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LABORE THE UNIVERSITY OF QUEENSLAND AUSTRALIA SCIENTIA AC ENGG 4103 Engineering Asset Maintenance and Management Practical No. 1 2024 Attach this to your submission. Case Study: Weibull distributions and Optimal Replacement Policies The largest optical telescope array in the world is the Very Large Telescope (VLT) array owned and operated by the European Southern Observatory and located on the 2,500 m peak of Cerro Paranal in the Atacama Desert in Chile. The array consists of four telescopes with 8 m diameter mirrors (see Fig 1). These telescopes produced the first direct images of planets outside of our solar system, weighed distant stars and have made important observations concerning black holes. The surface of each mirror has a curvature that has to be carefully controlled as the telescope track stars that are moving relative to the earth. To control this curvature, 64 hydraulic cylinders are mounted around the perimeter of each mirror, and 150 axial cylinders are mounted beneath. Fig. 1 ESO Telescope, Cerro Paranal 1 Fig.2 Base of 8 m mirror PART A In the attached file "Paranal_cylinder_replacements” you will find a list of the axial cylinders that were replaced during 2006. The data is classified as either a failure (F) or suspension (S) according to the nature of the replacement (suspensions refers to those components that are still in service at the time of analysis). It is required to fit a Weibull function to the failure data in order to determine the dominant failure mode of the cylinders. To do this you will have to: (i) (ii) (iii) (iv) An event is the name given to a failed or suspended item. Beginning by ordering all of the events by days of service in ascending order Determine the number of events, si (suspended items or failures) preceding each failure. (for the first event, so = 0) Create a new page by copying and pasting a copy of the current work page. On the new page, filter out all suspended items, leaving just failed items. List the failed components, i, ranked according to the hours of operation N+1-J Determine the mean rank ji, for each failure where: j₁ = ji-1 + N+1-S₁ where jo = 0. This is a way of taking into account the rank of each failed item given where it is located in the ordered list of all events (failed plus suspended items) (v) Calculate the median rank using: F(t) = J-0.3 N+0.4 This is the best (vi) (vii) estimate for the cumulative probability of failure F(t). Plot ln(ln(1/(1-F(t)) against ln(t-to), where to is the failure free time. Adjust a linear regression fit to the graph and vary to to obtain the best fit. Determine the shape factor, ẞ, from the gradient of the graph. (viii) Determine the scale factor, n = (-b/³) where b is the y intersect of the graph. Marking criteria: e 1 Mark - Discussion of use of Weibull curves for failure rate data 1 Mark – Inclusion of diagram showing Weibull failure rate curves for different ranges - of ẞ values 1 Mark - Inclusion of spreadsheet summarising results 2 Marks Correct estimations for Weibull parameters. 2 PART B (i) If the cost of performing a preventive replacement is C₁ = US$ 5,000 versus the cost of performing an unscheduled replacement Cf= US$ 20,000 calculate the interval at which the cylinders should be preventively replaced in order to optimise hourly operating costs. (Adapt the associated Excel file "Prac 1 optimal replacement”). Marking criteria 1 Mark - Brief inclusion of theory, including pdf graph 1 Mark - Inclusion of spreadsheet 1 Mark - inclusion of graph 1 Mark - Correct interpretation of replacement window. 1 Marks - neat, summarised report <4 pages in length plus spreadsheet appendices. Attach a copy of your working calculations Submit via Turnitin by 16:00 hrs on Friday 22nd March. Late penalty: zero marks in the absence of pre-approval from the course coordinator. P. F. Knights 15-03-2024. 3