Operations Management - II Post Graduate Program Session 13. Vinay Kumar Kalakbandi Assistant Professor Operations & Systems Area

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1 Operations Management - II Post Graduate Program Session 13 Vinay Kumar Kalakbandi Assistant Professor Operations & Systems Area 2/27/2016 Vinay Kalakbandi 1 Recap Agenda Statistical Quality Control Control charts Process capability Six sigma 2/27/2016 Vinay Kalakbandi 2 1

Starbucks Coffee is best served at 140+/-15 degrees

2 Key terms Quality metric User specifications Process parameters 2/27/2016 Vinay Kalakbandi 3 Starbucks Coffee is best served at 140+/-15 degrees What is the metric of quality? 2/27/2016 Vinay Kalakbandi 4 2

PVC pipes PVC pipes come in different diameters What

Solder bridges, Component shift Can happen anywhere

3 PVC pipes PVC pipes come in different diameters What is the metric of quality? 2/27/2016 Vinay Kalakbandi 5 Printed Circuit boards Three main causes of defects in PCBs are Opens, Solder bridges, Component shift Can happen anywhere on the board! Will need rework! What is the metric of quality? 2/27/2016 Vinay Kalakbandi 6 3

4 30 minute pizza delivery! What is the metric of quality? 2/27/2016 Vinay Kalakbandi 7 Metric of quality The nature of the quality dimension with the context Continuous data: PVC, Starbucks Count data: PCB Proportion data: Dominos 2/27/2016 Vinay Kalakbandi 8 4

5 Quality metric examples Sl. No. Type of Applications Quality metric 1 Component Manufacturing Conformance of physical measurements of components and sub-assemblies to specifications Conformance to operating characteristics of machines and other resources involved in the process 2 Final Assembly Number of defects in the product Conformance to test specifications Number of missing elements 3 Process Industries Temperature, Pressure and Heat specifications Conformance to product specifications Conformance to equipment specifications Vibrations and other variations in equipments and subsystems Conformance to specifications of the automation & control system 4 Service Systems Number of defects in various business processes Errors in processing documents Conformance to waiting time/lead time related specifications User specifications Starbucks Pizza delivery: PVC pipes: PCB manufacturing 140+/ minutes or free +/-0.01mm upto 3 defects Determined by industry standards Determined by the consumer 2/27/2016 Vinay Kalakbandi 10 5

6 Process parameters The process parameters impact the quality metric The quality metric varies due to Natural causes: Non-controllable; inherent variability in the system, noise, usually minor Assignable causes: Controllable, bring about a fundamental change on the nature of the process, causes considerable impact on quality The aggregate impact of process parameters is captured by the mean and the standard deviation of the quality metric 2/27/2016 Vinay Kalakbandi 11 What are the process parameters? Starbucks PCBs PVC pipes Pizza delivery 2/27/2016 Vinay Kalakbandi 12 6

7 Key terms Quality metric User specifications Process parameters Which comes first? How are they related? 2/27/2016 Vinay Kalakbandi 13 Funnel and Pencil Systems Always on the dot! 2/27/2016 Vinay Kalakbandi 14 7

8 Our orders Raw material: paper with circle Customer 1 Produce 10 dots per paper within the circle Will reject if any dots are outside circle Customer 2 Produce dots 3 cm away from the centre of circle We have a tolerance of +/- 3 mm Customer 3 Produce 10 dots per paper We will tolerate at most 3 dots inside circle. 2/27/2016 Vinay Kalakbandi 15 Objective of Process control To constantly monitor the quality metric 2/27/2016 Vinay Kalakbandi 16 8

9 Run charts Run charts plot the quality metric over time. Monitor every occurrence of the quality metric Downsides of run charts Might be difficult to monitor every item coming out of the line Not sure if variation is due to change in process parameters Not clear when to adjust input parameters We might be overreacting to random variation 2/27/2016 Vinay Kalakbandi 17 Objective of Process control To constantly monitor the quality metric Ensure that the quality metric has no assignable cause of variation 2/27/2016 Vinay Kalakbandi 18 9

10 Process control charts Information: Monitor process variability over time Control limits: Average + z * standard deviation Usually z = 3. Why? Decision Rule: Ignore variation outside abnormal Are control limits related to user specifications? 09/11/2014 Vinay Kalakbandi 19 Types of Data Depending on quality metric Continuous data X-bar and R charts Count data c-charts Proportion data P-charts 09/11/2014 Vinay Kalakbandi 20 10

Constructing a control chart Determine the quality metric Choose appropriate measurement method Collect sample data using a sampling procedure Choose appropriate control chart Calculate and plot

11 Constructing a control chart Determine the quality metric Choose appropriate measurement method Collect sample data using a sampling procedure Choose appropriate control chart Calculate and plot control limits on the control chart Control limits are + or 3*sigma Determine if data is in control If non-random variation is present, fix the problem and recalculate control limits. 09/11/2014 Vinay Kalakbandi 21 Standard deviation? 2/27/2016 Vinay Kalakbandi 22 11

12 Coefficients for computing LCL and UCL in X-bar and R charts* Sample size (n) A 2 D 3 D Source: Juran, J.M. and F.M. Gryna, (1995), Quality Planning and Analysis, Tata McGraw-Hill, 3 rd Edition, New Delhi, pp /11/2014 Vinay Kalakbandi 24 12

13 09/11/2014 Vinay Kalakbandi 25 09/11/2014 Vinay Kalakbandi 26 13

14 Utility of X-bar and R chart 09/11/2014 Vinay Kalakbandi 27 Utility of X-bar and R chart 09/11/2014 Vinay Kalakbandi 28 14

15 Other charts P-charts Calculate percentage defectives in a sample an item is either good or bad Based on binomial distribution 09/11/2014 Vinay Kalakbandi 29 Other charts c Charts Count number of defects in an item Based on poisson distribution 09/11/2014 Vinay Kalakbandi 30 15

16 Objective of Process control To constantly monitor the quality metric Ensure that the quality metric has no assignable cause of variation Detect and remove assignable cause of variation 2/27/2016 Vinay Kalakbandi 31 Output 09/11/2014 Vinay Kalakbandi 32 16

17 Performance variation patterns 09/11/2014 Vinay Kalakbandi 33 09/11/2014 Vinay Kalakbandi 34 17

18 Objective of Process control To constantly monitor the quality metric Ensure that the quality metric has no assignable cause of variation Detect and remove assignable cause of variation Adjust process parameters such that the quality metric falls within user specifications 2/27/2016 Vinay Kalakbandi 35 From Control to improvement 09/11/2014 Vinay Kalakbandi 36 18

19 Process capability 09/11/2014 Vinay Kalakbandi 37 Process Capability Process Capability is defined by the spread of the process Potential capability (C p ) is defined as the ratio of the difference in specification limits to the process spread C p = Actual capability (C pk ) takes into consideration the extent to which the process has deviated from the desired target C pk = Specification Range ( USL LSL) Process Capability 6 Pr ocess Centre LSL USL Pr ocess Centre Min,

Impact of 99% defectives! 2/27/2016 Vinay Kalakbandi 39 How good is good enough? 99.9% is already VERY GOOD But what could happen at a quality level of 99.9% (i.e., 1000 ppm), in our everyday lives (about 4.

20 Impact of 99% defectives! 2/27/2016 Vinay Kalakbandi 39 How good is good enough? 99.9% is already VERY GOOD But what could happen at a quality level of 99.9% (i.e., 1000 ppm), in our everyday lives (about 4.6 )? 4000 wrong medical prescriptions each year More than 3000 newborns accidentally falling from the hands of nurses or doctors each year Two long or short landings at American airports each day 400 letters per hour which never arrive at their destination 20

21 Process Capability & Defects Process Capability Index (C pk ) Total Products outside twosided specification limits ,255 ppm ,614 ppm ,861 ppm ,395 ppm ,700 ppm ppm ppm ppm ppm Source: Quality Planning & Analysis, Juran & Gryna, Chapter 17, 3e Sigma statistics 09/11/2014 Vinay Kalakbandi 42 21

22 Six sigma quality C p ( USL LSL) 2 ( USL LSL) 12 A spread 6 of 6 22

XIII Statistical Process Control

XIII Statistical Process Control MATHEMATICS 01-510-LW Business Statistics Martin Huard Fall 008 1. Suppose the statistics x = 14.1 and R= 17.5 are obtained from 50 samples of size 9. a) What is the centerline and the control limits for