以Wiener Process探討電子產品之可靠度

Abstract

電子產品可靠度一直為大家所重視的問題，雖電子產品出廠前，可能會實施一些測試，然而可靠度其實很難透過簡單的測試而得知。猶如其他產品，電子產品通常也存有隨時間衰退的品質特性，並可藉由加速衰退測試推估其失效率與平均失效時間。過往雖有部分學者提出以Wiener過程(Wiener Process)建構電子產品的衰退路徑並作相關的統計推論，但卻鮮少以實例驗證其數學模式，也少有人將其結論延伸至產品預燒相關的分析。本研究以某廠商所生產的通訊用連接器為案例，依其實際測試數據，以Wiener過程建構產品的衰退路徑，作為分析此產品可靠度的基礎，最後再以統計推論方法，探討產品的預燒問題。經由案例分析，我們驗證本文所建構以Wiener過程為基礎的分析模式確可應用於電子產品的可靠度分析與預燒時間評估。以本文所探討的特別案例而言，我們發現此型連接器的失效機率服從逆高斯分佈，其平均失效時間為92,340小時，在最小化總成本的條件考量及其他合理的假設下，其最佳預燒時間則為25.62小時。

The reliability of electronic products has long been an important subject to both manufacturers and customers. Although tests may be conducted before the delivery of a product, but in actuality it is difficult to assess the product's reliability by simple testing. Like other products, electronic products usually contain quality characteristics which degrade over time, and we can use this property to conduct certain accelerated degradation tests to assess their failure rates and mean times to failure. In the past, several researchers have applied Wiener process to model typical degradation paths and used statistic inferences to evaluate the reliability of electronic products. However, most of them did not take real examples into consideration. Neither did they use statistic inferences to propose an appropriate burn-in procedure for products. In the present study, the accelerated test result of a certain type of hard metric connector provided by a manufacturer is used as a demonstrative example. Based on real data, Wiener process is applied to construct the degradation path of the connector as a basis for further assessing its reliability. Statistic inference is then used to study the burn-in subject. It is found from analyzing the real data, the procedure of assessing the reliability and burn-in time of electronic products based on Wiener process is applicable. In particular, for the studied connector, its failure time is found to follow an inverse Gaussian distribution and its mean time-to-failure is 92,340 hours. Under considerations of minimal cost and other reasonable assumptions, the optimal burn-in time of the connector is found to be 25.62 hours.