Analytic redundancy(AR) signals produced by analytic relations between sensors are applied to assist Built-in
test(BIT) in determining a fault, and higher reliability sensors are involved in the BIT decision of sensors with high false alarm rate(FAR) or missing alarm rate(MAR). The prior distribution, FAR and MAR models are established for AR signals. After analyzing residuals, posterior distributions for the results of residual decision and BIT are given. Then, the final decision is the one which has minimum Bayesian-risk. Meanwhile, the requirements for Bayesian fusion are proposed. Experimental results show that the proposed method increases the credibility of decision-makings, which can be used in detecting false alarm and missing alarm.