Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies: Erlang time-to-failure distribution

Abstract

This article deals with a new redundancy allocation model for non-repairable series-parallel systems with multiple strategy choices. The proposed model simultaneously determines the type of components, number of active and standby components to maximize system reliability subject to design constraints. Traditionally, due to complexity and difficulty in obtaining the closed form version of system reliability, a convenient lower-bound on system reliability has been widely applied to approximate it. Assuming that switching mechanism time-to-failure is exponentially distributed, the closed form version of the reliability of subsystems with cold standby redundancy is derived analytically for the first time. This is successfully performed using Markov process and solving the relevant set of differential-difference equations. With respect to the obtained formulation, a semi-analytical expression for the reliability of subsystems with mixed redundancy strategy is also extracted. Component time-to-failure is assumed to follow an Erlang distribution which is suitable for most engineering design problems. The presented model is linear and in the form of standard zero-one integer programs and thus using integer programming algorithms guarantees optimal solutions. The computational results of solving a well-known example indicate the high performance of the proposed model in improving system reliability.

Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies and heterogeneous components: Erlang time-to-failure distribution

“…First, assuming that component time-to-failure is distributed according to an Erlang distribution and switch failure time is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. It should be mentioned that this closed-form formula was previously obtained in the work of Sadeghi and Roghanian 58 by defining a continuous-time Markov chain (CTMC) and solving the relevant system of differential-difference equations. This equation is also validated by evaluating a convolution integral analytically.…”

“…Therefore, maximizing system reliability approximation is not a useful and efficient surrogate for maximizing precise system reliability specifically in high reliability applications where system failure may cause irreparable damages. Addressing the mentioned drawback, Sadeghi and Roghanian 58 formulated the RAP of non-repairable series-parallel systems as a 0–1 integer linear programming (ILP) problem with the consideration of either active, cold standby or mixed redundancy strategy for each subsystem.…”

“…Although the mathematical model proposed by Sadeghi and Roghanian, 58 maximizes exact system reliability instead of its approximation, it has a limiting assumption on the basis that all components of a subsystem must be identical. This assumption restricts the solution space and thereby prevents achieving higher levels of system reliability.…”

Application of power law model in reliability evaluation of machine tools by considering working condition difference

“…At present, there are many models to evaluate the reliability of NC machine tools. Assuming that time between failures (TBF) of NC machine tools is independently and identically distributed, the model to evaluate their reliability mainly includes Weibull, log‐normal, exponential, gamma, and inverse gaussian processes . However, the opposite is true in actual situations .…”

The evolution of system reliability optimization

“…combining both active and cold-standby components within the same subsystem. Other recent meaningful system reliability optimization research considering mixed component redundancy have provided important models for more varied and practical applications[88][89][90]. There have also been multiple objective formulations to the problem with different redundancy types[91,92].More recently, other different redundancy strategies or types of problems have been considering including the standby element sequencing problem and the combined sequencing and inspection/checkpointing/allocation policy optimization for different types of standby (hot,A C C E P T E D M A N U S C R I P Tcold, warm, mixed).…”