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Adeyl Khan, Faculty, BBA, NSU Quality Control

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Adeyl Khan, Faculty, BBA, NSU Phases of Quality Assurance 10-2 Figure 10.1 Acceptance sampling Process control Continuous improvement Inspection of lots before/after production Inspection and corrective action during production Quality built into the process The least progressive The most progressive

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Adeyl Khan, Faculty, BBA, NSU Inspection How Much/How Often Where/When Centralized vs. On-site 10-3 InputsTransformationOutputs Acceptance sampling Process control Acceptance sampling Figure 10.2

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Adeyl Khan, Faculty, BBA, NSU Inspection Costs 10-4 Cost Optimal Amount of Inspection Cost of inspection Cost of passing defectives Total Cost Figure 10.3

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Adeyl Khan, Faculty, BBA, NSU Where to Inspect in the Process Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before a covering process 10-5

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Adeyl Khan, Faculty, BBA, NSU Examples of Inspection Points Type of business Inspection points Characteristics Fast FoodCashier Counter area Eating area Building Kitchen Accuracy Appearance, productivity Cleanliness Appearance Health regulations Hotel/motelParking lot Accounting Building Main desk Safe, well lighted Accuracy, timeliness Appearance, safety Waiting times SupermarketCashiers Deliveries Accuracy, courtesy Quality, quantity 10-6 Table 10.1

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Adeyl Khan, Faculty, BBA, NSU Statistical Control Statistical Process Control: Statistical evaluation of the output of a process during production The essence of statistical process control is to assure that the output of a process is random so that future output will be random. Quality of Conformance : A product or service conforms to specifications 10-7

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Adeyl Khan, Faculty, BBA, NSU Control Chart 10-8 0123456789101112131415 UCL LCL Sample number Mean Out of control Normal variation due to chance Abnormal variation due to assignable sources Figure 10.4

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Adeyl Khan, Faculty, BBA, NSU Control Chart Control Chart Purpose: to monitor process output to see if it is random A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means) Upper and lower control limits define the range of acceptable variation 10-9 Define Measure Compare Evaluate Correct Monitor results SPC (The Process) Random variation Natural variations in the output of a process, created by countless minor factors Assignable variation A variation whose source can be identified Variations and Control

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Adeyl Khan, Faculty, BBA, NSU Normal Distribution 10-10 Mean 95.44% 99.74% Standard deviation Figure 10.6

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Adeyl Khan, Faculty, BBA, NSU Control Limits: Sampling Distribution & Process Distribution 10-11 Sampling distribution Process distribution Mean Lower control limit Upper control limit Figure 10.7

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Adeyl Khan, Faculty, BBA, NSU SPC Errors Type I error Concluding a process is not in control when it actually is. Type II error Concluding a process is in control when it is not. 10-12 In controlOut of control In controlNo ErrorType I error (producers risk) Out of controlType II Error (consumers risk) No error

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Adeyl Khan, Faculty, BBA, NSU Type I Error 10-13 Mean LCLUCL /2 Probability of Type I error Figure 10.8

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Adeyl Khan, Faculty, BBA, NSU Observations from Sample Distribution 10-14 Sample number UCL LCL 1234 Figure 10.9

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Adeyl Khan, Faculty, BBA, NSU Control Charts for Variables 10-15 Variables generate data that are measured. Image: http://www.asprova.jp/mrp/glossary/en/cat254/x-r-1.html Mean control charts Used to monitor the central tendency of a process. X bar charts Range control charts Used to monitor the process dispersion R charts

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Adeyl Khan, Faculty, BBA, NSU Mean and Range Charts 10-16 Figure 10.10A UCL LC L UCL LC L R-chart x-Chart Detects shift Does not detect shift (process mean is shifting upward) Sampling Distribution

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Adeyl Khan, Faculty, BBA, NSU Mean and Range Charts 10-17 x-Chart UCL Does not reveal increase UCL LCL R-chart Reveals increase Figure 10.10B (process variability is increasing) Sampling Distribution

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Adeyl Khan, Faculty, BBA, NSU p chart Used to monitor the proportion of defectives in a process When observations can be placed into two categories. Good or bad Pass or fail Operate or don’t operate When the data consists of multiple samples of several observations each 10-18 Control Chart for Attributes Attributes generate data that are counted

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Adeyl Khan, Faculty, BBA, NSU c Chart Used to monitor the number of defects per unit Advantages Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Breaks or Tears per unit of area Bacteria or pollutants per unit of volume Calls, complaints, failures per unit of time 10-19

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Adeyl Khan, Faculty, BBA, NSU Use of Control Charts At what point in the process to use control charts What size samples to take What type of control chart to use Variables Attributes 10-20

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Adeyl Khan, Faculty, BBA, NSU Run Tests Run test – a test for randomness Any sort of pattern in the data would suggest a non- random process All points are within the control limits - the process may not be random 10-21

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Adeyl Khan, Faculty, BBA, NSU Nonrandom Patterns in Control charts Trend Cycles Bias Mean shift Too much dispersion 10-22

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Adeyl Khan, Faculty, BBA, NSU Counting Runs 10-23 Counting Above/Below Median Runs(7 runs) Counting Up/Down Runs(8 runs) U U D U D U D U U D B A A B A B B B A A B

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Adeyl Khan, Faculty, BBA, NSU NonRandom Variation Managers should have response plans to investigate cause May be false alarm (Type I error) May be assignable variation 10-24

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Adeyl Khan, Faculty, BBA, NSU Process Capability Tolerances or specifications Range of acceptable values established by engineering design or customer requirements Process variability Natural variability in a process Process capability Process variability relative to specification 10-25

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Adeyl Khan, Faculty, BBA, NSU Process Capability 10-26 Lower Specification Upper Specification A. Process variability matches specifications Lower Specification Upper Specification B. Process variability well within specifications Lower Specification Upper Specification C. Process variability exceeds specifications Figure 10.15

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Adeyl Khan, Faculty, BBA, NSU Process Capability Ratio 10-27 Process capability ratio, Cp = specification width process width Upper specification – lower specification 6 Cp = If the process is centered use Cp If the process is not centered use Cpk

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Adeyl Khan, Faculty, BBA, NSU Limitations of Capability Indexes Process may not be stable Process output may not be normally distributed Process not centered but Cp is used 10-28

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Adeyl Khan, Faculty, BBA, NSU Example 8 Machine Standard Deviation Machine CapabilityCpCp A0.130.780.80/0.78 = 1.03 B0.080.480.80/0.48 = 1.67 C0.160.960.80/0.96 = 0.83 10-29 Cp > 1.33 is desirable Cp = 1.00 process is barely capable Cp < 1.00 process is not capable

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Adeyl Khan, Faculty, BBA, NSU 3 Sigma and 6 Sigma Quality 10-30 Process mean Lower specification Upper specification 1350 ppm 1.7 ppm +/- 3 Sigma +/- 6 Sigma

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Adeyl Khan, Faculty, BBA, NSU Improving Process Capability Simplify Standardize Mistake-proof Upgrade equipment Automate 10-31

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Adeyl Khan, Faculty, BBA, NSU Taguchi Loss Function 10-32 Cost Target Lower spec Upper spec Traditional cost function Taguchi cost function Figure 10.17

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Adeyl Khan, Faculty, BBA, NSU Learning Objectives List and briefly explain the elements of the control process. Explain how control charts are used to monitor a process, and the concepts that underlie their use. Use and interpret control charts. Use run tests to check for nonrandomness in process output. Assess process capability. 10-33

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