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For the considered system, an enumeration method is applicable to evaluate the exact system reliability only for very small‐sized systems, because, when the size of system is large, it takes huge execution time. Therefore, the paper provides approximate values for the system reliability as useful for calculating the reliability of large systems in a reasonable execution time.

The paper provides upper and lower bounds of the system reliability, and limit theorem for the reliability of our considered system in i.i.d. case.

The paper experimentally finds that the proposed upper and lower bounds are effective when component reliabilities close to one or the value of k becomes larger. Next, it concludes approximate values for approximate equation derived from the limit theorem are always smaller than lower bound through numerical experiments.

The upper and lower bounds for the reliability of a system can be calculated by using the reliability of a small system by the same idea as previous study for two‐dimensional system.

Up to now some researchers studied multi‐dimensional consecutive‐k‐out‐of‐n:F systems, and showed promising applications of such multi‐dimensional models, e.g. diagnosis of a disease diagnosed by reading an X‐ray. As another examples, three‐dimensional system can be applied for the mathematical model of a three‐dimensional flash memory cell failure model, and so on.

The paper considers a kind of three‐dimensional k‐within‐consecutive‐r‐out‐of‐n:F system. It proposes upper and lower bounds of the system reliability and limit theorem.

This study aims to build on the well-documented case of the Olympus scandal to dissect how social networks and corporate culture enabled corporate elites to commit fraud across multiple generations of leaders.

A flexible pattern matching approach was used to identify matches and mismatches between behavioural theory in corporate governance and the patterns observed in data from diverse sources.

The study applies the behavioural theory of corporate governance from different perspectives. Social networks and relationships were essential for the execution of the fraud and keeping it secret. The group of corporate elites actively created opportunities for committing misappropriation. This research presents individuals committing embezzlement because the opportunity already exists, and they can enrich themselves. The group of insiders who committed the fraud elaborated the rationalizations to others and asked outside associates to help rationalise the activities, while usually individuals provide rationalizations to themselves only.

The social processes among actors described in this case can inform the design of mechanisms to detect these behaviours in similar contexts.

This study provides both perspectives on the fraud scandal: the one of the whistle-blowers, and the opposing side of the transgressors and their associates. The extant case studies on Olympus presented the timeframe of the scandal right after the exposure. The current study dissects the events during the fraud execution and presents the case in a neutral or a negative light.