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Product Reliability Estimation

Reliability theory developed apart from the mainstream of probability and statistics, and was used primarily as a tool to help nineteenth century maritime and life insurance companies compute profitable rates to charge their customers. Even today, the terms “failure rate” and “hazard rate” are often used interchangeably. Some of the concepts, terms, and models needed to describe, estimate and predict reliability include:

  • Reparable systems, non-repairable populations, and life-time distribution models
  • Reliability or survival function
  • Failure (or Hazard) rate

As one example, the failure rate is defined for non-repairable populations as the (instantaneous) rate of failure during the next instant of time among those who have survived to time t.

The failure rate is sometimes called a “conditional failure rate” since it is a rate giving survival past time t.

Product reliability for manufacturing and survival analysis for subjects (patients, or cohorts) use the same principle described above. However, the former is typically analyzed based on parametric models (i.e., logistic, normal, Weibull, etc.), while the latter is usually analyzed based on nonparametric (Kaplan-Meier) or semi-parametric models (Cox regression). Right or left censored data are often encountered. For example, a patient might withdraw from a study and his/her survival time is unknown and censored at the time of withdrawal (right censored).  Techniques are widely available to handle censored data.

Walker Downey & Associates, Inc. uses its expert Statistical Services to help clients evaluate their product reliability estimations.

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