{'fraction_non_alphanumeric': 0.013029315960912053, 'fraction_numerical': 0.004343105320304018, 'mean_word_length': 4.691358024691358, '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}}
On information-based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module

The first part of this paper is inspired by a somewhat surprising result in Arjas and Norros (1989). Here we give some results comparing remaining system lifetime just after a ‘black box' minimal repair of a system and after a natural minimal repair based on information on the component level. In the second part we consider the reduction in remaining system lifetime due to the failure of a specific module and explore the relation to the reduction in remaining system lifetime due to the failure of a component inside the module. This former reduction also equals the increase in remaining system lifetime due to a minimal repair of the module at its time of failure. The expected value of this reduction/increase is proportional to the so-called Natvig measure of the importance of the module.