Evaluating repeatability

Q: From a statistical point of view, what is the better way to evaluate the repeatability of an instrument: to repeat the measurement in each calibration point three times, or to take only one measurement in all the calibration points except one, in which five measurements are taken?

Pablo Alra
Campana, Buenos Aires, Argentina

A: You must understand the definition of repeatability before answering this question. The automotive Industry Action Group’s Measurement Systems Analysis (MSA) Manual explains repeatability as "the variation in measurements obtained with one measurement instrument when used several times by one appraiser while measuring the identical characteristic on the same part" (Figure 1).1

Figure 1

The manual also explains that "this is the variation in successive (short-term) trials under fixed and defined conditions of measurement" (Figure 2).2

Figure 2

On the other hand, uniformity is "the difference in variation throughout the operating range of the gage" or "the homogeneity (sameness) of the repeatability over size."3 Precision as "the net effect of discrimination, sensitivity and repeatability over the operating range (size, range and time) of the measurement system."4

Your question combines repeatability and uniformity. You cannot calculate repeatability with just one measurement. Taking more measurements reduces the error in the repeatability measurement. If you are interested in estimating uniformity, you must take more measurements at select intervals in your operating range, calculate repeatability over the operating range and verify if there is homogeneity (Figure 3 and Table 1).

Figure 3

Table 1

The MSA manual points out that for simple measuring equipment, the repeatability and uniformity are expected to be consistent. For a more complex measurement system, however, inconsistency may be significant.

The MSA manual provides a formula for estimated repeatability standard deviation.5 The d2 constant is selected based on the number of replications (trials). As you make more replications, the repeatability standard deviation improves. Four replications improve the repeatability by half. It will take an additional six replications to improve it by one-third. I would say making four replications is cost effective (Figure 4).

Figure 4

One additional benefit with measurement points at multiple locations (using a reference standard) is that you can use the same collected data to conduct bias and linearity studies, as well. This analysis can provide additional insight into other variations that contribute to gage variation.

Govind Ramu
Director, quality assurance
SunPower Corp.
San Jose, CA


  1. Automotive Industry Action Group, Measurement Systems Analysis Manual, fourth edition, pp. 54-58.

  2. Ibid.
  3. Ibid.
  4. Ibid.
  5. Ibid, pp. 170, 174.


Barrentine, Larry B., Concepts for R&R Studies, second edition, ASQ Quality Press, 2003.

Lead auditor qualification

Q: My manager and I have a question about internal lead auditor and auditor qualification. As stated in section 8.2.2 of ISO 9001:2008, "the organization shall conduct internal audits at planned intervals to determine whether the quality management system ..."

Our question is: Must internal lead auditors and auditors be certified by an organization or trained by a certified lead auditor? May a person read ISO 19011:2011 and use his or her work experiences to perform audit tasks, as stated in section 8.2.2 of ISO 9001:2008? If yes, would an ISO registrar consider it to be a nonconformance finding?

A: ISO 9001:2008 does not prescribe any specific requirements for the qualifications of people conducting quality management system (QMS) audits. ISO 19011:2011 provides guidance—not mandatory requirements—for determining auditor qualifications. Findings are typically based on specified requirements and not guidelines or notes. Therefore, it’s unlikely that a registrar would use ISO 19011:2011 as a basis for a finding, unless your organization or a client has identified this guideline as a requirement. As you are aware, an internal audit is one of the most valuable tools that an organization has to determine the effectiveness of its QMS and to identify opportunities for improvement.

For this reason, it is essential that the personnel or consultants used to conduct audit activities have the qualifications and experience needed to provide these services. At a minimum, I would suggest that your internal audit personnel attend auditor classroom training accredited by ASQ, Exemplar Global (formerly known as RABQSA) or the International Register of Certificated Auditors (IRCA). This training should be supported by arranging for the person’s participation in future audits as an audit team member. Preferably, this auditor training should be conducted by an individual who is an ASQ-certified quality auditor or an Exemplar Global or IRCA lead or principal auditor.

The benefits of using an auditor with the aforementioned credentials is that it provides assurance of the individual’s competency as an auditor and consistency with regard to audit practices and requirements for an audit log to be maintained, as well as continued auditor or related quality systems training for periodic recertification. This is of particular importance if the auditor is expected to facilitate the training of other Individuals. Another key point is to ensure that the auditor has a working knowledge of your organization’s product line, processes or services. The importance of using trained and experienced auditors can’t be overstated.

Bill Aston
Managing director
Aston Technical Consulting Services
Kingwood, TX

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