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Statistical Process Control PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh Edition Principles of Operations Management, Ninth Edition PowerPoint slides by Jeff Heyl 6 © 2014 Pearson Education, Inc. SUPPLEMENT

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Learning Objectives 1. Apply quality management tools for problem solving 2. Identify the importance of data in quality management 6S–2

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Introduction Statistical Quality Control Statistical Process Control (SPC) Acceptance Sampling (AS) Statistical process control is a statistical technique that is widely used to ensure that the process meets standards. Acceptance sampling is used to determine acceptance or rejection of material evaluated by a sample. 6S–3

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Introduction Firing Preparing the clay for throwing Wedging Throwing Pinching pots Painting Pottery Making Process 6S–4

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Introduction 6S–5

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Statistical Process Control Chart (SPC) Variability is inherent in every process. Natural variation – can not be eliminated Assignable variation -- Deviation that can be traced to a specific reason: machine vibration, tool wear, new worker. Variation Natural Variation Assignable Variation 6S–6

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Statistical Process Control Chart (SPC) The essence of SPC is the application of statistical techniques to prevent, detect, and eliminate defective products or services by identifying assignable variation. 6S–7

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UCL LCL Sample number Mean Out of control Natural variation due to chance Abnormal variation due to assignable sources A control chart is a time-ordered plot obtained from an ongoing process 6S–8 Statistical Process Control Chart (SPC)

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Control Charts Control Charts for Variable Data Control Charts for Attribute Data -charts (for controlling central tendency) R-charts (for controlling variation) p-charts (for controlling percent defective) c-charts (for controlling number of defects) Attribute Data (discrete): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go. Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc. 6S–9

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1. Take random samples 2. Calculate the upper control limit (UCL) and the lower control limit (LCL) 3. Plot UCL, LCL and the measured values 4. If all the measured values fall within the LCL and the UCL, then the process is assumed to be in control and no actions should be taken except continuing to monitor. 5. If one or more data points fall outside the control limits, then the process is assumed to be out of control and corrective actions need to be taken. Statistical Process Control Chart (SPC) 6S-10

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x-Charts Lower control limit (LCL) = x - A 2 R Upper control limit (UCL) = x + A 2 R whereR=average range of the samples A 2 =control chart factor from Table S6.1(page 241) x=average of the sample means 6S–11

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Range=18-13=5 Hour 1 BoxWeight of NumberOat Flakes x-Charts 6S–12 Range=17-14=3 Hour 2 BoxWeight of NumberOat Flakes R=(5+3)/2 = 4

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x-Charts Lower control limit (LCL) = x - A 2 R Upper control limit (UCL) = x + A 2 R whereR=average range of the samples A 2 =control chart factor from Table S6.1 (page241) x=average of the sample means 6S–13

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Average=(17+13+…+16)/9=16.11 Hour 1 BoxWeight of NumberOat Flakes x-Charts 6S–14 Average=(14+16+…+17)/9=15.22 Hour 2 BoxWeight of NumberOat Flakes x=( )/2 =

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x-Charts Lower control limit (LCL) = x - A 2 R Upper control limit (UCL) = x + A 2 R whereR=average range of the samples A 2 =control chart factor from Table S6.1 (page241) x=average of the sample means 6S–15

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x-Charts Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D S–16

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x-Charts Lower control limit (LCL) = x - A 2 R Upper control limit (UCL) = x + A 2 R whereR=average range of the samples A 2 =control chart factor from Table S6.1 (page241) x=average of the sample means 6S–17

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x-Charts Example S6.1: Eight samples of seven tubes were taken at random intervals. Construct the x-chart with 3- control limit. Is the current process under statistical control? Why or why not? Should any actions be taken? Sample size = n = 7 A 2 = ? 6S–18

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x-Charts 6S–19 Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D

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x-Charts Example S6.1: Eight samples of seven tubes were taken at random intervals. Construct the x-chart with 3- control limit. Is the current process under statistical control? Why or why not? Should any actions be taken? A 2 = S–20

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x-Charts Control Chart for sample of 7 tubes 6.43 = UCL 6.29 = LCL 6.36 = Mean Sample number |||||||||||| It is assumed that the central tendency of process is in control with 99.73% confidence. No actions need to be taken except to continuously monitor this process. 6S–21

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Steps in Creating Charts 1.Take samples from the population and compute the appropriate sample statistic 2.Use the sample statistic to calculate control limits 3.Plot control limits and measured values 4.Determine the state of the process (in or out of control) 5.Investigate possible assignable causes and take actions 6S–22

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R-Charts Lower control limit (LCL) = D 3 R Upper control limit (UCL) = D 4 R where R=average range of the samples D 3 and D 4 =control chart factors from Table S6.1 (Page 241) 6S–23

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R-Charts 6S–24 Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D

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R-Charts Average range R = 5.3 pounds Sample size n = 5 From Table S6.1 D 4 = ? D 3 = ? Example S6.2 6S–25

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R-Charts 6S–26 Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D

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R-Charts UCL R = D 4 R = (2.12)(5.3) = 11.2 pounds LCL R = D 3 R = (0)(5.3) = 0 pounds Average range R = 5.3 pounds Sample size n = 5 From Table S6.1 D 4 = 2.12, D 3 = 0 UCL = 11.2 Mean = 5.3 LCL = 0 Example S6.2 6S–27

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R-Charts n=7 Example S6.3: Refer to Example S6.1. Eight samples of seven tubes were taken at random intervals. Construct the R-chart with 3- control limits. Is the current process under statistical control? Why or why not? Should any actions be taken? D 3 =? D 4 = ? 6S–28

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R-Charts 6S–29 Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D

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R-Charts 6S–30 Example S6.3: Refer to Example S6.1. Eight samples of seven tubes were taken at random intervals. Construct the R-chart with 3- control limits. Is the current process under statistical control? Why or why not? Should any actions be taken? D 3 =0.08, D 4 = 1.92

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R-Charts Control Chart for sample of 7 tubes 0.33 = UCL 0.01 = LCL Sample number |||||||||||| = R The variation of process is in control with 99.73% confidence. 6S–31

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Mean and Range Charts R-chart (R-chart detects increase in dispersion) UCLLCL (a) The central tendency of process is in control, but its variation is not in control. x-chart (x-chart does not detect dispersion) UCLLCL 6S–32

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Mean and Range Charts (b) The variation of process is in control, but its central tendency is not in control. R-chart (R-chart does not detect changes in mean) UCL LCL x-chart (x-chart detects shift in central tendency) UCLLCL 6S–33

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R-Chart and X-Chart Example S6.4: Seven random samples of four resistors each are taken to establish the quality standards. Develop the R-chart and the x-chart both with 3- control limits for the production process. Is the entire process under statistical control? Why or why not? D 3 = 0, and D 4 = 2.28 n = 4 R = ( … + 4)/7 = 3.0 6S–34

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R-Chart and X-Chart Control Chart for sample of 4 resistors 6.84 = UCL 0 = LCL Sample number |||||||||||| = R The variation of process is in control with 99.73% confidence. 6S–35

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R-Chart and X-Chart X= ( … )/7 n = 4, A 2 = 0.73 R = ( … + 4)/7 = 3.0 6S–36

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R-Chart and X-Charts Control Chart = UCL 97.6 = LCL = Mean Sample number |||||||||||| The central tendency of process is not in control with 99.73% confidence. In conclusion, with 99.7% confidence, the entire resistor production process is not in control since its central tendency is out of control although its variation is under control. 6S–37

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EX 1 in class A part that connects two levels should have a distance between the two holes of 4”. It has been determined that x-bar chart and R-chart should be set up to determine if the process is in statistical control. The following ten samples of size four were collected. Calculate the control limits, plot the control charts, and determine if the process is in control No. of SampleMeanRange S–38

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R-Chart and X-Chart 6S–39 Example S6.5: Resistors for electronic circuits are manufactured at Omega Corporation in Denton, TX. The head of the firm’s Continuous Improvement Division is concerned about the product quality and sets up production line checks. She takes seven random samples of four resistors each to establish the quality standards. Develop the R-chart and the chart both with 3- control limits for the production process. Is the entire process under statistical control? Why or why not? # of sampleReadings of Resistance (ohms)

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R-Chart and X-Chart # of Sample Sample range Sample mean n=4 D 3 =0 D 4 = = UCL 0 = LCL Sample number |||||||||||| = R variation of process is in control with 99.73% confidence. 6S–40

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R-Chart and X-Chart # of Sample Sample range Sample mean n= = UCL 97.6 = LCL Sample number |||||||||||| = X central tendency of process is not in control with 99.73% confidence. Thus, entire process is not in control. 6S–41 A 2 =0.73 X= ( … )/7 99.8

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EX 2 in class A quality analyst wants to construct a sample mean chart for controlling a packaging process. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below. Set up control charts to determine if the process is in statistical control DayPackage 1Package 2Package 3Package 4 Monday Tuesday Wednesday Thursday Friday S–42

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Statistical Process Control Chart (SPC) Control Charts Control Charts for Variable Data Control Charts for Attribute Data -charts (for controlling central tendency) R-charts (for controlling variation) p-charts (for controlling percent defective) c-charts (for controlling number of defects) Attribute Data (discrete): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go. Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc. 6S–43

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Control Charts for Attribute Data Categorical variables Good/bad, yes/no, acceptable/unacceptable Measurement is typically counting defectives Charts may measure Percentage of defects (p-chart) Number of defects (c-chart) 6S–44

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P-Charts wherep=mean percent defective overall the samples z=number of standard deviations = 3 n=sample size 6S–45

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P-Charts SampleNumberPercentSampleNumberPercent Numberof ErrorsDefectiveNumberof ErrorsDefective Total = 80 Example S6.6: Data-entry clerks at ARCO key in thousands of insurance records each day. One hundred records entered by each clerk were carefully examined and the number of errors counted. Develop a p-chart with 3- control limits and determine if the process is in control. 6S–46

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P-Charts n = 100 Because we cannot have a negative percent defective 6S–47

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P-Charts – – – – – – – – – – – – Sample number Percent defective |||||||||| UCL= 0.10 LCL= 0.00 p = 0.04 Possible assignable causes present Possible good assignable causes present The process is not in control with 99.73% confidence. 6S–48

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C-Charts A c-chart is used when the quality cannot be measured as a percentage. Number of car accidents per month at a particular intersection Number of complaints the service center of a hotel receives per week Number of scratches on a nameplate Number of dimples found on a metal sheet 6S–49

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C-Charts wherec=mean number defective overall the samples UCL = c + 3 c UCL = c + 3 c LCL = c - 3 c LCL = c - 3 c 6S–50

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C-Charts c = 54 / 9 = 6 complaints /week |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 Week Number Number of defect – – – 8 8 – 6 6 – 4 – 2 – 0 0 – UCL = LCL = 0 c = 6 Example S6.7: Over 9 weeks, Red Top Cab company received the following numbers of calls from irate passengers: 3, 0, 8, 9, 6, 7, 4, 9, 8, for a total of 54 complaints. Determine the 3- control limits of a c-Chart. Because we cannot have the negative number of defective records UCL= c + 3 c UCL= c + 3 c = = LCL= c - 3 c LCL= c - 3 c = = => 0 The process is in control with 99.73% confidence. 6S–51

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1. Effective quality management is data driven 2. There are multiple tools to identify and prioritize process problems 3. There are multiple tools to identify the relationships between variables Managing Quality Summary 6S–52

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