Statistical Sampling

Many product safety standards require that 3-samples pass a specific test to show that the product sufficiently meets a requirement. In most cases three samples is not a sufficient sample size to determine statistical validity. The sample size of a known population size can be calculated based on desired precision and confidence level and is determined by [1]:

The variables in EQ1 are defined as: n = samples size, N = population size, P = estimated population within compliance, Q = 1-P, B = allowable error (precision), and s = desired level of confidence

Specifically, in UL 1449 (Standard for Safety, Surge Protective Devices), assessing how a surge protective device (SPD) fails from an abnormal overvoltage limited current (ABOV-LC) requires that three samples be tested [2].  Three samples of SPDs are subjected to the test.  If the SPDs meet the minimum pass criteria for each mode (line-to-neutral, line-to-ground, neutral-to-ground), then the SPD has successful met the requirements of the test. While the SPD may meet the minimum requirements, it easy to state that this is not a statistically valid.

To determine the number of samples required to have a statistical valid representation for the product, let’s use the following data in EQ1.

·         Anticipated number of SPDs to be manufactured (N) is 10,000

      ·         Percentage of each unit for the mode of protection is 0.429
                  o    3-phase SPD
                  o    Line-to-Neutral protection (Phase A-N, Phase B-N, and Phase C-N)
                  o    Line-to-Ground protection (Phase A-G, Phase B-G, and Phase C-G)
                  o    Neutral-to-Ground protection (N-G)
      ·         Allowable error (B) or failure rate of 10 percent
      ·         Desired confidence level (z) of 95 percent.

Based on the data, the number of samples that should be evaluated for a statistically valid experiment is 93 test samples for the line-to-neutral mode, assuming that all line-to-neutral modes are identical.  This is considerable more than the 3 samples required by the UL test standards.

If the company can accept an allowable error of 20 percent, the number of samples that should be evaluated is reduced to 23 samples.

All too often I see where a company has subjected their SPDs or other equipment to the test programs designed only to pass relevant safety standards.  While this proves compliance with the standards, this does not prove that the tests results are statistically valid nor do they accurately reflect the performance attributes of the equipment.  Establishment of a baseline of the equipment’s performance can only be accomplished through statistical sampling.

Reference:

1. Underwriters Laboratories (2007), Standard for Safety, Surge Protective Devices, UL 1449 3^rd edition, Northbrook, IL USA
2. Anderson, D.R., Sweeney, D.J, Davis, D., Utts, J.M, Williams, T.A., and Simon, M (2001).  Statistic and Research Methods for Managerial Decisions.  South-Western, Thomas Learning.