I'm trying to build a simulation for a quality control process, where quality analysts inspect the product and report faults if they found any.
I have a dataset of this bug reports, so I'm trying to fit the inter-arrival time of this report to a probability distribution. All the literature I found mentioned that an exponential distribution would be a would choice, however I got this results while applying the Anderson-Darling test:
# This is using Python's Scypy library statistic, critical_values, significance_level = stats.anderson(data_series, "expon")
Anderson-Darling Test for expon : statistic 370.733327629 Critical Value: 0.921 Significance Level: 15.0 Critical Value: 1.077 Significance Level: 10.0 Critical Value: 1.339 Significance Level: 5.0 Critical Value: 1.604 Significance Level: 2.5 Critical Value: 1.954 Significance Level: 1.0
Which seems to agree with what I obtain with Kolmogorov-Smirnov:
#cdf_function is the exponential distribution fitted using Maximum Likelihood d, p_value = stats.kstest(data_series, cdf_function)
Kolmogorov-Smirnov Test for expon : d 0.38586872273 p_value: 0.0
So, apparently my dataset is not a good fit for the exponential distribution. Which other distributions are used for inter-arrival time modelling?
UPDATE: Here is an histogram of the inter-arrival times found on the dataset. The y-axis is in hours.
SECOND UPDATE: The histogram above corresponds to the inter-arrival time (in hours) for fault reports by the most productive quality analyst of the team, during a 20 month period. If we apply the base-10 log to the inter-arrival time, the histogram is the following: