Availability Modeling for the Application of Manufacturing Equipment (Brall)
Abstract: This paper shows that two significant areas of manufacturing availability are not addressed with traditional reliability modeling. First, manufacturing goals—quality parts at the required production rate—can be met despite the “fact” that the system did not meet its uptime requirements. Second, process failures can contribute more to manufacturing downtime than actual hardware failures. Proper modeling of manufacturing systems, to include all sources of downtime, whether hardware, software, human, or process as well as the production rates, will provide a more accurate depiction of operation. Methods have been developed by others to model software and human reliability. The approach paper details a Raptor model for including process reliability and production capacity. The resultant analysis provides a method to help assure that reliability improvement efforts are focused on the primary root causes of downtime—in many cases process problems—and not more costly and sometimes technologically infeasible hardware improvement. The analysis also points to addressing the production capabilities so that the operational goal for the manufacturing equipment is not missed.
—Presented at the IEEE RAMS Conference, 2002

Determining the Ballistic Missile Defense Shield's Effective Reliability (Murphy)
Abstract: The Ballistic Missile Defense System (BMDS) is a phased arrangement of equipment that is designed to engage a limited number of ballistic missiles launched against the United States and her allies. A phased system is one that changes its characteristics over time. Determining the reliability of phased systems requires a rather complex aggregation of results across phases. For any realistic equipment architecture, simulation is the only technique with the capability to resolve the reliability of a phased system. The current method used by the BMDS community is to simulate numerous mission cycles of a phased mission representing a hostile launch and determine how many cycles were successfully completed without a hardware or software failure. Unfortunately, this approach only takes into consideration the traditional suitability aspects of the BMDS and disregards key effectiveness issues. This paper will develop a new reliability parameter, which will henceforth be known as effective reliability, to better estimate the characteristics of the BMDS. Using realistic but non-classified data, it will be demonstrated that the BMDS community’s current reliance on the mission reliability parameter will overestimate the abilities of the system while our effective reliability parameter will yield a better estimator of the system’s true potential to negate ballistic missiles.
—Presented at the Applied Reliability Symposium, 2007

The Exponential Repair Assumption: Practical Impacts (Carter)
Abstract: For repairable systems, we assessed the impact of assuming that the repair follows an exponential distribution versus a lognormal distribution for systems with various ratios of MTBF to MRT and various levels of redundancy. Real repair times, as a rule, generally curve fit to the lognormal distribution. We analyzed the system reliability parameters of R(t), Ao, and MTBDE. We found that reliability was sensitive to low values of the ratio MTBF to MRT, and to moderate and low redundancies. In all cases that displayed a statistically significant difference, the exponential repair assumption inflated system reliability.
—Presented at the IEEE RAMS Conference, 2007

Reliability Analysis of Phased-Mission Systems: A Correct Approach (Murphy)
Abstract: At the 2006 RAMS Conference, a paper entitled Reliability Analysis of Phased-Mission Systems: A Practical Approach was presented. This paper established an alleged novel and simple approach to reliability analysis of phased-mission systems. The technique presented in that paper transformed a phased-mission system into several non-phased systems, thus allowing for each phase to be analyzed independently. The paper then presented a method for combining the individual results into a composite solution that spanned all the phases of the system in question. Unfortunately, we discovered that the paper contained grave errors in its methodology, leading the authors to draw inaccurate conclusions. Our paper will demonstrate a mathematically accurate solution for the main example of the previously presented paper in addition to a simulation solution to verify our own methodology. Moreover, our paper presents a solution for the examples shown in the previous paper that are mathematically intractable. In summary, the ultimate objective of this paper is to correct the errant phased-mission methodology presented at the last RAMS Conference.
—Presented at the IEEE RAMS Conference, 2007

The Exponential Distribution: the Good, the Bad and the Ugly. A Practical Guide to Its Implementation (Murphy, Carter, and Brown)
Abstract: Our paper discusses the widespread applicability and mathematical tractability of the exponential distribution, as well as the profound implications of Drenick's Theorem. We demonstrate the risks of the exponential assumption when used to represent redundant subsystems and when used within simulations. We caution our readers about the use of the exponential distribution to represent component repairs and the failure of many to appreciate the implications of the exponential distribution's memory-less property. In summary, this paper provides insight into the good aspects of using the exponential distribution but more importantly, into the ubiquitous misuse of the most commonly implemented reliability distribution.
—Presented at the IEEE RAMS Conference, 2002

How Long Should I Simulate, and for How Many Trials? A Practical Guide to Reliability Simulations (Murphy, Carter, and Wolfe)
Abstract: We have provided reliability, availability, and maintainability (RAM) analysts with practical rules of thumb that facilitate the resolution of how long and how many trials are appropriate for simulations that focus on particular RAM parameters. The rules of thumb provide a structured methodology that determines a solution space as a function of simulation length and number of trials such that the value of the RAM parameter in question can be considered "good enough." What is defined to be good enough depends on the analyst's tolerance for the magnitude of the error in the output. This paper provides the applied RAM analyst with a philosophy as to how to approach the resolution of the two most ubiquitous yet burdensome of RAM simulation questions.
—Presented at the IEEE RAMS Conference, 2001

What is Truth? A Practical Guide to Comparing Reliability Equation Answers to Simulation Results. (Murphy, Malerich, and Carter)
Abstract: When an analyst does not fully trust a modern analysis technique and wishes to confirm that a new method accurately predicts the truth as well as their old method, a reliability comparison may be performed. More often than not a mathematically derived reliability equation—the older accepted method—is considered the truth. This “truth” is used as a benchmark and compared with the results of the new, as-yet-to-be-proven method. For example, if simulation results do not match the mathematical solution, the simulation method is assumed to be inaccurate. This conclusion is often incorrect and is instigated by the human instinct to accept the dogma of the past methods over the newer methods. By its very nature, a correctly derived mathematical method cannot be wrong, but it can and often is applied erroneously. Determining what truth is so that a sound foundation exists allowing accurate comparative analysis is a difficult journey with many potential pitfalls. The profound conclusions of this simple exercise will surprise many of the most seasoned reliability experts as well as provide a roadmap to how best to compare two or more reliability methods.
—Presented at the IEEE RAMS Conference, 2005

Who's Eating Your Lunch? A Practical Guide to Determining the Weak Points of Any System (Murphy, Carter, and Gass)
Abstract: This paper describes a technique for focusing system-level improvement efforts on those areas that are contributing most to undesirable RAM performance. Monte Carlo simulation that incorporates localized performance reporting is used to identify the key culprits affecting a system’s availability or reliability. This ranking technique accounts for issues such as distributional variability, logistical constraints, complex redundancy, internal dependencies, and dynamic components that are often overlooked using traditional mean life ranking methods. This methodology was applied to the V-22 Osprey tilt-rotor aircraft and produced some insightful results.
—Presented at the IEEE RAMS Conference, 2003