Undetectable Error in Independent Dual Programming Validation Long Zheng Data Science Institute, Takeda Pharmaceutical Company Limited in Boston, Massachusetts

Types of Errors Undetectable Error: Detectable Error: If two programmers make the same mistake in a unit process Detectable Error: If only one programmer makes a mistake in a unit process 2019 Joint Statistical Meetings of 9

Distribution of Undetectable Error Number of Undetectable errors follows the Poisson distribution with error rate 2019 Joint Statistical Meetings of 9

Distribution of Undetectable Error (4) 2019 Joint Statistical Meetings of 9

Distribution of Detectable Error Number of detectable errors follows the Poisson distribution with error rate 2019 Joint Statistical Meetings of 9

Using Detectable Errors to Estimate Undetectable Errors If mean of detectable error number is in validation, and , then where 2019 Joint Statistical Meetings of 9

Estimating Reliability of Results from Outsourcing Estimate total number of errors from outsourcing … 2019 Joint Statistical Meetings of 9

Acknowledgments I would like to thank Michael Hale, John Anthony and Xiao Li for their valuable feedback and support. 2019 Joint Statistical Meetings of 9

2019 Joint Statistical Meetings of 9