Parametric O&S Cost Estimation Using Markov Chains and the Influence Function Method
This paper reports on an effort at Galorath Incorporated to apply parametric methods to the system O&S estimation problem. As a goal, we wanted to reduce the number of user inputs as much as possible in keeping with maintaining decent accuracy.
We also wanted a high degree of model flexibility so that the same general architecture would suffice for most kinds of vehicles and infrastructure. After some preliminary study, we decided that:
• The parametrics should be based on the influence function method (IFM), first developed at Galorath. In this method, parametrics are developed gradually, as more data is collected. The initial model may have limited accuracy, but it will improve as more data is integrated into the model. As opposed to regression methods, a reasonably accurate IFM model may result from as few as three or even two carefully chosen data points. Moreover, an IFM model may get by with fewer than ten user entries per system element.
• Markov chains have properties that make them extremely useful for O&S estimating. Most O&S models develop period costs (usually annual). Using Markov chains, the user can, as an alternative, focus on costs per mission, which often is a more realistic approach, especially for systems that have irregular or sporadic patterns of use. The mathematics is sufficiently flexible that systems ranging from one time use to years of life with (or without) frequent refurbishments can be modeled. For systems subject to attrition or wearout, Markov chains are especially useful because they predict average system life.
This paper discusses general approaches and presents several simplified examples for various O&S situations.
Evin Stump is a senior systems engineer for Galorath Incorporated. He has recently managed the Darwin project, aimed at developing an advanced cost model for estimating the effects on projects of “evolutionary acquisition.” Other recent or ongoing assignments include development of the Spyglass model for estimating costs and schedules of development and production of electro-optical sensors used in space, updating the SEER-IC model for estimating costs and schedules of development and production of integrated circuits, and development of parts of the SEER-IT infrastructure complement to the SEER- SEM software development cost model.
Mr. Stump has over 54 years of experience in the aerospace industry, having worked as a test engineer, design engineer, systems engineer, project engineer, cost engineer, engineering manager, and independent consultant. Major projects to which he has made significant contributions include BQM-74C, Mercury, Gemini, Apollo, Parawing, Saudi Army Test Range, Tacit Rainbow, Brilliant Eyes, C-17, EELV, and RSA IIA. Mr. Stump is a former president of the Southern California chapter of the International Society of Parametric Analysts (ISPA), and also of the Southern California chapter of the Society of Cost Estimating and Analysis (SCEA).
Mr. Stump holds the BS in Engineering from Loyola University of Los Angeles, and the MS in Operations Research from the University of Texas at Austin. He has also earned the professional designation in government contract management from UCLA/NCMA.
Alexandra Minevich is a Systems Engineer/Cost Analyst for Galorath Incorporated. She has recently assisted in development of the labor effort and duration allocation schemes for SEER-SEM Client for MS Project. She also participated in the development process of SEER-H Client for MS Project, and has developed and tested prototypes of a number of new estimating methods.
Ms. Minevich holds the BS in Computer Science from the University of California at Los Angeles. As a student at UCLA, Ms. Minevich participated in a project to develop a health alert and monitoring system. The project involved establishing system requirements, subsystem specifications, organizational arrangements, work breakdown structures, marketing approach, and risk analysis.