System reliability computation and estimation based on a cumulative damage–threshold–shock model

This article considers a reliability model where the failure is due to cumulative damage exceeding a threshold level. The concept that the threshold level of cumulative damage at each arrival of shock can change based on whether the magnitude of each shock exceeds its defined threshold level is considered to compute the system reliability.

The stochastic process approach is used to obtain the cumulative damage based on Poisson arrival of shocks. The general expression for reliability is obtained using the conditional probability over each arrival of shock. The method of maximum likelihood estimation is used to obtain the estimators of the parameters and system reliability. A sensitivity analysis is performed to measure the effect of the parameter representing the rate of arrival of shock.

The maximum likelihood estimates of the reliability approach the actual reliability for increasing sample size. A sensitivity analysis study on the parameter representing the rate of arrival of shock shows that as the values of parameter increase (decrease), the reliability value decreases (increases).

Obtained a new expression for the cumulative damage–shock model and the findings are positively supported by presenting the general trend of estimated values of reliability approaching the actual value of reliability. The sensitivity analysis also genuinely supports our findings.