---
title: Using Intervals to Get at the Tail Ends of the Problem in Healthcare and Medical Devices
description: Demonstrating process improvement often involves showing improvement in the mean, so we focus on the center of a distribution. Defects don’t fall in the center, though. They're in the tails.
image: https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/blog-intervals-tail-end-feature-2.png
---
English
- [English](https://blog.minitab.com/en/?hsLang=en)
- [Français](https://blog.minitab.com/fr/?hsLang=en)
- [Deutsch](https://blog.minitab.com/de/?hsLang=en)
- [Português](https://blog.minitab.com/pt/?hsLang=en)
- [Español](https://blog.minitab.com/es/?hsLang=en)
- [日本語](https://blog.minitab.com/ja/?hsLang=en)
- [한국어](https://blog.minitab.com/ko/?hsLang=en)
- [中文（简体）](https://blog.minitab.com/zh/?hsLang=en)
- [English](https://blog.minitab.com/en/blog/using-intervals-to-get-at-the-tail-ends-of-the-problem)
- [Deutsch](https://blog.minitab.com/de/blog/problemloesung-mit-hilfe-von-intervallen)
- [Français](https://blog.minitab.com/fr/blog/comment-utiliser-les-intervalles-pour-ameliorer-la-qualite-des-soins-de-sante-et-des-dispositifs-medicaux-0)
- [ Partners](https://www.minitab.com/en-us/company/partners/)
- [ Contact](https://www.minitab.com/en-us/company/contact-us/)
- [ Talk to Minitab](https://www.minitab.com/en-us/talk-to-minitab/)
- [ My Account](https://licensing.minitab.com/account/manage)
[](https://www.minitab.com/en-us/)
- Products
Back
[Products](https://www.minitab.com/en-us/products/)
[All Products](https://www.minitab.com/en-us/products/)
- [Minitab Solution Center](https://www.minitab.com/en-us/products/minitab-solution-center/)
- [Minitab Statistical Software](https://www.minitab.com/en-us/products/minitab/)
- [Minitab Connect](https://www.minitab.com/en-us/products/connect/)
- [Minitab Model Ops](https://www.minitab.com/en-us/products/model-ops/)
- [Minitab Education Hub](https://www.minitab.com/en-us/products/education-hub/)
- [Minitab Engage](https://www.minitab.com/en-us/products/engage/)
- [Minitab Workspace](https://www.minitab.com/en-us/products/workspace/)
- [Real-Time SPC](https://www.minitab.com/en-us/products/real-time-spc/)
- [Prolink Data Collection & SPC](https://www.minitab.com/en-us/products/prolink)
- [Simul8 Discrete Event Simulation](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [SPM](https://www.minitab.com/en-us/products/spm/)
- Solutions
Back
[Solutions](https://www.minitab.com/en-us/solutions/)
[All Solutions](https://www.minitab.com/en-us/solutions/)
- [Analytics](https://www.minitab.com/en-us/solutions/analytics/)
- [Statistics & Predictive Analytics](https://www.minitab.com/en-us/solutions/analytics/statistical-analysis-predictive-analytics/)
- [Data Science & Machine Learning](https://www.minitab.com/en-us/solutions/analytics/data-science-machine-learning/)
- [Business Analytics & Intelligence](https://www.minitab.com/en-us/solutions/analytics/business-analytics-intelligence/)
- [Statistical Process Control](https://www.minitab.com/en-us/solutions/analytics/statistical-process-control/)
- [Quality Analytics](https://www.minitab.com/en-us/solutions/analytics/quality-analytics/)
- [Live Analytics](https://www.minitab.com/en-us/solutions/analytics/live-analytics/)
- [Reliability & Life Data Analysis](https://www.minitab.com/en-us/solutions/analytics/reliability/)
- [Discrete Event Simulation](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [Process Mining](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [Key Capabilities](https://www.minitab.com/en-us/solutions/key-capabilities/)
- [Continuous Improvement](https://www.minitab.com/en-us/solutions/key-capabilities/continuous-improvement/)
- [Data Integration & Data Prep](https://www.minitab.com/en-us/solutions/key-capabilities/data-integration-data-prep/)
- [Diagramming & Mind Mapping](https://www.minitab.com/en-us/solutions/key-capabilities/diagramming-mind-mapping/)
- [Digital Twins](https://info.minitab.com/en/new-to-simul8?hsLang=en)
- [Model Deployment & ML Ops](https://www.minitab.com/en-us/solutions/key-capabilities/model-deployment-ml-ops/)
- [Innovation & Project Management](https://www.minitab.com/en-us/solutions/key-capabilities/innovation-project-management/)
- [Process Excellence: Detect, Correct & Prevent](https://www.minitab.com/en-us/solutions/key-capabilities/process-excellence/)
- [Featured Industries](https://www.minitab.com/en-us/solutions/industry/)
- [Academic](https://www.minitab.com/en-us/solutions/industry/academic/)
- [Energy & Natural Resources](https://www.minitab.com/en-us/solutions/industry/energy-resources/)
- [Government & Public Sector](https://www.minitab.com/en-us/solutions/industry/government/)
- [Healthcare](https://www.minitab.com/en-us/solutions/industry/healthcare/)
- [Insurance](https://www.minitab.com/en-us/solutions/industry/insurance/)
- [Manufacturing & Industrial](https://www.minitab.com/en-us/solutions/industry/manufacturing-industrial/)
- [Services](https://www.minitab.com/en-us/solutions/industry/service-industries/)
- [Software & Technology](https://www.minitab.com/en-us/solutions/industry/software-technology/)
- [Construction](https://www.minitab.com/en-us/solutions/industry/construction/)
- [Featured Roles](https://www.minitab.com/en-us/solutions/role/)
- [Engineering](https://www.minitab.com/en-us/solutions/role/engineering/)
- [Business Analysis](https://www.minitab.com/en-us/solutions/role/business-analysts/)
- [Information Technology](https://www.minitab.com/en-us/solutions/role/information-technology/)
- [Supply Chain](https://www.minitab.com/en-us/solutions/role/supply-chain/)
- [Customer Service & Contact Center](https://www.minitab.com/en-us/solutions/role/customer-service-contact-center/)
- [Human Resources](https://www.minitab.com/en-us/solutions/role/human-resources/)
- [Marketing](https://www.minitab.com/en-us/solutions/role/marketing/)
- [Research and Development](https://www.minitab.com/en-us/solutions/role/research-and-development/)
- Resources & Services
Back
[Resources & Services](https://www.minitab.com/en-us/resources-services/)
[All Resources & Services](https://www.minitab.com/en-us/resources-services/)
- [Resources](https://www.minitab.com/en-us/resources-services/resources/)
- [Case Studies](https://www.minitab.com/en-us/resources-services/resources/case-studies/)
- [eBooks & White Papers](https://www.minitab.com/en-us/resources-services/resources/ebooks-and-white-papers/)
- [Blog](https://blog.minitab.com/blog/?hsLang=en)
- [Data Sets](https://www.minitab.com/en-us/resources-services/resources/data-set/)
- [Webinars & Events](https://www.minitab.com/en-us/resources-services/resources/events/)
- [Education Hub](https://www.minitab.com/en-us/resources-services/resources/education-hub/)
- [Services](https://www.minitab.com/en-us/resources-services/services/)
- [Training](https://www.minitab.com/en-us/resources-services/services/training/)
- [Deployment](https://www.minitab.com/en-us/resources-services/services/deployment/)
- [Consulting](https://www.minitab.com/en-us/resources-services/services/statistical-consulting/)
- [Self-Paced Learning](https://www.minitab.com/en-us/resources-services/services/self-paced-learning/)
- [Continuing Education](https://www.minitab.com/en-us/resources-services/services/continuing-education/)
- Support
Back
[Support](https://www.minitab.com/en-us/support/)
[Technical Support](https://www.minitab.com/en-us/support/)
- [Subscriptions & Activation](https://www.minitab.com/en-us/support/subscriptions-and-activation/)
- [Minitab Quick Start](https://www.minitab.com/en-us/support/quick-start/)
- [Training](https://www.minitab.com/en-us/resources-services/services/training/)
- [Installation Support](https://www.minitab.com/en-us/support/installation/)
- [Support Videos](https://www.minitab.com/en-us/support/videos/)
- [Support Documentation](https://www.minitab.com/en-us/support/documents/)
- [Software Updates](https://www.minitab.com/en-us/support/software-updates/)
- [Product Downloads](https://www.minitab.com/en-us/support/downloads/)
- [Support Policy](https://www.minitab.com/en-us/support/policy/)
- Company
Back
[Company](https://www.minitab.com/en-us/company/)
[Company](https://www.minitab.com/en-us/company/)
- [About Us](https://www.minitab.com/en-us/company/our-company/)
- [Leadership Team](https://www.minitab.com/en-us/company/leadership-team/)
- [Partners](https://www.minitab.com/en-us/company/partners/)
- [Careers](https://www.minitab.com/en-us/company/careers/)
- [Contact](https://www.minitab.com/en-us/company/contact-us/)
- [News](https://www.minitab.com/en-us/company/press-releases/)
[Try/Buy](https://www.minitab.com/en-us/try-buy/)
- [Statistics](https://blog.minitab.com/en/blog/tag/statistics)
- [Data Analysis](https://blog.minitab.com/en/blog/tag/data-analysis)
-
- [Quality Improvement](https://blog.minitab.com/en/blog/tag/quality-improvement)
- [Subscribe](https://info.minitab.com/blog/subscribe?hsLang=en)
## Notice
You are now leaving minitab.com.
Click Continue to proceed to:
Continue
Go Back
# Using Intervals to Get at the Tail Ends of the Problem in Healthcare and Medical Devices
[Cheryl Pammer](https://blog.minitab.com/en/blog/author/cheryl-pammer) | 3/21/2019
Topics: [Medical Devices](https://blog.minitab.com/en/blog/tag/medical-devices), [Healthcare](https://blog.minitab.com/en/blog/tag/healthcare), [Data Analysis](https://blog.minitab.com/en/blog/tag/data-analysis), [Statistics](https://blog.minitab.com/en/blog/tag/statistics), [Quality Improvement](https://blog.minitab.com/en/blog/tag/quality-improvement)
- [Share](https://www.linkedin.com/shareArticle?mini=true&url=https://blog.minitab.com/en/blog/using-intervals-to-get-at-the-tail-ends-of-the-problem)
- [Share](https://www.facebook.com/sharer.php?u=https://blog.minitab.com/en/blog/using-intervals-to-get-at-the-tail-ends-of-the-problem)
Confidence intervals show the range of values we can be fairly, well, confident, that our true value lies in, and they are very important to any quality practitioner. I could be 95% confident the volume of a can of soup will be 390-410 ml. I could be 99% confident under 2% of the products in my batch are defective.
Demonstrating an improvement to the process often involves proving a significant improvement in the mean, so that’s what we tend to focus on – the center of a distribution.
Defects don’t fall in the center, though. They fall in the tails. You can find more beneficial insights in many situations through examining the tails of the distribution rather than just focusing on the mean.
Let’s take a look at some non-traditional [confidence intervals](https://support.minitab.com/en-us/minitab/18/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/what-is-a-confidence-interval/) that are particularly useful in estimating the percent that fall inside or outside the specification limits.
# Estimating the 99th Percentile on Time to Complete Hospital Lab Work
**
A [probability plot](https://support.minitab.com/en-us/minitab/18/help-and-how-to/graphs/how-to/probability-plot/before-you-start/overview/) is most often used to help you determine whether your data follows a normal distribution (based on how linear the points appear to be). It provides a good starting point for understanding percentiles. A [percentile](https://support.minitab.com/en-us/minitab/18/help-and-how-to/calculations-data-generation-and-matrices/calculator/calculator-functions/statistics-calculator-functions/percentile-function/) is the value at which a given percentage of the population is estimated *to fall below*.
But did you know probability plots also provide estimates of the percentiles of the distribution? You can choose any percentile you want on the Y axis and find the corresponding data value on the X axis. The corresponding confidence intervals on the probability plot are confidence intervals for the specific percentile.
I was recently working on a project with a hospital that needed to estimate within how many minutes 99% of their pre-surgery lab work falls.
The X value corresponding to Y = 99 on the probability plot was 204 minutes. In other words, 99% of all pre-lab work should be complete by 204 minutes.
The confidence interval around the estimate indicated that we could be 95% confident that 99% of the lab work would be complete by 171-244 minutes. This explained why the surgeries were often falling behind schedule.
# Demonstrating Reliability of Medical Tubing Using Tolerance Intervals
While percentiles estimate the percent of observations that fall below a certain value, [tolerance intervals](https://support.minitab.com/en-us/minitab/18/help-and-how-to/quality-and-process-improvement/quality-tools/supporting-topics/tolerance-interval-basics/) provide a range that you can be confident a certain percentage *will fall between*.
They are very useful for determining where a certain percentage of the population will fall relative to your specification limits.
For example, a medical device company I was working with needed to show 95/99 reliability on the tensile strength of plastic tubing. The specific requirement was that they needed to be 95% confident that the tubing would withstand 3 pounds of force for 99% of product.
Like the hospital data, these data were non-normal. Because a tolerance interval estimates what is going on in the tails of the distribution – not the mean – the distribution assumption is important. Here, an extreme value distribution provided a good distribution fit. Because the tubing could not be too strong, a one-sided tolerance limit, a lower bound, was appropriate. The value of the 99% lower tolerance bound with 95% confidence was 10.7 pounds. In other words, we could be 95% confident that 99% of the tubing population has a tensile strength of at least 10.7 pounds – well above the specification limit of 3 pounds.
# Percentiles vs Tolerance
Consider using confidence intervals on percentiles or tolerance intervals the next time you are interested in interval estimation involving the tails of a distribution:
- Percentiles estimate the value that a given percentage of the population falls below.
- Tolerance intervals estimate the range of measurements a given percentage of the population will falls within.
## You Might Also Like
[New Minitab Updates Unite Data Collection, Preparation, and Predictive Analytics](https://blog.minitab.com/en/blog/new-minitab-updates-unite-data-collection-preparation-and-predictive-analytics?hsLang=en)
[Data Preparation](https://blog.minitab.com/en/blog/tag/data-preparation) | 5 Minute Read
[Artemis II Heat Shield: How Do You Decide in Uncertain Conditions?](https://blog.minitab.com/en/blog/artemis-ii-heat-shield-how-do-you-decide-under-uncertainty?hsLang=en)
[Data Analysis](https://blog.minitab.com/en/blog/tag/data-analysis) | 4 Minute Read
[Do You Really Need That New Machine? How Minitab Can Help You Find Out](https://blog.minitab.com/en/blog/do-you-really-need-that-new-machine-how-minitab-can-help-you-find-out?hsLang=en)
[Quality Improvement](https://blog.minitab.com/en/blog/tag/quality-improvement) | 4 Minute Read
---
- [Careers](https://www.minitab.com/en-us/company/careers/)
- [Trust Center](https://www.minitab.com/en-us/trust-center/)
- [Suppliers](https://www.minitab.com/en-us/suppliers/)
- [Site Map](https://www.minitab.com/en-us/site-map/)
- [](https://www.linkedin.com/company/minitab/)
- [](https://www.facebook.com/Minitab/)
- [](https://www.youtube.com/user/MinitabInc)
- [](https://www.instagram.com/minitab/)
---
© 2025 Minitab, LLC. All Rights Reserved.
- [Terms of Use](https://www.minitab.com/en-us/legal/terms-of-use/)
- [Privacy Policy](https://www.minitab.com/en-us/legal/privacy-policy/)
- [Legal](https://www.minitab.com/en-us/legal/)
- Cookies Settings