Marlin U. Thomas

Optimum Warranty Policies for Nonreparable Items

An approach is presented for establishing and evaluating warranty policies for products receiving renewable warranties when failure occurs during warranty. A general rebate model is described that allows total compensation to a consumer for failures during a fixed period and prorated compensation for a remaining interval of time. Associated warranty costs are weighed against the s-expected benefit to be derived from the program. Conditions for optimum warranty intervals are provided. Closed form results are given for exponentially and uniformly distributed failure times. The more complicated case of Weibull failure times is demonstrated by example. A sensitivity analysis of the parameters is included.

An Approximate Test of Markov Chain Lumpability

Abstract Under certain conditions the state space of a discrete parameter Markov chain may be partitioned to form a smaller lumped chain that retains the Markov property. The problem of formulating lump-ability hypotheses when the transition probability matrix P is not known and is possibly of large dimension is discussed. An approximate test of these hypotheses is described, based on well-known nonparametric methods. The procedure is illustrated with an application to a Markov manpower model.

Repair and Replacement Decisions for Warranted Products Under Markov Deterioration

An important problem in maintenance planning is the repair versus replacement problem which consists of a sequence of decision points over time, whereby decisions are made to repair or replace a machine based on its condition. This problem can be further complicated by prevailing failure characteristics, and costs. The failure modes for many machines are such that failure emerges through a series of deterioration levels rather than as an abrupt event. Zuo et al. [12] presented a policy for multistage deterioration for machines under warranty. This paper extends that work by treating a larger, more general state space with time parameters at each state. This approach allows for a more cost effective policy. We consider a piece of equipment, such as a production machine that is reviewed for repair verses replacement at various times. The machine is sold with a free repair warranty (FRW) policy. So if it fails during the warranty period, it is maintained at the expense of the manufacturer. Two kinds of repairs are adopted: minimal repair, and replacement. We assume that there is no form of maintenance provided between failures, and the manufacturer decides on the repair action to be taken once a failure and warranty claim is filed. The approach is to model the process as a continuous time Markov Chain. The state decision variables are based on the expected costs to the manufacturer for failures and repairs occurring during the warranty period. The criterion for an optimum policy is to minimize the expected total cost to the manufacturer during the warranty period. A development of the method is provided for the case of three functioning states. Under the policy, if a machine fails early in the warranty period, and its deterioration before failure is large, it is economic to replace that machine with a new one.

Warranty-based method for establishing reliability improvement targets

Modern day competition in manufacturing requires producers to rely heavily on continuous quality improvement methods to remain competitive. Reliability being a significant element of quality is the primary means for making design and process improvements. Current reliability allocation methods to establish improvement goals focus on cost reduction but do not necessarily give due consideration to the relative impact of component cost. A method is presented that uses warranty burden rates as a weighting factor to develop component improvement goals. A sample application is given to illustrate application of the method.

Quantification of the PICK chart for process improvement decisions

The goal of this article is to encourage the use of quantitative techniques to improve decision making and operational processes and ultimately facilitate organizational transformation. An Air Force process improvement case is used as the backdrop for the methodology introduced in this article, specifically, the quantification of the Possible, Implement, Challenge, Kill (PICK) quadrant chart for process improvement decisions. The authors use the case example of laboratory chemicals and hazardous materials procurement for Environmental Safety and Occupational Health (ESOH) at the Air Force Institute of Technology (AFIT). The challenge was to improve the procurement process for chemicals and hazardous materials for laboratories. Effective process improvement decisions can improve overall organizational effectiveness, thereby leading to sustainable organizational transformation. The Department of Defense (DoD) has recognized for several years the need for operational improvement in acquisitions, but only limited quantitative approaches have been implemented. This article illustrates how quantitative approaches in industrial engineering can facilitate improved operational decisions. It is anticipated that this article will encourage the use of analytical tools and techniques in working toward military process improvement goals.

Models for Managing Contingency Construction Operations

A contingency is a crisis situation such as a national disaster, civil disorder, or military invasion that creates a major threat to the safety and security of a population. Essentially all contingencies require construction support that is generally mission critical and inherently challenging due to the dynamics and uncertainty with the availability of resources and the demands for the projects. This paper considers a military contingency for which all construction projects must be completed within a fixed time to achieve mission success. The effectiveness in accomplishing the construction mission is based on mission time reliability assessed using the probability of interference between load measured in the number of days required for the project, and the capacity which is taken as the available allotted resources. Two models are developed to assist in managing the allocation of resources for the construction operations; one based on conditions of moderate risk with randomly occurring repetitive loads, and the other a Markov chain model for high risk conditions. Examples are provided.