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**Determination of burn-in parameters and residual life for highly reliable products.**
*(English)*
Zbl 1044.90022

Summary: Today, many products are designed and manufactured to function for a long period of time before they fail. Determining product reliability is a great challenge to manufacturers of highly reliable products with only a relatively short period of time available for internal life testing. In particular, it may be difficult to determine optimal burn-in parameters and characterize the residual life distribution. A promising alternative is to use data on a quality characteristic (QC) whose degradation over time can be related to product failure. Typically, product failure corresponds to the first passage time of the degradation path beyond a critical value. If degradation paths can be modeled properly, one can predict failure time and determine the life distribution without actually observing failures. In this paper, we first use a Wiener process to describe the continuous degradation path of the quality characteristic of the product. A Wiener process allows nonconstant variance and nonzero correlation among data collected at different time points. We propose a decision rule for classifying a unit as normal or weak, and give an economic model for determining the optimal termination time and other parameters of a burn-in test. Next, we propose a method for assessing the product’s lifetime distribution of the passed units. The proposed methodologies are all based only on the product’s initial observed degradation data. Finally, an example of an electronic product, namely contact image scanner (CIS), is used to illustrate the proposed procedure.

### MSC:

90B25 | Reliability, availability, maintenance, inspection in operations research |

### Keywords:

burn-in test; degradation data; economic cost model; optimal termination time; residual lifetime assessment; Wiener process
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\textit{S.-T. Tseng} et al., Nav. Res. Logist. 50, No. 1, 1--14 (2003; Zbl 1044.90022)

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### References:

[1] | Alexanian, IEEE Trans Reliab R-26 pp 359– (1977) |

[2] | Bai, Nav Res Logistics 42 pp 1081– (1995) |

[3] | and The inverse Gaussian distribution: Theory and methodology, and applications, Marcel Dekker, New York, 1989. |

[4] | Doksum, Technometrics 34 pp 74– (1992) |

[5] | and Burn-in: An engineering approach to the design and analysis of burn-in procedures, Wiley, New York, 1982. |

[6] | Creating quality: Process design for results, McGraw-Hill, New York, 1999. |

[7] | Kuo, IEEE Trans Reliab 2 pp 145– (1984) |

[8] | Kuo, Proc IEEE 71 pp 1257– (1983) |

[9] | Leemis, IIE Trans 22 pp 172– (1990) |

[10] | Meeker, Int Stat Rev 61 pp 147– (1993) |

[11] | Accelerated testing: Statistical models, test plans, and data analysis, Wiley, New York, 1990. |

[12] | Nguyen, IIE Trans 14 pp 167– (1982) |

[13] | Stochastic differential equations: An introduction with applications, 5th ed., Springer-Verlag, Berlin, 1999. |

[14] | Plesser, IEEE Trans Reliab R-26 pp 195– (1977) |

[15] | Rice, Biometrics 35 pp 451– (1979) |

[16] | Tseng, IEEE Trans Reliab R-46 pp 130– (1997) |

[17] | Washburn, IEEE Trans Reliab R-19 pp 134– (1970) |

[18] | Yu, Nav Res Logistics 46 pp 699– (1999) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.