for carbon fixation, and an appropriate light regime. Although these conditions were often satisfied in ancient seas, as shown by the distinctive carotenoid and chlorophyll pigments preserved in geological samples going back as far as 1.65 billion y, we can find no record of these organisms growing in today’s generally well-ventilated oceans. An array of carotenoids in sediments from the Namibian shelf suggests that green sulfur bacteria, despite their sensitivity to oxygen, can proliferate during episodic toxic gas eruptions in the Benguela Upwelling System.

Ma, Jian↗

Assessing the exposure of three diving bird species to offshore wind areas on the U.S. Atlantic Outer Continental Shelf using satellite telemetry

Abstract Aim The United States Atlantic Outer Continental Shelf (OCS) has considerable offshore wind energy potential. Capturing that resource is part of a broader effort to reduce CO 2 emissions. While few turbines have been constructed in U.S. waters, over a dozen currently planned offshore wind projects have the potential to displace marine birds, potentially leading to effective habitat loss. We focused on three diving birds identified in Europe to be vulnerable to displacement. Our research aimed to determine their potential exposure to areas designated or proposed for offshore wind development along the Atlantic OCS. Methods Satellite tracking technology was used to determine the spatial and temporal use and movement patterns of Surf Scoters ( Melanitta perspicillata ), Red‐throated Loons ( Gavia stellata ) and Northern Gannets ( Morus bassanus ), and calculate their exposure to each offshore wind area. We tagged 236 adults in 2012–2015 on the Atlantic OCS from New Jersey to North Carolina; an additional 147 birds tagged in previous tracking studies were integrated into our analyses. Tracking data were analysed in two‐week intervals using dynamic Brownian bridge movement models to develop composite spatial utilization distributions. For each species, these distributions were then used to calculate the spatio‐temporal exposure to each offshore wind area. Results Surf Scoters and Red‐throated Loons were exposed to offshore wind areas almost exclusively during migration because these species were distributed among coastal and inshore waters during winter months. In contrast, Northern Gannets ranged over a much larger area, reaching farther offshore and south in winter, thus exhibited the greatest exposure to extant offshore wind areas. Conclusions Results of this study provide better understanding of how diving birds use current and potential future offshore wind areas on the Atlantic OCS, and can inform permitting, risk assessment and pre‐ and post‐construction impact assessments of offshore energy infrastructure.

Stenhouse, Iain J.↗

Enhancing trap and fault seal analyses by integrating observations from HR3D seismic data with well logs and conventional 3D seismic data, Texas inner shelf

An understanding of trap and fault seal quality is critical for assessing hydrocarbon prospectivity. To achieve this, modern analytical techniques leverage well data and conventional industry-standard 3D seismic data to evaluate the trap, and any faults displacing the reservoir and top seal intervals. Above all, geological interpretation provides the framework of trap and fault seal analyses, but can be hindered by the data resolution, quality and acquisition style of the conventional seismic data. Furthermore, limiting the analysis to only the petroleum system at depth may lead to erroneous perceptions because interpreting overburden features, such as shallow faults or gas chimneys, can provide valuable observations with respect to container performance, and can to help validate trap and fault seal predictions. Here, a supplement to conventional 3D data are high-resolution 3D seismic (HR3D) data, which provide detailed images of the overburden geology. This study utilizes an HR3D seismic volume in the San Luis Pass area of the Texas inner shelf, where shallow fault tips and a sizeable gas chimney are interpreted over an unsuccessful hydrocarbon prospect. Static post-drill fault seal and trap analyses suggest that the primary fault displacing the structural closure could have withheld columns of gas c. 100 m high, but disagree with our HR3D seismic interpretations and dry-well analyses. From our results, we hypothesize that tertiary gas migration through fault conduits reduced the hydrocarbon column in the prospective Early Miocene reservoir, and may have resulted from continued movement along the intersecting faults. Overall, this study reinforces the importance of understanding the overburden geology and geohistory of faulted prospects, and demonstrates the utility of pre-drill HR3D acquisition when conducting trap and fault seal analyses.

3D seismic↗

A new mud shrimp of the genus Pugnatrypaea from outer continental shelf waters of the northern Gulf of Mexico, commonly associated with hydrocarbon seeps (Crustacea: Decapoda: Callianassidae)

A new species of callianassid mud shrimp is described from outer continental shelf waters of the northwestern Gulf of Mexico, where it appears to commonly live in close association with sediments on or near natural hydrocarbon seeps. Recent genus-level taxonomic revisions of the Callianassidae, based on gene sequence analyses and comparative morphological studies, included specimens representing this new species, assigning it with strong support to the genus Pugnatrypaea Poore et al., 2019. The other known species of this genus are also typically found in offshore waters of continental shelves, but are all restricted in distribution to the Indo-West Pacific and are known from relatively few specimens. Collections of this new Gulf of Mexico representative of the genus are all from slightly deeper waters than for other known congeners, and commonly occur near hydrocarbon seeps, on some occasions being directly associated with sulfidic substrates that include waxy crude oil globules.

Zoology↗

Improving Process Level Understanding of Boundary Layer Winds over the Northeast U.S. Shelf: The Third Wind Forecast Improvement Project (WFIP3)

The third Wind Forecast Improvement Project (WFIP3), a U.S. Department of Energy and National Oceanic and Atmospheric Administration sponsored investigation, sought to improve understanding of the physical phenomena in the atmosphere and ocean that dictate the structure and variability of wind and thermodynamic fields within the marine atmospheric boundary layer. WFIP3 focused on mesoscale and submesoscale flows -- including sea breezes, low-level jets, low-level clouds, and coastal storms -- and the ability of advanced numerical model parameterizations to represent them within fully coupled oceanic and atmospheric modeling systems and foundational weather forecast models. WFIP3 conducted a comprehensive 18-month observational study over the Northeast U.S. outer continental shelf, a high-use coastal zone, using a 3D multiscale sensor array to highly resolve the temporal, vertical, and horizontal structure of the coupled atmospheric and oceanic boundary layers. Multiple land-based study sites adjacent to the coastal ocean observed surface meteorology and vertical profiles of atmospheric properties via passive infrared and microwave radiometers, active lidars and radars, and radiosondes. At sea, an array of surface flux buoys and two vertical profiling lidar buoys observed both atmospheric and oceanic properties, augmented by land-based oceanographic radar systems and routine ship-based surveys. Intensive observations of the marine atmospheric boundary layer over the ocean was done from an air-sea interaction flux tower and extended deployments of a large autonomous barge platform. Numerous critical forecasting phenomena were observed that are being evaluated within regional coupled and uncoupled modeling systems, including the National Oceanic and Atmospheric Administration's foundational High-Resolution Rapid Refresh forecast model.

Kirincich, Anthony↗

Curing inhibition and shelf stability in silicone formulations for direct ink writing

Various potential hydrosilylation inhibitors were incorporated into a silicone formulation for 3D printing. Different inhibitors resulted in peak cure temperatures from 42.8 to 180.3°C. The curing behavior of formulations with 1-ethynyl-1-cyclohexanol (ETCH), which exhibited a peak cure temperature of 98.4°C, was characterized for different ETCH concentrations and storage conditions. The curing was modeled using time temperature superposition, revealing an activation barrier of 89 kJ/mol. Overall, characterization resulted in a conservative recommended shelf life of 90 days. In conclusion, these studies offer insights into the stability of these formulations and the importance of inhibition for producing reliable, printable inks.

36 MATERIALS SCIENCE↗

Turbulent controls on ice-shelf melting [PowerPoint]

The presentation discusses the fundamental gaps in our understanding of ocean turbulence below ice shelves and how they were addressed via Large-Eddy Simulations (LES) specifically tailored for ice-shelf settings.

58 GEOSCIENCES↗

Offshore Wind Resource Assessment for the California Pacific Outer Continental Shelf (2020)

This report presents a state-of-the-art wind resource data set produced by the National Renewable Energy Laboratory (NREL) for the California Pacific Outer Continental Shelf (OCS). This data set replaces NREL's Wind Integration National Dataset (WIND) Toolkit for the California OCS, which was produced and released publicly in 2013 and is currently the principal data set used by stakeholders for wind resource assessment in the continental United States.

17 WIND ENERGY↗

Use of Commercial Off-The-Shelf Parts with 3-D Printed Connectors for Powered Air Purifying Respirators

This report presents preliminary results from the performance evaluation of a powered air purifying respirator (PAPR) assembled from commercial off-the-shelf (COTS) parts. Cost is a major limiting factor to PAPR adoption in healthcare. Moreover, the lack of standardization for filters and batteries poses a challenge for clinics and hospitals. Rapid prototyping of connectors, both mechanical and electrical, offers a possible solution in addressing both issues. We used 3-D printed connectors to assemble COTS components into a prototype PAPR. Large-scale manufacturing of 3-D printed connectors may be accomplished by converting the computer-aided design (CAD) drawings to pressure-injection molds.

42 ENGINEERING↗

Causes of and Solutions to Wind Speed Bias in NREL's 2020 Offshore Wind Resource Assessment for the California Pacific Outer Continental Shelf

This report provides the results of a detailed analysis into the causes of high wind speed bias in the 20-year wind resource data set for offshore California the National Renewable Energy Laboratory (NREL) released in 2020, herein called CA20. The data set was developed using the state-of-the-art Weather Research and Forecasting (WRF) model. Notably, no floating lidars were available at the time in offshore California to validate offshore hub-height wind speeds. In late 2020, the Pacific Northwest National Laboratory (PNNL) deployed two floating lidars in the California outer continental shelf (OCS), near the Bureau of Ocean Energy Management (BOEM) call areas of Humboldt and Morro Bay. Using these observations through 2021, NREL found considerable bias in modeled hub-height winds at both locations: up to +2 m/s at Humboldt over a 6-month period, and up to +1 m/s at Morro Bay over a one-year period. Upon the discovery of this bias, the Department of Energy (DOE) and BOEM funded NREL and PNNL to investigate the causes of, impacts of, and solutions to the bias in the CA20 data set. This report summarizes the findings of this research. We first investigated whether different WRF model setups could lead to reduced bias. We found that the choice of planetary boundary layer (PBL) scheme - which controls the vertical turbulent mixing of momentum, heat, and moisture in the lowermost part of the atmosphere - greatly affected hub-height wind speeds in the region. Specifically, switching from the Mellor-Yamada-Nakanishi-Niino (MYNN) scheme used in CA20 (and widely used across a range of operational and research weather models) to the less common Yonsei University (YSU) scheme nearly eliminated the bias at both the Humboldt and Morro Bay lidar locations. The large discrepancy between the MYNN- and YSU-modeled hub-height winds pointed towards the role of atmospheric stability. In general, PBL schemes agree well in conditions of high turbulence and mixing, normally referred to as "unstable" conditions. By contrast, PBL schemes start to diverge in "stable" conditions, where turbulence is low and thermal stratification (i.e., higher temperature air sitting on top of colder air) greatly suppresses vertical mixing. Under such conditions, winds aloft can decouple from surface effects and greatly accelerate, causing high wind speeds at hub-height and frequent low-level jets (LLJs). We determined that these stable conditions are in fact dominant in offshore California. The region is characterized by moderate-to-extreme stable stratification with a LLJ on average around 200 meters above sea-level. To our knowledge, no wind energy area globally has as strongly stable stratification as offshore California. Under these extreme conditions, we determined that the MYNN scheme models higher stability than YSU, resulting in less vertical turbulent mixing than YSU, allowing for the acceleration of hub-height winds, more intense LLJs, and higher-amplitude inertial oscillations. Using surface observations, we found that MYNN overestimates near-surface stability, whereas YSU tends to model stability better. We then considered several short-term case studies to assess additional meteorological drivers of the bias at Humboldt. We found that during synoptic scale northerly flows driven by the North Pacific High and inland thermal low, a coastal warm bias in the MYNN case studies contributes to the modeled wind speed bias by altering the boundary layer thermodynamics via a thermal wind mechanism. Given the strong performance of the YSU-based runs in offshore California, NREL has produced and published an updated version of the CA20 data set with YSU as the PBL scheme. This updated data set is now part of NREL's 2023 National Offshore Wind (NOW-23) data set, which covers all the U.S. offshore waters. The development and final validation of the NOW-23 data set in offshore California is documented in this report.

17 WIND ENERGY↗

Statistical Framework for Planning a Shelf Life Program with Binary Performance Data

This document outlines a statistical framework for establishing a shelf-life program for components whose performance is measured by a binary response, usually ‘pass’ or ‘fail.’ The approach applies to both single measurement devices and repeated measurement devices. The high-level objective of these plans is to quickly detect any sizeable increase in fraction defective as the product ages. The statistical approach is to choose a sample size and monitoring technique that alarms when the fraction defective increases to an unacceptably high level, but does not alarm when the process is at nominal. The nominal (acceptable) fraction defective is used, and an increased fraction defective (unacceptable) is assumed as part of the control chart design. The control chart recommended for this problem is the Bernoulli Cumulative Sum (CUSUM) control chart.

97 MATHEMATICS AND COMPUTING↗