standard deviation

A Study of Estimates of Sigma in Small Sample Sizes

This paper looks at some of the methods of estimating standard deviation (which I will usually refer to as ‘sigma’). Additionally, I propose a new formula for estimating sigma for small sample sizes and also present a means to mathematically evaluate these competing estimates of sigma. The question was posed to me: “I have five…


Understanding Process Sigma Level

Six Sigma is a data-driven approach to quality, aimed at reducing variation and the associated defects, wastes and risks in any process. This article explores the basics of Six Sigma process quality – definition and measurement. In a set of data, mean (μ) and standard deviation (σ) are defined as: μ = x1 + x2…


Getting the Most out of a Capability Analysis

The process capability indices Pp and Cp describe how closely a process can operate within its specification limits. Many articles describe the difference between Pp and Cp simply: one is short term, one is long term. Moving beyond such a description, this article focuses on the untapped power of capability analysis and shows you how…


Calculating Call Center Interarrival and Service Times

Two Six Sigma professionals recently posed questions in the iSixSigma Discussion Forum relating to queuing theory in a call center. One reader wanted to know how to calculate average and standard deviation for service time and interarrival time – the amount of time between the arrival of one customer and the arrival of the next….

Variation – The Root of All Process Evil

As a customer, the worst experience I can imagine is being a casualty of process variation. ‘It doesn’t seem that bad,’ you may be thinking to yourself. Just remember back to the last time you: Went grocery shopping only to select the slowest teller in the store. Received a haircut that was shorter or longer…

Estimation Method Helps Analysis of Truncated Data Sets

A data set with a physical limit – such as time, which has a lower bound of zero – often cannot be transformed using the usual tools for non-normal data. To determine process capability and perform further statistical analysis, use the standard deviation calculated as if the data were not truncated, along with a correction factor.