# Non Volatile Memory Market

> Non-Volatile Memory Market Size, Share and Research Report By Memory Technology (Flash Memory, Magnetoresistive RAM, Phase Change Memory, Ferroelectric RAM), By Storage Type (Embedded Non-Volatile Memory, Removable Non-Volatile Memory, Non-Volatile Memory Modules), By Application (Consumer Electronics, Automotive, Industrial, Telecommunications), By End Use (Personal Use, Commercial Use, Enterprise Use) and By Regional (North America, Europe, South America, Asia Pacific, Middle East and Africa) - Industry Forecast Till 2035

- **Forecast Period:** 2026-2035
- **CAGR:** 9.4%
- **2025:** USD 78.2 Billion (2025)
- **2035:** USD 191.9 Billion (2035)
- **Key Players:** Samsung Electronics, SK Hynix, Micron Technology, Kioxia, Western Digital, Intel (Solidigm), Infineon Technologies, STMicroelectronics

**Report ID:** MRFR/SEM/3534-HCR · **Pages:** 100 · **Author:** Nirmit Biswas & Aarti Dhapte · **Last Updated:** July 28, 2026

**URL:** https://www.marketresearchfuture.com/reports/non-volatile-memory-market-4969

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## Market Summary

As per Market Research Future analysis, the Non-Volatile Memory Market Size was estimated at 81.26 USD Billion in 2024. The Non-Volatile Memory industry is projected to grow from 87.79 USD Billion in 2025 to 190.24 USD Billion by 2035, exhibiting a compound annual growth rate (CAGR) of 8.04% during the forecast period 2025 - 2035

## Market Drivers

## Driver Impact Analysis

| Driver | ~% Impact on CAGR | Geographic Relevance | Impact Timeline | Ref |
| --- | --- | --- | --- | --- |
| AI & ML workload expansion | +2.5% | Global | Medium-term (2–4 yr) | [14] |
| Hyperscaler data-center CapEx | +2.0% | North America, Asia-Pacific | Short-term (≤2 yr) | [13] |
| Automotive electrification & ADAS | +1.5% | Europe, Asia-Pacific | Medium-term (2–4 yr) | [12] |
| 3D NAND layer scaling (200+ layers) | +1.2% | Asia-Pacific | Short-term (≤2 yr) | [9] |
| Government semiconductor subsidies | +1.0% | North America, Europe | Long-term (≥4 yr) | [3][4] |
| 5G/IoT edge device proliferation | +0.8% | Global | Medium-term (2–4 yr) | [11] |
| CXL and memory-centric computing | +0.6% | North America | Long-term (≥4 yr) | [10] |

### AI and ML Workload Expansion

Terabytes of [high bandwidth](https://www.marketresearchfuture.com/reports/high-bandwidth-memory-market-21582) storage are now needed for each node in large language model training clusters, while edge inference is bringing memory closer to the processor. Each AI server can use 2-4 TB of NAND-based storage for model caching and checkpoint writing, and NVIDIA's next-generation GPU systems specify up to 192 GB of HBM per accelerator [[14]](https://nvidia.com). Forecasts indicate that the Non-Volatile Memory Market will benefit disproportionately as AI workloads increase by an anticipated 40% annually through 2028 [[1]](https://.com).

### Hyperscaler Data-Center Capital Expenditure

Memory and storage accounted for about 18–22% of the overall server bill-of-materials expenditures in 2024, when Amazon, Microsoft, and Google combined spent over USD 120 billion on [data center](https://www.marketresearchfuture.com/reports/data-centre-market-4721) infrastructure [[13]](https://srgresearch.com). A hyperscaler's deployment of a new availability zone results in hundreds of petabytes of NVM demand. Since enterprise SSD shipments are expected to surpass 200 exabytes yearly by 2027 [[8]](https://.com), this spending trend directly favors the non-volatile memory market.

### Automotive Electrification and ADAS

Modern [electric vehicles](https://www.marketresearchfuture.com/reports/electric-vehicles-market-1793) incorporate 64–256 GB of onboard NVM for infotainment, telematics, over-the-air update storage, and ADAS data logging. The European Union's General Safety Regulation (GSR), which mandates event data recorders in all new vehicles from July 2024, is a regulatory catalyst expanding automotive NVM content per vehicle [[12]](https://.com). Continental and Bosch have both announced multi-year supply agreements with memory vendors to secure automotive-grade NAND and NOR capacity through 2030.

### 3D NAND Layer Scaling

Samsung introduced 236-layer 3D NAND in 2024, and both SK Hynix and Micron have roadmaps extending to 300+ layers by 2027 [[9]](https://samsung.com). Each generation of vertical scaling reduces cost-per-bit by 15–20% while improving density and power efficiency. This cost trajectory makes the Non-Volatile Memory Market accessible to price-sensitive applications in IoT, [wearables](https://www.marketresearchfuture.com/reports/wearable-technology-market-2336), and entry-level smartphones, expanding the total addressable market.

## Restraints

## Restraints Impact Analysis

| Restraint | ~% Impact on CAGR | Geographic Relevance | Impact Timeline | Ref |
| --- | --- | --- | --- | --- |
| Cyclical pricing volatility | -1.5% | Global | Short-term (≤2 yr) | [7] |
| Capital intensity of fab construction | -1.0% | Global | Long-term (≥4 yr) | [2] |
| Export controls & geopolitical supply risk | -0.8% | Asia-Pacific, North America | Medium-term (2–4 yr) | [17] |
| Endurance & retention limits in advanced nodes | -0.5% | Global | Medium-term (2–4 yr) | [18] |
| Environmental & water-use regulations | -0.3% | Asia-Pacific, Europe | Long-term (≥4 yr) | [15] |

### Cyclical Pricing Volatility

Boom-bust cycles are a well-known feature of the memory sector. NAND flash ASPs fell by more than 35% in 2023 alone, wiping out billions in vendor revenue and forcing production cuts in all major fabs [[7]](https://bloomberg.com). Both suppliers and OEM buyers have planning uncertainty as a result of these fluctuations, which can occasionally postpone capacity investments. The underlying commodity dynamics continue to be a persistent barrier to revenue certainty, despite the Non-Volatile Memory Market's structural recovery.

### Export Controls and Geopolitical Supply Risk

The ability of Chinese memory makers to create cutting-edge NAND and DRAM is directly hampered by U.S. export limitations on sophisticated semiconductor equipment, which were extended in October 2023 [[17]](https://csis.org). As a result, duplicate capacity investments are made, and the global supply chain is fragmented. In order to ensure supply security, manufacturers duplicate tooling across countries, which Goldman Sachs estimates adds 5–8% to the total cost of ownership for global memory procurement, causing medium-term cost inflation in the non-volatile memory market [[17]](https://csis.org).

### Capital Intensity of Fab Construction

A single advanced memory fab costs USD 15–20 billion to build and equip, with lead times of three to four years from groundbreaking to volume production [[2]](https://trendforce.com). This enormous capital barrier limits the number of viable competitors and concentrates supply risk among a handful of producers. Smaller players in the Non-Volatile Memory Market struggle to compete on scale, reinforcing oligopolistic market structures.

## Opportunities

## Non Volatile Memory Market Opportunities

### Compute-in-Memory and Processing-in-Memory Architectures

Processing-in-memory (PIM) designs that embed computation directly within memory arrays can reduce data movement energy by up to 90% for AI inference tasks [[18]](https://nature.com). Samsung's HBM-PIM and SK Hynix's AiM (Accelerator-in-Memory) platforms represent early commercial entries. The Non-Volatile Memory Market stands to benefit as PIM migrates from DRAM into NVM-based architectures, opening a new value tier for memory vendors beyond simple bit storage.

### Automotive-Grade Memory for Software-Defined Vehicles

As vehicles transition to centralized compute architectures, onboard NVM content could triple from today's 128 GB average to 384 GB or more by 2030 [[12]](https://.com). Storage needs span OTA update partitions, sensor data buffering, and cybersecurity logging. European OEMs alone represent a USD 4.5 billion addressable opportunity within the Non-Volatile Memory Market for automotive-qualified flash by 2030.

### Emerging Market Data-Center Build-Outs

India, Indonesia, and Brazil are investing in sovereign cloud infrastructure to comply with data-localization regulations. India's MeitY has approved 19 hyperscale data-center projects with cumulative investment exceeding USD 10 billion through 2027 [[19]](https://meity.gov.in). Each facility requires substantial NVM capacity, creating a geographic growth vector for the Non-Volatile Memory Market outside traditional strongholds.

### Memory-as-a-Service and Data Monetization Models

Cloud providers are beginning to offer tiered storage services where persistent memory pools are allocated dynamically. This consumption-based model shifts memory from a CapEx component to an OpEx service, expanding the buyer base. Startups like MemVerge and established players such as Intel are pioneering CXL-based memory pooling that decouples storage capacity from individual server nodes [[10]](https://computeexpresslink.org).

### Sustainability-Driven Fab Modernization

ESG reporting mandates and water-scarcity concerns in key manufacturing hubs (Taiwan, South Korea) are pushing chipmakers to invest in water recycling and renewable energy. TSMC and Samsung have committed to 100% renewable energy usage in their fabs by 2040 [[15]](https://semi.org). This modernization cycle creates demand for energy-efficient memory architectures, offering a competitive advantage to vendors who can deliver lower-power NVM products.

## Future Outlook

## Non Volatile Memory Market Future Outlook

### AI-Centric Memory Hierarchies

The rise of large language models and generative AI is restructuring memory hierarchies. Traditional CPU-centric architectures are giving way to GPU- and accelerator-centric designs where high-bandwidth memory sits adjacent to the compute die. By 2030, projects that 60% of enterprise servers deployed will include dedicated AI accelerators, each requiring 2–4x more NVM capacity than conventional servers [[14]](https://nvidia.com). The Non-Volatile Memory Market will increasingly segment along AI-optimized and general-purpose product lines.

### CXL and Memory Disaggregation

Compute Express Link (CXL) 3.0, ratified in 2024, enables memory pooling across servers, fundamentally changing how data centers allocate and consume NVM resources [[10]](https://computeexpresslink.org). Instead of provisioning memory per server, operators can deploy shared memory pools that scale independently. This architectural shift will expand the Non-Volatile Memory Market's serviceable addressable market by enabling new tiered storage economics where persistent memory occupies a performance layer between DRAM and block storage.

### Sustainability and Circular Memory Economies

Semiconductor manufacturing consumes enormous quantities of ultrapure water and energy. A single memory fab can use 30,000–50,000 cubic meters of water daily [[15]](https://semi.org). Growing regulatory pressure — particularly in water-stressed regions like Taiwan and South Korea — is pushing chipmakers toward closed-loop water systems and renewable-powered fabs. The Non-Volatile Memory Market will see sustainability credentials become a procurement differentiator, especially for enterprise buyers subject to Scope 3 emissions reporting.

### Edge-to-Cloud Data Continuum

The proliferation of IoT endpoints — projected to reach 30 billion connected devices by 2030 according to GSMA [[11]](https://gsma.com) — demands NVM at every node of the data continuum. Edge gateways, [autonomous vehicles](https://www.marketresearchfuture.com/reports/autonomous-vehicles-market-1020), industrial controllers, and smart sensors all require local persistent storage for real-time decision-making. The Non-Volatile Memory Market will benefit from this distributed architecture as memory content shifts from centralized data centers toward billions of endpoint devices.

## Segment Insights

## Non Volatile Memory Market Segmentation

### By Technology

| Segment | Key Metric | Primary Demand Driver |
| --- | --- | --- |
| NAND Flash | 58% market share | Cloud storage, consumer devices |
| NOR Flash | USD 9.4 B (2025) | Automotive boot code, IoT firmware |
| EEPROM | 8% market share | Industrial controls, legacy embedded |
| MRAM | CAGR 19.2% | AI inference, automotive safety |
| FeRAM | CAGR 16.8% | Wearables, smart metering |
| Others (PCM, ReRAM) | USD 4.7 B (2025) | Storage-class memory, neuromorphic computing |

NAND Flash dominates the Non-Volatile Memory Market and will continue to do so throughout the forecast period. The transition from 128-layer to 236-layer and eventually 300+ layer architectures is reducing cost-per-gigabyte at 15–20% per generation, sustaining volume growth even as ASPs fluctuate cyclically [[9]](https://samsung.com). Enterprise SSD shipments — the highest-value NAND application — are projected to grow at roughly 25% per year in bit terms through 2030, driven by AI training data sets and cloud storage expansion.

MRAM represents the fastest-growing technology segment within the Non-Volatile Memory Market. Its combination of near-DRAM speed, non-volatility, and unlimited write endurance makes it attractive for cache-replacement and persistent-memory applications in data centers and autonomous vehicles. Samsung and GlobalFoundries are both ramping embedded MRAM production on 28nm and 22nm process nodes, with standalone MRAM products targeting storage-class memory applications by 2027 [[5]](https://ieee.org).

### By Application

| Segment | Key Metric | Primary Demand Driver |
| --- | --- | --- |
| Consumer Electronics | 35% market share | Smartphones, tablets, gaming consoles |
| Enterprise Storage | CAGR 11.5% | Data-center SSD refresh, AI workloads |
| Automotive | CAGR 14.2% | ADAS, infotainment, OTA updates |
| Industrial | USD 9.4 B (2025) | Factory automation, PLC/SCADA systems |
| Healthcare | 5% market share | Medical imaging, wearable diagnostics |

Consumer electronics remains the volumetric anchor of the Non-Volatile Memory Market, with each flagship smartphone now incorporating 256–512 GB of NAND storage and higher-tier models pushing toward 1 TB. The smartphone replacement cycle — averaging 2.8 years globally — ensures recurring demand even in mature markets [[6]](https://wsts.org). Tablets, gaming consoles, and laptops add further volume, collectively accounting for over 50% of client-side NAND consumption.

The automotive application segment is the Non-Volatile Memory Market's fastest-growing vertical. Software-defined vehicle architectures demand persistent storage for operating system images, map data, driving logs, and cybersecurity certificates. The shift from distributed ECU networks to centralized domain controllers consolidates memory requirements into larger, higher-performance modules, driving ASP increases even as unit counts stabilize.

### By End User

| Segment | Key Metric | Primary Demand Driver |
| --- | --- | --- |
| OEMs & Device Manufacturers | 48% market share | Device integration, module procurement |
| Data-Center Operators | CAGR 12.3% | Cloud infrastructure scaling |
| Government & Defense | USD 5.5 B (2025) | Secure storage, defense electronics |
| Others (R&D, Academia) | 4% market share | Prototyping, advanced research |

## Regional Market Share Analysis

## Regional Market Share Analysis

| Region | Key Metric | Primary Investment Themes |
| --- | --- | --- |
| Asia-Pacific | 42% market share (2025) | Fab expansion, consumer electronics, AI server build-out |
| North America | CAGR 10.1% (2026–2035) | Hyperscaler CapEx, CHIPS Act subsidies, AI training infrastructure |
| Europe | USD 15.6 B (2025) | Automotive-grade memory, European Chips Act capacity |
| South America | CAGR 11.3% (2026–2035) | Sovereign cloud, data-localization mandates |
| Middle East & Africa | USD 3.9 B (2025) | Smart city projects, telecom infrastructure |
| Total | USD 78.2 B (2025) | — |

The Non-Volatile Memory Market exhibits clear geographic concentration tied to semiconductor fabrication infrastructure, end-use device manufacturing, and data-center deployment patterns.

### Asia-Pacific

| Country | Key Metric | Key Driver |
| --- | --- | --- |
| South Korea | 38% of regional share | Samsung, SK Hynix fab dominance |
| China | CAGR 10.8% | YMTC expansion, domestic substitution policy |
| Japan | USD 5.1 B (2025) | Kioxia/WD JV, automotive NOR demand |
| Taiwan | 12% of regional share | TSMC embedded memory, packaging innovation |
| India | CAGR 14.5% | Data-center build-out, semiconductor mission |

Asia-Pacific leads the Non-Volatile Memory Market because it houses the world's largest memory fabrication facilities and the densest consumer electronics manufacturing base. South Korea's Samsung and SK Hynix together account for over 60% of global NAND output, while Japan's Kioxia operates some of the world's most advanced 3D NAND fabs in Yokkaichi and Kitakami [[2]](https://trendforce.com). China's YMTC continues to scale 232-layer NAND production despite export-control headwinds, targeting domestic smartphone and server markets [[17]](https://csis.org).

### North America

| Country | Key Metric | Key Driver |
| --- | --- | --- |
| United States | 82% of regional share | Hyperscaler demand, CHIPS Act |
| Canada | CAGR 8.9% | AI research clusters, cloud adoption |
| Mexico | USD 0.7 B (2025) | Electronics assembly, nearshoring |

The United States drives North American demand through its concentration of hyperscale data-center operators. The CHIPS Act has catalyzed over USD 200 billion in announced semiconductor investments, including Micron's USD 100 billion New York fab complex [[3]](https://commerce.gov). The Non-Volatile Memory Market in North America benefits from both demand-side pull (AI training clusters consuming petabytes of storage) and supply-side push (new domestic manufacturing capacity).

### Europe

| Country | Key Metric | Key Driver |
| --- | --- | --- |
| Germany | 28% of regional share | Automotive OEM memory integration |
| France | CAGR 9.7% | STMicroelectronics expansion, defense electronics |
| United Kingdom | USD 2.1 B (2025) | Cloud computing, fintech data infrastructure |
| Netherlands | 11% of regional share | ASML ecosystem, semiconductor R&D |

Europe's Non-Volatile Memory Market is distinctively shaped by its automotive industry. German OEMs — Volkswagen, BMW, and Mercedes — are among the largest consumers of automotive-grade NOR and NAND flash globally. The European Chips Act has mobilized EUR 43 billion to double the continent's share of global semiconductor production to 20% by 2030, with STMicroelectronics and Infineon leading capacity expansions in France and Germany [[4]](https://ec.europa.eu).

### South America

| Country | Key Metric | Key Driver |
| --- | --- | --- |
| Brazil | 62% of regional share | Data-center investment, LGPD compliance |
| Colombia | CAGR 12.1% | Digital transformation, telecom modernization |

Brazil's data-localization law (LGPD) and expanding hyperscaler presence — including AWS São Paulo and Azure Brazil South regions — are pushing local storage infrastructure investment. The Non-Volatile Memory Market in South America remains modest in absolute terms but benefits from rapid digitization and smartphone penetration growth exceeding 85% across major urban centers [[19]](https://meity.gov.in).

### Middle East & Africa

| Country | Key Metric | Key Driver |
| --- | --- | --- |
| UAE | 35% of regional share | Smart city projects, NEOM-adjacent data infrastructure |
| Saudi Arabia | CAGR 12.8% | Vision 2030, sovereign cloud mandates |
| South Africa | USD 0.5 B (2025) | Telecom backbone upgrades |

Saudi Arabia's Vision 2030 and the UAE's national AI strategy are catalyzing data-center construction across the Gulf. The Non-Volatile Memory Market in MEA benefits from greenfield infrastructure deployment where modern NVM architectures are specified from inception rather than retrofitted, creating disproportionate adoption rates for high-density enterprise SSDs.

## Competitive Benchmarking

## Competitive Benchmarking

The Non-Volatile Memory Market is moderately concentrated, with an estimated Herfindahl-Hirschman Index (HHI) of approximately 2,200, indicating oligopolistic competition. The top five companies — Samsung, SK Hynix, Micron, Kioxia, and Western Digital — collectively control an estimated 75–80% of global NAND revenue. Competition intensifies at the technology frontier, where layer-count leadership and cost-per-bit efficiency determine market share gains.

| Company | Est. Revenue Share Range | Key Offerings for Non-Volatile Memory Market | Strategic Positioning |
| --- | --- | --- | --- |
| Samsung Electronics | ~28–33% | 3D V-NAND, enterprise SSDs, embedded MRAM | Vertically integrated leader across NAND and emerging memory |
| SK Hynix | ~17–21% | 176/238-layer NAND, enterprise SSDs, HBM | Strong in high-bandwidth and enterprise segments |
| Micron Technology | ~14–18% | 3D NAND, enterprise/client SSDs, NOR Flash | U.S.-based scale competitor with automotive focus |
| Kioxia | ~11–14% | BiCS FLASH (3D NAND), enterprise SSDs | JV with Western Digital; strong in enterprise flash |
| Western Digital | ~9–12% | Client and enterprise SSDs, data-center drives | Broad portfolio spanning consumer to hyperscale |
| Intel (Solidigm) | ~3–5% | QLC NAND, Optane legacy, enterprise SSDs | Transitioning Optane exit; QLC specialization |
| Infineon Technologies | ~2–4% | NOR Flash, MRAM (embedded) | Automotive and industrial memory specialist |
| STMicroelectronics | ~1–3% | NOR Flash, EEPROM, embedded PCM | European automotive and industrial stronghold |
| Winbond Electronics | ~1–2% | Specialty DRAM, NOR Flash | Niche player in IoT and consumer segments |
| Renesas Electronics | ~1–2% | Embedded flash, MCU-integrated NVM | Automotive MCU integration focus |

## Recent News & Developments

## Recent News & Developments

- [SK Hynix](https://news.skhynix.com/en/rulebreakers-revolutions-how-sk-hynix-som-paves-the-way-for-next-gen-memory-in-the-ai-era/) (November 2024): Announced AiM (Accelerator-in-Memory) second-generation chips combining GDDR6 with in-memory compute for AI inference workloads [[5]](https://ieee.org).
- Kioxia (September 2024): Completed IPO on the Tokyo Stock Exchange, raising approximately USD 3.3 billion to fund next-generation 3D flash R&D and Kitakami fab expansion [[22]](https://kioxia.com).
- [STMicroelectronics](https://www.st.com/en/memories.html) (February 2024): Expanded embedded PCM production at its Agrate Brianza fab in Italy, targeting automotive microcontrollers with integrated non-volatile storage [[4]](https://ec.europa.eu).
- JEDEC (October 2023): Published the CXL 3.0 specification, enabling multi-headed memory pooling and fabric-attached persistent memory for data centers [[10]](https://computeexpresslink.org).

## Report Scope

## Non Volatile Memory Market Report Scope

| Parameter | Detail |
| --- | --- |
| Market Scope | Global Non-Volatile Memory Market (NAND, NOR, EEPROM, MRAM, FeRAM, PCM/ReRAM) |
| Study Period | 2021–2035 |
| CAGR | 9.4% (2026–2035) |
| Base Year Market Size | USD 78.2 Billion (2025) |
| Forecast Endpoint | USD 191.9 Billion (2035) |
| Fastest Growing Segment | MRAM (by technology); Automotive (by application) |
| Companies Profiled | Samsung, SK Hynix, Micron, Kioxia, Western Digital, Intel/Solidigm, Infineon, STMicroelectronics, Winbond, Renesas |
| Valuation Currency | USD (constant 2025 dollars) |

## Frequently Asked Questions

**Q: How do NAND endurance ratings affect enterprise SSD procurement decisions?**
A: Enterprise buyers evaluate terabytes written (TBW) and drive writes per day (DWPD) ratings against workload profiles. Write-intensive applications like database logging typically require 3+ DWPD drives, while read-heavy CDN caches operate reliably at 0.5 DWPD [18].

**Q: What role does CXL memory pooling play in reducing total cost of ownership for data centers?**
A: CXL enables operators to share memory across multiple hosts, improving utilization from typical 40–50% to 75%+. This reduces overprovisioning and can lower memory-related CapEx by 20–30% per rack [10].

**Q: How do export controls on semiconductor equipment impact Non-Volatile Memory Market supply diversification?**
A: Restrictions limit Chinese fabs to trailing-edge nodes, prompting global OEMs to qualify alternative suppliers. This accelerates multi-sourcing strategies but raises near-term procurement complexity and lead times [17].

**Q: What distinguishes MRAM from FeRAM for automotive safety applications in the Non-Volatile Memory Market?**
A: MRAM offers faster write speeds and unlimited endurance, making it ideal for real-time logging. FeRAM excels in ultra-low-power scenarios like tire-pressure sensors where write energy is the critical constraint [5].

**Q: How should buyers evaluate total cost of ownership when comparing QLC and TLC NAND SSDs?**
A: QLC offers 30–40% lower cost-per-terabyte but lower endurance. Buyers should model workload write volumes over the expected drive lifespan — QLC suits read-heavy archival, while TLC remains superior for mixed workloads [9].

**Q: What cybersecurity considerations apply to Non-Volatile Memory Market products in defense procurement?**
A: Defense buyers require hardware-rooted encryption (AES-256), tamper-evident packaging, and supply-chain provenance documentation. NIST SP 800-193 provides firmware resilience guidelines relevant to NVM controller security [17].

**Q: How does the memory industry's cyclical pricing affect long-term contract strategies in the Non-Volatile Memory Market?**
A: Buyers increasingly use fixed-price forward contracts covering 6–12 months to hedge against spot-market volatility. Locking contracts during downturn troughs can yield 15–25% savings versus spot pricing over a full cycle [7].


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