Optimal reliability and upgrading decisions for capital goods

Advanced technical systems, also called advanced capital goods (e.g. medical systems, material handling systems, defense systems, manufacturing systems, packaging lines, computer networks) are used in core processes by their users. By core processes, we mean the processes which are essential for operational continuity. For example, baggage handling at airports, transactions in a bank, data processing in a computer network, can be considered as core processes. Operational interruptions of these systems lead to significant losses for the users and keeping the systems up and running (availability of the systems) is crucial. A high level of system availability can be provided by maintaining • a low frequency of system failures, and/or • a high speed of system repair activities (short downtime per system failure). The frequency of failures of a system depends heavily on its design. The focus of this thesis is on two major design decisions in this context: (i) reliability of components that compose the system, and (ii) redundancy (i.e., having a number of identical components in parallel instead of a single component). We refer to these decisions as reliability decisions. The speed of system repair is commonly accelerated by using the repair-by-replacement concept during the exploitation phase. That is, if a part fails and leads to a system failure, the system is restored by replacing the failed part with a ready-for-use one. Spare parts are kept on stock at a short distance of the installed systems to prevent long downtimes. For a fixed system design, the spare parts inventory level is a key factor affecting the system availability. We take the spare parts inventory into account when investigating the optimal reliability decisions. The primary goal of this thesis is to develop quantitative models and methods for optimal reliability decisions in the design phase. In Chapter 2 and 3, we study the optimal reliability level of a critical component and the redundancy optimization for serial systems, respectively. Typically, Original Equipment Manufacturers (OEMs) of capital goods are responsible for the availability of their systems in the field through service contracts. OEMs redesign components that fail too often and therefore have a strong negative effect on availability. It is then economical to improve the reliability of those components and upgrade the systems by replacing the old parts in the field with the redesigned ones. After the redesign, there are multiple policies that can be followed by an OEM for upgrading the systems. In Chapter 4, we study two common upgrading policies and investigate their optimality. In Chapter 1 and 5, an introduction and the conclusions are given. In Appendix A, we provide several results for the Erlang loss system which are motivated by the problem studied in Chapter 2. In Chapter 2, we develop a model for the optimization of the reliability level of a critical component. In this model, portions of the Life Cycle Costs (LCC -total costs incurred throughout the lifetime of systems) of a general number of systems that are affected by component reliability and the spare parts inventory level are formulated. We develop an efficient solution procedure for the problem. By conducting a numerical experiment, we show that taking the spare parts inventory level into account for the optimization of component reliability in the design phase lead to significant cost reductions compared to solutions generated by sequential consideration the component reliability and the spare parts inventory level. The results of the experiment also reveal that the optimal component reliability is much higher for a cheap component than for an expensive component and increases as the number of the systems increases, the downtime penalty rate increases; and, the exploitation phase gets longer. We also show that the optimal LCC have negligible or limited sensitivity to the most of the major parameters in our model. In Chapter 3, we introduce a redundancy optimization model for a capital good with a serial structure (from the reliability point of view). We refer to the units which are connected to each other in series in the capital good as stages. When there is no redundancy in a stage, the stage is composed of a single component. If a stage is designed with redundancy, then it includes two units of the same component which are connected to each other in parallel (from the reliability point of view). In the problem that we studied, three policies per stage are defined. Redundancy is included by one of the policies. Each of the three policies provides different levels of uptime (availability). We formulate the problem as the minimization of the Total Cost of Ownership (TCO -equivalent to LCC from the customer perspective) of a general number of systems under a defined constraint on the expected downtime of the systems throughout their life cycle. We decompose the problem into single-stage problems and show that a solution for the multi-stage problem can be generated by solutions of each of the single-stage problems. We develop an efficient procedure to find optimal solutions of the single-stage problems for varying levels of the downtime constraint. Solutions for the multi-stage problem for varying levels of the downtime constraint are generated efficiently by repeating this procedure for each stage. We derive the following major results through the analysis of the single-stage and multi-stage problem formulations: • Single-stage: When level of the downtime constraint is decreased from a high value to zero; i.e., the constraint was initially loose and got tighter and tighter, the policy to include redundancy becomes optimal at a certain level and remains optimal for all smaller levels. • Multi-stage: – One can generate an efficient frontier which reflects the trade-off between the uptime and the TCO . – An optimal ordering of the stages to include redundancy one-by-one can be generated. In Chapter 4, we develop a model for studying the following two upgrading policies that an OEM may follow for multiple systems in the field after the redesign of a component (we denote the time just after the redesign by time 0): • Policy 1 - Upgrade all systems preventively at time 0. • Policy 2 - Upgrade systems one-by-one correctively. Under Policy 2, new (improved) parts are kept on stock for upgrading while no inventory of new parts is kept under Policy 1. Under Policy 2, the initial supply quantity of new parts is a decision variable and new parts can be replenished in batches with a fixed size after the initial supply. The unit price of the new parts might increase after time 0. We develop a problem formulation for the comparison of the two policies and perform exact analysis. We conduct a numerical study and find out that Policy 1 is favored by low values of the number of the systems, long lifetime of the systems, low values of the MTBF of the old parts (for fixed percentage improvement in MTBF), high values of the percentage improvement in MTBF, high values of the increase in the unit price of the new parts after time 0, large batch sizes for new parts under Policy 2, and high values of the downtime costs per failures. The reverse of each of these conditions favors Policy 2. Our numerical study showed that the optimal policy may change by varying any of the mentioned factors.