Cryptographic accumulators are now fundamental for secure applications across blockchain, IoT, and big data, powering anonymous credentials, streamlining key management, and enabling efficient data filtering. However, existing accumulator methods, like RSA, bilinear pairing, and Merkle trees, are hampered by storage bloat, computational burdens, and reliance on trusted administrators. To solve these problems, we introduce a hash-chain-based ordered universal accumulator that eliminates these drawbacks. Our scheme uses collision-resistant hash functions to dynamically manage sets while providing strong, verifiable membership and non-membership proofs, all without a trusted administrator. The benefits include self-certification, batch verification, and consistent representation of accumulated sets. Testing shows our scheme cuts storage by roughly 50% compared to Merkle trees and significantly speeds up computation over RSA-based approaches. This lightweight and scalable solution is ideal for constrained environments like IoT and blockchain, unlocking wider decentralized application adoption.