Estimating Alarm Thresholds for Process Monitoring Data under Different Assumptions about the Data Generating Mechanism

Table 1

The estimated probability rounded to the nearest 0.01 of inferring the likelihood model using BIC. The inferred likelihood is in columns and the true likelihood is in rows, for sample sizes 𝑛 = 25, 50, and 1000. The true likelihood is either normal, 𝑡(2), lognormal, or gamma(1, 0.1) in the experiment.

True	Inferred
	Normal	𝑡(2)	Lognormal	Gamma(1, 0.1)
Normal	0.86, 0.90, 0.99	0.02, 0.07, 0	0, 0, 0	0.11, 0.03, 0
𝑡(2)	0.81, 0.83, 0.98	0.06, 0.10, 0.02	0, 0, 0	0.13, 0.07, 0
Lognormal	0, 0, 0	0, 0, 0	0.64, 0.83, 1.0	0.36, 0.17, 0
Gamma(1, 0.1)	0, 0, 0	0, 0, 0	0.37, 0.24, 0.01	0.63, 0.76, 0.99