Reliability Growth Planning

This chapter includes the following sections:

Background

In developmental reliability growth testing, the objective is to test a system, find problem failure modes, at some point incorporate corrective actions, and therefore increase the reliability of the system. This process is continued for the duration of the test time. If the corrective actions are effective then the system Mean Time Between Failures (MTBF) will move from an initial low value to a higher value.

Typically the objective of reliability growth testing is not to just increase the MTBF, but to increase it to a particular value. In other words, increase the MTBF to meet a goal or requirement. Therefore, determining how much test time is needed for a particular system is generally always of interest in reliability growth testing. This brings us to the topic of growth planning.

In this chapter, we will address the common questions engineers and managers face at the planning stage of product development, in terms of meeting the design reliability goals. Planning for required test time, setting realistic reliability goals and creating a strategy for meeting those goals are all essential parts of project management. It is therefore necessary to have a tool that can be utilized for such planning purposes. The basis of the tool will be the Duane Postulate and a model will be developed which incorporates the realities faced during development and generates a plan that can be used as a guideline during developmental testing.

The Duane Postulate is based on empirical observations and reflects a learning curve pattern for reliability growth. This identical learning curve pattern forms the basis of the Crow-AMSAA (NHPP) model. The Duane Postulate is also reflected in the Crow Extended model in the form of the discovery function $h(t)$.

The discovery function is the rate in which new, distinct problems are being discovered during reliability growth development testing. The Crow-AMSAA (NHPP) model is a special case of the discovery function. Consider that when a new, distinct failure mode is first seen the testing is stopped and a corrective action is incorporated before the testing is resumed. In addition, suppose that the corrective action is highly effective so that the failure mode is unlikely to be seen again. In this case, the only failures observed during the reliability growth test are first occurrences of failure modes. Therefore, if the Crow-AMSAA (NHPP) model and the Duane Postulate are accepted as the pattern for a test-fix-test reliability growth testing program, then the form of the Crow-AMSAA (NHPP) model must be the form for the discovery function, $h(t)$.

To be consistent with the Duane Postulate and the Crow-AMSAA (NHPP) model the discovery function must be of the same form. This form of the discovery function is an important property of the Crow Extended model and its application in growth planning. As with the Crow-AMSAA (NHPP) model, this form of the discovery function ties the model directly to real-world data and experiences

The use of the Duane Postulate as a reliability growth planning model poses two significant drawbacks:The first drawback is that the Duane Postulate's MTBF is zero at time equal to zero. This was addressed in MIL-HDBK-189 by specifying a time $T_{i}$ where growth starts after $T_{i}$ and the Duane Postulate applies [13]. However, determining $T_{i}$ is subjective and is not a desirable property of MIL-HDBK-189. The second drawback is that the MTBF for the Duane Postulate increases indefinitely to infinity, which is not realistic.

Therefore a desirable feature of a planning model is that:

  1. The discovery function must have the form of the Crow-AMSAA (NHPP) model and the Duane Postulate.
  2. The start time $T_{i}$ is not required as an input.
  3. An upper bound on the system MTBF is specified in the model.

All of these desirable features are included in the planning model discussed in this chapter, which is based on the Crow Extended model.