MGS 8020 Business Intelligence Measure Jul 15 2017

MGS 8020 Business Intelligence Measure Jul 15, 2017 Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 1

Measure - SMART “Voice of the Process” (The “Voice of the Data”) Based on natural (common cause) variation Tolerance limits (The “Voice of the Customer”) Customer requirements/Specs Process Capability A measure of how “capable” the process is to meet customer requirements Compares process limits to tolerance limits Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 2

Agenda 1. Analysis Tools 2. Control Charts 3. Process Capability Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 3

Data Analysis Tools Run Chart Can be used to illustrate the relationships between factors such us quality and training Can be used to identify when equipment or processes means are drifting away from specs Histogram Control Chart Frequency Scatter Diagram Data Ranges Can be used to display the shape of variation in a set of data Georgia State University - Confidential Use to identify if the process is predictable (in control) MGS 8020 Measure. ppt/Jul 15, 2017/Page 4

Cause and Effect Diagram Machine Man Effect Environmental Method Georgia State University - Confidential Material MGS 8020 Measure. ppt/Jul 15, 2017/Page 5

Pareto Charts Root Cause Analysis 80% of the problems may be attributed to 20% of the causes Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 6

Agenda 1. Analysis Tools 2. Control Charts 3. Process Capability Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 7

Statistical Process Control (SPC): Used to determine if process is within process control limits during the process and to take corrective action when out of control Statistical process control is the use of statistics to measure the quality of an ongoing process Process in Statistical Control UCL LCL A Process is in control when all points are inside the control limits UCL LCL A Process is not in control when one or more points is/are outside the control limits Process not in Statistical Control UCL LCL Georgia State University - Confidential Special Causes MGS 8020 Measure. ppt/Jul 15, 2017/Page 8

When to Investigate Even if in control the process should be investigated if any non random patterns are observed OVER TIME UCL In Control LCL 1 Trend - Constant Increase/Decrease 2 3 4 5 6 UCL Close to Control Limit UCL LCL 1 2 3 4 5 6 LCL 1 2 3 4 5 Cycles UCL Consecutive Points Below/Above Mean LCL 5 10 15 20 LCL 1 Georgia State University - Confidential 2 3 4 5 6 MGS 8020 Measure. ppt/Jul 15, 2017/Page 9

Types of Variation Special cause (unexpected) variation Prediction e m Ti Common cause (expected) variation Prediction m Ti e Georgia State University - Confidential E Caused by factors that can be clearly identified and possibly managed; assignable causes evident, not in statistical control Short-term objective - to eliminate unexpected variation Inherent in the process E Normal variation only, stable, predictable, in statistical control Long-term objective - to reduce expected variation MGS 8020 Measure. ppt/Jul 15, 2017/Page 10

Control Chart Development Steps 1 2 Identify Measurement Collect Data INPUTS OUTPUT X’s 3 Y’s Improve Process 4 Determine Control Limits Start Eliminate Special Causes Reduce Common Cause Variation Improve Average Defects A Georgia State University - Confidential B C D MGS 8020 Measure. ppt/Jul 15, 2017/Page 11

Quality Measures – Attributes & Variables • An attribute is a product characteristics such as color, surface texture, cleanliness, or perhaps smell or taste. Attributes can be evaluated quickly with a discrete response such as good or bad, acceptable or not, yes or no. An attribute measure evaluation is sometimes referred to as a qualitative classification, since the response is not measured. • A variable measure is a product characteristics that is measured on a continuous scale such as length, weight, temperature, or time. For example, the amount of liquid detergent in a plastic container can be measured to see if it conforms to the company’s product specifications. Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 12

Control Charts • Control Charts have historically been used to monitor the quality of manufacturing process. SPC is just as useful for monitoring quality in services. The difference is the nature of the “defect” being measured and monitored. Using Motorola’s definition – a failure to meet customer requirements in any product or service. • Control Charts are graphs that visually show if a sample is within statistical control limits. The control limits are the upper and lower bands of a control chart. They have two basic purposes, to establish the control limits for a process and then to monitor the process to indicate when it is out of control. All control charts look alike, with a line through the center of a graph that indicates the process average and lines above and below the center line that represent the upper and lower limits of the process. Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 13

Control Charts for Attributes • • The quality measures used in attribute control charts are discrete values reflecting a simple decision criterion such as good or bad. A p-chart uses the proportion of defective (defectives) items in a sample as the sample statistics; a c-chart uses the actual number of defects per item in a sample. p-charts Although a p-chart employs a discrete attribute measure (i. e. number of defective items) and thus is not continuous, it is assumed that as the sample size gets larger, the normal distribution can be used to approximate the distribution of the proportion defective. Z Source: Selected Chapters on Business Analysis – Ch 15 Statistical Process Control Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 14

Control Charts for Attributes ~ p-chart • The p-formula – the sample proportion defective; an estimate of the process average Total defectives Total sample observations • k = the number of samples n = the sample size The standard deviation of the sample proportion δp = • n To calculate control limits for the p-chart: Z n • Normal Distribution: Z-Value m -3 -2 -1 0 1 2 3 Z Z- VALUE is the number of Standard Deviations from the mean of the Normal Curve z = the number of standard deviations from. Zthe process average. In the control limit formulas for p-charts (and other control charts), z is occasionally equal to 2. 00 but most frequently is 3. 00. A z value of 2. 00 corresponds to an overall normal probability of 95 percent and z = 3. 00 corresponds to a normal probability of 99. 74 percent. Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 15

Control Charts for Attributes ~ p-chart (Example) • The Western Jeans company produces denim jeans. The company wants to establishes p-chart to monitor the production process and maintain high quality. Western believes that approx. 99. 74 percent of the variability in the production process (z = 3. 00) is random and thus should be within control limits, whereas 0. 26 percent of the process variability is not random and suggests that the process is out of control. • The company has taken 20 samples (one per day for 20 -days), each containing 100 pairs of jeans (n=100), and inspected them for defects. The total number of defectives are 200. • Find the control limits. Z Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 16

Control Charts for Attributes ~ c-chart • f • • A c-chart is used when it is not possible to compute a production defective and the actual number of defects must be used. For example, when automobiles are inspected, the number of blemishes (i. e. defects) in the paint job can be counted for each car, but a proportion cannot be computed, since the total number of possible blemishes is not known. = the total number of defects / total number of samples The standard deviation δc = • To calculate control limits for the p-chart: Z Z Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 17

Control Charts for Attributes ~ c-chart (Example) • The Ritz Hotel believes that approximately 99% of the defects (corresponding to 3 -sigma limits) are caused by natural, random variations in the housekeeping and room maintenance service, with 1% caused by nonrandom variability. They want to construct a c-chart to monitor the housekeeping service. • 15 inspections samples are selected by the hotel. An inspection sample includes 12 rooms and the total number of defects is 190. • Find the control limits. Z Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 18

Control Charts for Variables ~ R-chart • • • Variable control charts are for continuous variables that can be measured, such as weight or volume. Two commonly used variable control charts are the range chart (R-chart) and the mean chart (x-bar chart). R-chart In an R-chart, the range is the difference between the smallest and largest values in a sample. This range reflects the process variability instead of the tendency toward a mean value. R is the range of each sample k is the number of samples. Z Upper control limit Lower control limit Source: Selected Chapters on Business Analysis – Ch 15 Statistical Process Control Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 19

Control Charts for Variables ~ R-chart (Example) • In the production process for a particular slip-ring bearing the employees have taken 10 samples (during 10 -day period) of 5 slip-ring bearings (n=5). Please define the control limits for R-chart. The individual observations from each sample are shown as follows: Sample k 2 3 4 5 1 5. 02 5. 01 4. 94 4. 99 4. 96 4. 98 0. 08 2 5. 01 5. 03 5. 07 4. 95 4. 96 5. 00 0. 12 3 4. 99 5. 00 4. 93 4. 92 4. 99 4. 97 0. 08 4 5. 03 4. 91 5. 01 4. 98 4. 89 4. 96 0. 14 5 4. 92 5. 03 5. 05 5. 01 4. 99 0. 13 6 4. 97 5. 06 4. 96 5. 03 5. 02 0. 10 7 5. 05 5. 01 5. 10 4. 96 4. 99 5. 02 0. 14 8 5. 09 5. 10 5. 08 5. 05 0. 11 9 5. 14 5. 10 4. 99 Z 5. 08 5. 09 5. 08 0. 15 10 5. 01 4. 98 5. 07 4. 99 5. 03 0. 10 50. 11 1. 15 sum average Georgia State University - Confidential R R 1 0. 115 MGS 8020 Measure. ppt/Jul 15, 2017/Page 20

Control Charts for Variables ~ x-bar chart • For an x-bar chart, the mean of each sample is computed and plotted on the chart; the points are sample means. The samples tend to be small, usually around 4 or 5. n is the sample size (or number of observations) k is the number of samples Upper control limit Lower control limit Georgia State University - Confidential Z MGS 8020 Measure. ppt/Jul 15, 2017/Page 21

Control Charts for Variables ~ x-bar chart (Example) • Use the data from R-Chart and define the control limits for x-bar chart. Z Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 22

Control Charts for Variables ~ Tabular values for X-bar and R charts (Given) Sample Size n A 2 D 3 D 4 2 1. 880 0 3. 268 3 1. 023 0 2. 574 4 0. 729 0 2. 282 5 0. 577 0 2. 114 6 0. 483 0 2. 004 7 0. 419 0. 076 1. 924 8 0. 373 0. 136 1. 864 9 0. 337 0. 184 1. 816 10 0. 308 0. 223 1. 777 11 0. 285 0. 256 1. 744 12 0. 266 0. 283 1. 717 13 0. 249 0. 307 1. 693 14 0. 235 0. 328 1. 672 15 0. 223 0. 347 1. 653 Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 23

Control Charts for Variables ~ Tabular values for X-bar and R charts (Given) Sample Size n A 2 D 3 D 4 16 0. 212 0. 363 1. 637 17 0. 203 0. 378 1. 622 18 0. 194 0. 391 1. 608 19 0. 187 0. 403 1. 597 20 0. 180 0. 415 1. 585 21 0. 173 0. 425 1. 575 22 0. 167 0. 434 1. 566 23 0. 162 0. 443 1. 557 24 0. 157 0. 451 1. 548 25 0. 153 0. 459 1. 541 Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 24

Process Capability n n n Process Capability – A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits. There are three main elements associated with process capability – process variability (the natural range of variation of the process), the process center (mean), and the design specifications. Process limits (The “Voice of the Process” or The “Voice of the Data”) based on natural (common cause) variation Tolerance limits (The “Voice of the Customer”) – customer requirements Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 25

Agenda 1. Analysis Tools 2. Control Charts 3. Process Capability Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 26

Process Capability • Variation that is inherent in a production process itself is called common variation. (1 ) (3 ) specification common variation (2 ) (4 ) specification common variation Georgia State University - Confidential common variation MGS 8020 Measure. ppt/Jul 15, 2017/Page 27

Process Capability Ratio • One measure of the capability of a process to meet design specifications is the process capability ratio (Cp). It is defined as the ratio of the range of the design specifications (the tolerance range) to the range of process variation, which for most firms is typically ± 3δ or 6δ • If Cp is less than 1. 0, the process range is greater than the tolerance range, and the process is not capable of producing within the design specifications all the time. If Cp equals 1. 0, the tolerance range and the process range are virtually the same. If Cp is greater than 1. 0, the tolerance range is greater than the process range. • Companies would logically desire a Cp equal to 1. 0 or greater, since this would indicate that the process is capable of meeting specifications. Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 28

Process Capability Ratio (Example) • The XYZ Snack Food Company packages potato chips in bags. The net weight of the chips in each bag is designed to be 9. 0 oz, with a tolerance of +/- 0. 5 oz. The packaging process results in bags with an average net weight of 8. 80 oz and a standard deviation of 0. 12 oz. The company wants to determine if the process is capable of meeting design specifications. Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 29

Process Capability Index • • • The Process Capability Index (Cpk) differs from the Cp in that it indicates if the process mean has shifted away from the design target, and in which direction it has shifted – that is, if it is off center. If the Cpk index is greater than 1. 00 then the process is capable of meeting design specifications. If Cpk is less than 1. 00 then the process mean has moved closer to one of the upper or lower design specifications, and it will generate defects. When Cpk equals Cp, this indicates that the process mean is centered on the design (nominal) target. Please read Example 7 on page 354. where • x-bar is the mean of the process • sigma is the standard deviation of the process • UTL is the customer’s upper tolerance limit (specification) • and LTL is the customer’s lower tolerance limit Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 30

Interpreting the Process Capability Index n Cpk < 1 Not Capable n Cpk > 1 Capable at 3 n Cpk > 1. 33 Capable at 4 n Cpk > 1. 67 Capable at 5 n Cpk > 2 Capable at 6 Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 31

Process Capability Index (Example) • A process has a mean of 45. 5 and a standard deviation of 0. 9. The product has a specification of 45. 0 ± 3. 0. Find the Cpk. Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 32

Process Capability Index (Example) n = min { (45. 5 – 42. 0)/3(0. 9) or (48. 0 -45. 5)/3(0. 9) } n = min { (3. 5/2. 7) or (2. 5/2. 7) } n = min { 1. 30 or 0. 93 } = 0. 93 (Not capable!) n However, by adjusting the mean, the process can become capable. Georgia State University - Confidential MGS 8020 Measure. ppt/Jul 15, 2017/Page 33