Home > Articles > Engineering > Six Sigma and Process Improvement

This chapter is from the book

Measurement System Analysis

Once the critical parameters have been selected, and specification limits have been set, it seems reasonable that the next steps might be to set things up so that progress towards achieving expectations can be monitored. As discussed in Chapters 7 and 9, the critical parameters have been defined in measurable terms. The next logical step is to set up the measurement systems and determine whether each is capable of measuring appropriate critical parameters.

Figure 10.10 summarizes the purpose, results, and outputs from measurement system analysis, focusing on MSA for critical parameters that are continuous rather than discrete. There are several indices used to determine if the measurement system is adequate for the purposes of optimization and validation of the critical parameters, including assessments of stability, linearity, accuracy, and measurement error. MSA is discussed further in Chapter 16.

Figure 10.10

Figure 10.10 Summary for measurement system analysis

The assessment and estimate of measurement error is a key, recurring topic in DFSS, and this is an appropriate point to begin that discussion. The measurement error is one of several "noises" that can be flowed down, as discussed later in this chapter, and that will be encountered along the way as the design team uses approaches such as design of experiments (DOE) and response surface methodology (RSM).

This aspect of the flow-down process is illustrated in Figure 10.11, which starts with the concept of squared deviation from the target. If the target is the desired value, as discussed in the previous section, then one can define a statistical index, the second moment about the target, which can represent the degree of customer satisfaction. The ideal case, in which every product is exactly on target with no variation, would have a value of zero for this statistical index. As further illustrated in Figure 10.11, this squared deviation from (or second moment about) the target corresponds to the Taguchi Loss Function for a target-is-best situation. A useful aspect of this equivalence is that the deviation from the ideal situation can be partitioned into two parts: the degree to which the deviation is a result of the average being off-target, and the variance about the mean. This variance can be further partitioned into variance as a result of the measurement system (discussed here) and variance as a result of manufacturing variation and variations in usage and environment (including system interactions).

Figure 10.11

Figure 10.11 Partitioning of squared deviation from the target, including variance associated with the measurement system

MSA for continuous parameters provides an estimate for the variance caused by the measurement system, and compares it to the tolerance in terms of the precision to tolerance ratio (P/T ratio), and to the total observed variance in terms of the GR&R ratio (gauge repeatability and reproducibility). The P/T ratio is defined as six times the standard deviation of the measurement system divided by the difference between the upper and lower specification limits. The GR&R ratio is defined as the standard deviation of the measurement system divided by the total observed standard deviation, combining sources of variation including measurement error, variation from manufacturing, variation from how the customers use it, variations from the environments where the product will be used, and variations in how the interactions among the subsystems and the product with other systems affect the parameter.

If the measurement variance consumes too much of the tolerance window, or obscures the ability to assess the other sources of variation, then the measurement system is not acceptable. For many situations, the rule of thumb is that both the P/T ratio and the GR&R ratio should be less than 30 percent; for other situations, a rule that both should be less than 10 percent is imposed. Acceptable values for the P/T ratio derive from statistical analyses that indicate that a P/T ratio more than 30 percent corresponds to a very high risk of incorrectly passing bad parts or incorrectly rejecting good parts.

The measurement system for critical parameters at the system or product level will generally link to the test and evaluation plan for the product, as illustrated by the arrow to the deliverable initial critical parameter (CP) test plan in Figure 10.2. This deliverable is a starting point for the verification of capability discussed in Chapter 16, and summarized in Figure 10.12. Clearly, the preparation of the measurement systems to be used for verification do not need to wait, and should not wait, but should be initiated with the initial measurement systems analysis effort.

Figure 10.12

Figure 10.12 DFSS flowchart, drilled down to detailed flowchart that includes actions for improving the measurement system if MSA results are unacceptable

If the GR&R or the P/T ratio, or both, fail to meet acceptable guidelines, then there are a series of actions for improving the measurement system that are summarized in Figure 10.12 and discussed in Chapter 16.

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.


Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.


If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information

Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.


This site is not directed to children under the age of 13.


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure

Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact

Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice

We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020