Six Sigma Fundamentals: A Complete Introduction to the System, Methods, and Tools

LCC involves all costs associated with the system life cycle, and includes:

• Research and development (R&D) cost. These include the cost of feasibility studies; system analyses; detail design and development, fabrication, assembly, and test of engineering models; initial system test and evaluation; and associated documentation.

• Production and construction cost. These include the cost of fabrication, assembly, and test of operational systems (production models); operation and maintenance of the production capability; and associated initial logistic support requirements (e.g., test and support equipment development, spare/repair parts provisioning, technical data development, training, entry of items into the inventory and facility construction).

• Operation and maintenance cost. This is the cost of sustaining operation, personnel and maintenance support, spare/repair parts and related inventories, test and support equipment maintenance, transportation and handling, facilities, modifications and technical data changes and so on.

• System retirement and phase-out cost. This is the cost of phasing the system out of the inventory due to obsolescence or wear-out, and subsequent equipment item recycling and reclamation as appropriate.

Life cycle costs may be categorized many different ways, depending on the type of system and the sensitivities desired in cost-effectiveness measurement.

Cost-effectiveness. The development of a system or product that is cost-effective, within the constraints specified by operational and maintenance requirements, is a prime objective. Cost-effectiveness relates to the measure of a system in terms of mission fulfillment (system effectiveness) and total life cycle cost. Cost-effectiveness, which is similar to the standard cost-benefit analysis factor employed for decision-making purposes in many industrial and business applications, can be expressed in various terms (i.e., one or more figures of merit), depending on the specific mission or system parameters that one wishes to measure.

Reliability factors

In determining system support requirements, frequency of maintenance becomes a significant parameter. Maintenance frequency for a given item is highly dependent on the reliability of that item. In general, as the reliability of a system increases, the frequency of maintenance will decrease, and conversely maintenance frequency will increase as system reliability is degraded. Unreliable systems will usually require extensive maintenance. In any event, logistic support requirements are highly influenced by reliability factors. Thus, a basic understanding of reliability terms and concepts is required. Some of the key reliability quantitative factors used in the system design process, and for the determination of logistic support requirements, are briefly defined here.

The reliability function

Reliability can be defined simply as the probability that a system or product will perform in a satisfactory manner for a given period of time when used under specified operating conditions. The reliability function, R(t), may be expressed as:

R(t) = 1 - F(t)

where F(t) is the probability that the system will fail by time t. F(t), showing the failure distribution function, or the "unreliability" function. If the random variable t has a density function of f(t), then the expression for reliability is:

Assuming that the time to failure is described by an exponential density function, then:

where theta (θ) is the mean life, t is the time period of interest, and e is the natural logarithm base (2.7183). The reliability at time t is:

Mean life theta (θ) is the arithmetic average of the lifetimes of all items considered. The mean life theta for the exponential function is equivalent to mean time between failure (MTBF). Thus:

where lambda (λ) is the instantaneous failure rate and M is the MTBF. If an item has a constant failure rate, the reliability of that item at its mean life is approximately 0.37. In other words, there is a 37 percent probability that a system will survive its mean life without failure, Mean life and failure rates are related in the following equation:

We must emphasize here that the failure characteristics of different items are not necessarily the same. There are a number of well-known probability density functions which, in practice, have been found to describe the failure characteristics of different equipments. These include the binomial, exponential, normal, Poisson, gamma and Weibull distributions. Therefore, one should take care not to assume that the exponential distribution is applicable in all instances, or the Weibull distribution is the best, and so on.