Modeling a sequentially inspected system prone to degradation and shocks

Purpose: In certain environments, the system may not fail completely, but undergoes degradation, and the system productivity might decrease. Meanwhile, at the same time, the system may be vulnerable to shocks. A single-unit system prone to degradation and shocks is proposed in this study, and emphasis is placed upon determining its availability and cost rate. Design/methodology/approach: The considered single-unit system is expected to have three states, namely, normal, degraded and failed. As the system enters the degraded state, it is said to be partially failed. The degraded state incurs higher degradation than the normal state and is more prone to shocks. Inspections are used to determine the state and failure type of the system. Inspections are predetermined to be carried out sequentially at time <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>I</m:mi><m:mo>,</m:mo><m:mo> </m:mo><m:mi>I</m:mi><m:mo>+</m:mo><m:mi>a</m:mi><m:mi>I</m:mi><m:mo>,</m:mo><m:mo> </m:mo><m:mi>I</m:mi><m:mo>+</m:mo><m:mi>a</m:mi><m:mi>I</m:mi><m:mo>+</m:mo><m:msup><m:mi>a</m:mi><m:mn>2</m:mn></m:msup><m:mi>I</m:mi><m:mo>,</m:mo><m:mo>…</m:mo></m:mrow></m:math> where 0 < a ≤ 1, until the detection of degradation/failure. Perfect repairs are conducted instantly on spotting the partial/complete failure. Two cases have been considered of repair taking constant times and random times. Findings: Explicit results on the reliability, availability (both point and limiting availability) and long-run average cost rate (LRACR) of a sequentially inspected single-unit system prone to degradation and shocks under constant and random repair times are given. Numerical example of an oil pipeline system is taken to clarify the acquired results. Originality/value: A sequentially inspected single-unit system prone to degradation and shock is studied unlike done previously.