# Decision Problem on Imperfect Inspections Combined under Two-Stage Inspection Policy
## 4 Applicability of Two-Stage Inspection Policy to Piston Seal Diagnosing in Hydraulic Cylinder  
### Failure Process and Inspection Methods  
To illustrate the results of the potential application of the proposed two-stage inspection policy, an example of inspections of internal sealing condition, placed on a piston in a hydraulic cylinder, is presented. The case study concerns hydraulic cylinders installed in a group of loaders operating in a Polish mine. The degradation process of a seal can be divided into two phases [42; 43]: (1) the phase of normal operation during which the sealing material has its desired features, (2) the defective state starting from the moment when material characteristics worsen rapidly, for example, due to increased fluid temperature, the aging process, excessive system pressure, wear, etc. The defective state is estimated to be rapid and finally ends with the leakage and total degradation of sealing material leading to further contamination of the hydraulic fluid with particles, which increases the 'rate of wear mechanisms such as abrasive wear, scoring of moving parts, adhesive wear, fatigue wear, and corrosion of hydraulic cylinder parts' [43] (p. 1). Finally, such a defect can exclude a cylinder and the entire machine with the cylinder from operation or even cause a danger situation due to the lack of ability to maintain operation parameters of a cylinder. This moment is understood in this study as a failure. Usually, predictive sealing diagnosis is limited in practice to periodic inspections of visible leakages in an actuator. However, if maintenance staff want to diagnose the condition of a piston seal, which is hidden inside a cylinder, it is not possible to observe leakages. There are numerous methods that have been developed to diagnose an internal leakage in an actuator; however, most of them are not available commercially [43] and are not provided to diagnose sealing degradation before the leakage starts. Observations of practice in the mining industry let one to identify a few methods that could be used to conclude whether a state of internal seal of the cylinder is good or defective. There are, among others, operators' 'feeling' of how the machine with a cylinder works, the periodic measurement of the energy consumption by a machine in which a cylinder is installed, the temperature measurement of the cylinder surface, the temperature measurement of hydraulic oil in the system, the measurement of the oil pressure generated when working (if special equipment is provided in a cylinder) or disassembly of a cylinder and detailed visual inspection of its seal. Only the last method is that which directly tests the diagnosed seal, while the rest can only indicate premises of the seal degradation and are imprecise. They can diagnose a defect that actually does not exist as well as not diagnose an existing defect. However, due to the high cost and time loss when disassembling the cylinder, the direct diagnosis method is never used for planned inspections, unless on occasion of other maintenance activities which require disassembly. Instead of the direct method, which is almost perfect, other testing methods can be applied. However, the question is: which methods should be applied and how frequently, if they are imprecise. For the purposes of this example, only a few of the mentioned methods are chosen for comparison. They are chosen because they are available for every cylinder without any additional equipment provided structurally.