{'fraction_non_alphanumeric': 0.015432098765432098, 'fraction_numerical': 0.0, 'mean_word_length': 5.555555555555555, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Note on reliabilities of parallel system with cascading failure

This paper considers an extended Parallel System with Cascading Failure: compared with the conventional parallel system with independent failure, the factor that cascading failure could reduce reliability of the system due to redistribution of the workload. Reliability measures of this model are derived, using the theory of stochastic process. To counteract the impact of cascading failure, a preventive maintenance policy is put forward into this paper. Optimal maintenance policy which minimizes the expected cost is derived. Finally, some examples and some discussions are made.