Reliability HotWire Issue 55, September 2005 Tool Tips Two components are arranged in a series configuration. There is a probability p that the two components would fail when they are put together in the system. How could BlockSim model this situation? A simple way to handle such situations in BlockSim is to use static blocks. A static block can be interpreted either as a block with a reliability value that is known only at a given time (but the block's entire distribution is unknown) or as a block with a probability of success that is constant with time. To demonstrate this idea, consider a system made of two components A and B arranged in a series configuration (i.e. if either of them fails, then the system fails). The A component follows a Weibull distribution with β = 1.5 and η = 10,000 hours and the B component follows a Weibull distribution with β = 2 and η = 30,000 hours. The two components are modeled in BlockSim with two blocks that contain the failure distributions describing A and B failure behavior. When the two components are put together in the system, there is a p = 0.01 probability that they do not work properly. This probability can be modeled in BlockSim using an additional block that is in series with the other two blocks. In this block, the p probability is specified as follows. Note that p is defined as the probability that the interaction failure occurs. In RBDs, this would be specified as 1-p, which is the probability of the failure not occurring (success). The system's RBD is as follows. The system's reliability at t = 1000 hours can be found using the QCP as follows. Other forms of complex interactions can be modeled with the use of the Load Sharing feature in BlockSim. How can interactions be modeled in ALTA if one or more of the factors is a categorical factor? Issue 53 of HotWire featured a Hot Topics article about modeling interactions between variables in accelerated life testing or life-stress analysis. Interaction terms that involve one or more categorical (qualitative) factors are modeled using n additional columns, where n is product of the number of indicator variables used by the categorical factors in the interaction term. For example, if the interaction term being modeled is A B: If A is a numerical factor and B is a categorical factor that uses 3 indicator variables, then 3 more columns are needed. If A is a categorical factor that uses 2 indicator variables and B is a categorical factor that uses 3 indicator variables, then 2 3 = 6 more columns are needed. The same idea can be used if more complex interaction terms are modeled. For example, if the interaction term being modeled is A2 B and A is a categorical factor that uses 2 indicator variables and B is a categorical factor that uses 3 indicator variables, then 22 3 = 24 more columns are needed. To illustrate modeling interaction terms that involve categorical factors in ALTA, let us consider the same example presented in the Issue 53's Reliability Basics article. In this example, if the interaction between the Temperature factor and the Lot factor is to be considered (Temperature Lot), then two additional columns would be required to model the interaction term because the Lot factor is a categorical factor that uses two indicator variables (the Lot factor has 3 categories). The interaction columns would contain the values of the multiplication of the Temperature level and Lot indicators values (0 or 1). The ALTA folio would then look as follows. Note: To stay consistent with the original example, because a reciprocal exponential LSR transformation was used for the Temperature factor, the interaction shown in the figure above is actually expressed as (1/Temperature) Lot. In RENO, can a simulation of the Flowchart be followed in detail to make sure it works the way it is intended? The Debug window allows you to view one or more simulations of the Flowchart step by step. It can be accessed by selecting Debug from the Tools menu or by clicking the Debug icon on the toolbar or in the Flowchart Control Panel. To view one step of the simulation at a time, use the Step Into button. Each time you click the Step Into button, RENO executes the next step in the Flowchart. The current block is highlighted in the Flowchart and details of the step are displayed in the Debug window. As you execute the steps, the information from previous steps remains in the Debug window for your review. The Flowchart shown next has had two steps executed. Note that if desired, you can select Show Block Values from the Flowchart menu to display the value of each block at each step in the simulation. If the next block in the Flowchart is a Subchart Block, you can use Step Into to view the simulation of the subchart or Step Over to step over the Subchart Block (i.e. the subchart will be executed but that part of the simulation will not be shown). You can also use the Run button to view one or more complete step-by-step simulations of the Flowchart. The settings used by the Debug window can accessed by clicking Options. Copyright 2005 ReliaSoft Corporation, ALL RIGHTS RESERVED