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Types of Data This module was developed by Business Process Improvement. For more modules, please contact us at or visit our website

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Introduction Control charts give us a picture of our process over time. This picture tells us when to leave our process alone (i.e., the process is in control) or when to look for a problem (i.e., an assignable cause is present). There are many different types of control charts. However, you can group control charts into two major categories. The type of data being charted distinguishes these two categories. There are two types of data you can have: attributes data and variables data. Both these types of data are introduced in this module. With attributes data, there is a need to develop specific descriptions. These descriptions, which are called operational definitions, are also introduced in this module. For variables data, the standard deviation is an important measurement as well as the average. Both of these terms are explored in more detail below.

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Objectives In this module you will learn: 1. What attributes data are. 2. What an operational definition is. 3. What variables data are. 4. What the average and standard deviation are. It is important to know what type of data you will collect so you can determine what type of control chart to construct. Different charts will give different information. Attributes charts include p, np, c and u charts. Variables charts include Xbar-R charts, Xbar-s charts, individuals charts and moving average and moving range charts.

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Attributes Data Attributes control charts are based on attributes data. These types of data are often referred to as discrete data. There are two kinds of attributes data: yes/no type of data and counting data. p and np control charts are used with yes/no type data; c and u charts are used with counting type data. The two types of attributes data are described below.

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Yes/No Data For one item, there are only two possible outcomes: either it passes or it fails some preset specification. Each item inspected is either defective (i.e., it does not meet the specifications) or is not defective (i.e., it meets specifications). Examples of the yes/no attributes data are: mail delivery: is it on time or not on time? phone answered: is it answered or not answered? invoice correct: is it correct or not correct? stock item: is it in stock or not in stock? cycle count: is it correct or not correct? product : in-spec or out of spec? supplier: material received on-time or not on-time?

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Counting Data With counting data, you count the number of defects. A defect occurs when something does not meet a preset specification. It does not mean that the item itself is defective. For example, a television set can have a scratched cabinet (a defect) but still work properly. When looking at counting data, you end up with whole numbers such as 0, 1, 2, 3; you can't have half of a defect. To be considered counting data, the opportunity for defects to occur must be large; the actual number that occurs must be small. For example, the opportunity for customer complaints to occur is large. However, the number that actually occurs is small. Thus, the number of customer complaints is an example of counting type data. Other examples are: number of mistakes in picking number of items shipped incorrectly number of accidents for delivery trucks

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Exercise For your organization, what are some examples of yes/no type data and counting type data. List your responses below. Yes/No: Counting:

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Operational Definitions When working with attributes data, you have to have a clear understanding of whether the item you are looking at is defective or not (yes/no type data) or whether it should be counted as a defect (counting type data). In order to know whether a shipment was on time or to count the number of on- time shipments, you have to have a definition of what "on time" means. Is "on time" anywhere from 1:55 p.m. to 2:05 p.m., anytime before 2:00 p.m., or anytime between 2:00 p.m. and 2:15 p.m.? This clear understanding of a quality expectation is called an operational definition.

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Operational Definition According to Dr. W. Edwards Deming, an operational definition includes: a written statement (and/or a series of examples) of criteria or guidelines to be applied to an object or to a group. a test of the object or group for conformance with the guidelines that includes specifics such as how to sample, how to test, and how to measure. a decision: yes, the object or the group did meet the guidelines; no, the object or group did not meet the guidelines; or the number of times the object or group did not meet the guidelines.

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Operational Definitions Using an invoice error example, the written statement may read "An invoice error is an incorrect shipping amount or a wrong price." The test could be to: compare every invoice to the packing list to check for incorrect shipping amounts and, compare every invoice to a price schedule to check for wrong prices. Based on these guidelines and a test for conformance with these guidelines, you could make a decision as to whether an invoice is defective or how many defects an invoice contains.

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Exercise Select one of the variables below. Develop an operational definition for the variable. On-Time Delivery Rework in a Department Injury at Work Customer Complaint Invoice Error

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Variables Data Variables control charts are based on variables data. Variables data consist of observations made from a continuum. That is, the observation can be measured to any decimal place you want if your measurement system allows it. Some examples of variables data are contact time with a customer, sales dollars, amount of time to make a delivery, height, weight, and costs.

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Exercise For your organization, what are some examples of variables data? Record your answers below.

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Average and Standard Deviation In dealing with variables data, the average and standard deviation are very important parameters. One must understand what is meant by these terms. The average (also called the mean) is probably well understood by most. It represents a "typical" value. For example, the average temperature for the day based on the past is often given on weather reports. It represents a typical temperature for the time of year. The average is calculated by adding up the results you have and dividing by the number of results. For example, suppose the last five customer complaints took 5, 6, 2, 3, and 8 days to close. The average is determined by adding up these five numbers and dividing by 5. The average is denoted by and in this case is;

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Average and Standard Deviation While the average is understood by most, few understand the standard deviation, denoted by the letter s. The standard deviation can be thought of as an average distance (the standard) that each individual point is away from the mean. The equation for the standard deviation is given below. We will be using control charts to estimate what our process average is and what the process standard deviation is. For these two numbers to have any meaning, the process must be in statistical control.

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Summary Control charts can be divided into two major categories: attribute control charts and variable control charts. Attribute control charts are based on attribute data. There are two types of attributes data: yes/no type and counting data. Yes/no type attributes data have only two possible outcomes: either the item is defective or it is not defective. With counting type attributes data, the number of defects is counted. With attributes data, there is the need for operational definitions. Operational definitions are used to determine what constitutes a defective item or a defect. Variable control charts are based on variables data. Variables data are data from a continuum. The basic probability distribution underlying the calculation of control limits for variables data is the normal distribution.

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