Unit 5 Statistical Process Control

Overview

Welcome to Unit 5 of LDRS 220. In this unit, with our study of organizational financial documents behind us, we will start into the second major portion of this course by examining Statistical Process Control.

Within this theme, the first step is to build the foundation of how statistics work. This foundation is built on both formulae of Standard Deviation.

For many students, the simple fact that math is used in Statistical Process Control may invoke panic. For others, these calculations may seem unassuming once they are explained. The calculations for standard deviation may seem complicated but, once broken down in to smaller segments, they are rather simple.

There are two formulae used to calculate Standard Deviation. If your data is a sample, then the denominator is n-1.” If your data is made up of ALL the data available, referred to as the Population, then the denominator is just “n.”

The differences may seem significant, but there is a simple reason… because the ‘sample’ formula does not contain ALL of the data, it represents a more conservative view of the result.

We will examine the formulae deeper, including calculating standard deviation both ways. We will use the automatic calculation formulae available in Excel.

Topics

This unit is divided into the following topics:

  1. Calculating Standard Deviation
  2. “Population” vs. “Sample” Standard Deviation Calculations

Learning Outcomes

When you have completed this unit, you should be able to:

  • Understand, and apply, the components that make up the two standard deviation calculations.
  • Use data to determine which standard deviation formula to use.
  • Apply how standard deviation analysis fits into statistical process control to better an organization.

Activity Checklist

Here is a checklist of learning activities you will benefit from in completing this unit. You may find it useful for planning your work.

Learning Activities

  • Read chapters 1-6 in your The Cartoon Introduction to Statistics textbook
  • Complete the Create Data and Calculate “Population” Standard Deviation activity
  • Complete the Building a UCL/LCL Chart activity

Assessment

  • In this course you demonstrate your understanding of the course learning outcomes in different ways, including papers, projects, discussions and quizzes. Please see the Assessment section in Moodle for assignment details and due dates.

Resources

Here are the resources you will need to complete this unit.

  • Kline, G. and Dabney, A. ; (2013) The Cartoon Introduction to Statistics. New York: Hill and Wang
    • 978-0-8090-3359-1
    • (CIS)
  • Mullis, D. and Orloff, J.; (1998) The Accounting Game. Naperville, Ill: Sourcebooks.
    • 978-1-4022-1186-7
    • (TAG)
  • Other online resources will be provided in the unit.

Planning Ahead

Before you examine the topics in this unit, take a moment to watch this video that has been provided by the instructor. This video will introduce each topic and help support your learning. You are encouraged to re-watch this video if you are struggling with any of the concepts you will be learning about in this section.

Activity: Read

To help you prepare for what you will be learning in this unit, read the following:

  • Chapters 1-6 and the Glossary from your The Cartoon Introduction to Statistics textbook
    • The reading, this week, introduces us to the world of statistics. For this course, we are focusing on what makes up the calculations of standard deviatiom. (you may not know it but Standard Deviation is the foundational concept of Statistical Process Control).
    • If you have limited math experience, it is likely best to read these sections more than once

5.1 Calculating Standard Deviation

As we begin our study of statistics, it is important to understand that the true power of statistics is the ability to determine when something varies enough to consider it acceptable, or not. This “variation”, sometimes call “deviation”, cannot be subjective. Standard deviation provides empirical data to determine if the process is *“in control”* or not.

In the “Planing Ahead” section on the Overview page, you were asked to read chapters 1-6 of your The Cartoon Introduction to Statistics textbook - the following video offers a visual illustration of the standard deviation calculations you were introduced to in your reading:

Watch: How to Calculate Standard Deviation

Note: It might be helpful to watch this video while following along in your textbook if you are finding this content challenging.

5.2 “Population” vs. “Sample” Standard Deviation Calculations

Building upon Topic 1, you may now be thinking that the existence of two different calculations for standard deviation seems confusing - but they are closely related and have only a minor dissimilarity between them. There might be a mild visual difference to the two formulae, but as noted in the last section, the alpha symbols function in the same manner; with the exception of the denominator of the “population” calculation being “n” and the “sample” formula being “n-1.”

The tradition of the “sample” formulae is that it provides a more conservative answer since ALL of the data is NOT included in the calculation. The following video helps to explain the main difference in the “population” and “sample” formulae:

Watch: n vs n-1. Why are there 2 formulas for the standard deviation?

Activity: Create Data and Calculate “Population” Standard Deviation

The activity will focus on helping you better comprehend statistics by applying some of the content we have learned to better understand standard deviation.

In order to calculate standard deviation, data must exist. The collection point of data is called the monitoring phase; Decisions made from the data analysis results occur in the controlling phase.

To begin this activity, you will need to create the data – once you have created the data, you can perform the “population” calculation.

To begin:

  • Randomly select ten (10) whole numbers between 25 and 50

    • These ten numbers will become your data set

Next:

Use these ten numbers to calculate:

  • The MEAN average for the data
  • The VARIANCE for each data point (MINUS the MEAN average)

This reveals the POPULATION Standard Deviation

We can adjust the data to reflect SAMPLE data and then recalculate using the denominator of “n-1.”

With this happily behind us, now let us repeat the calculations using the automatic Excel formula. With this method, the hard part is choosing to use the Population or Sample formula.

Be prepared to defend your conclusions and share your thoughts with other members of the class.

Note: Learning activities in this course are ungraded, unless specified. They are designed to help you succeed in your assessments in this course, so you are strongly encouraged to complete them.

Activity: Building a UCL/LCL Chart

In this next activity, we are going to follow the concepts of the previous Activity (Create Data and Calculate “Population” Standard Deviation), and build a very practical chart that could be used in an ongoing manner (WHILE a process is happening) to ensure acceptable outcomes (avoiding unacceptable levels of variance).

To begin:

Use the same data you created in the previous activity (the 10 whole numbers you chose between 25-50). Then, we will add a time factor (leaving room for future data entry), and then focus on formatting the chart to gain readability and understanding.

We will choose a sigma that suits out customer’s requirements. (Based on the from the previous activity)

Time will then be offered to allow all to practice chart building and formatting.

Assessment

Refer to the course schedule for graded assignments you are responsible for submitting. All graded assignments, and their due dates, can be found on the “Assessment” tab.

In addition to any graded assignments you are responsible for submitting, be sure to complete all the Learning Activities that have been provided throughout the content - these are intended to support your understanding of the content.

Checking your Learning

Before you move on to the next unit, you may want to check to make sure that you are able to:

  • Understand, and apply, the components that make up the two standard deviation calculations.
  • Use data to determine which standard deviation formula to use.
  • Apply how standard deviation analysis fits into statistical process control to better an organization.