1. OPSM 301 Operations Management Class 17: Quality: Statistical process control Koç University Zeynep Aksin zaksin@ku.edu.tr

2. Announcement  Group Case Assignment 2  See Web page to download a copy  Due Thursday in class or Friday in my or Buse’s office

3. Statistical Quality Control Objectives  1.Reduce normal variation (process capability) –If normal variation is as small as desired, Process is capable –We use capability index to check for this  2.Detect and eliminate assignable variation (statistical process control) –If there is no assignable variation, Process is in control –We use Process Control charts to maintain this

4. Natural Variations  Also called common causes  Affect virtually all production processes  Expected amount of variation, inherent due to: - the nature of the system - the way the system is managed - the way the process is organised and operated  can only be removed by - making modifications to the process - changing the process  Output measures follow a probability distribution  For any distribution there is a measure of central tendency and dispersion

5. Assignable Variations  Also called special causes of variation  Exceptions to the system  Generally this is some change in the process  Variations that can be traced to a specific reason  considered abnormalities  often specific to a  certain operator  certain machine  certain batch of material, etc.  The objective is to discover when assignable causes are present  Eliminate the bad causes  Incorporate the good causes

6. 1. Process Capability Design requirements: Diameter: 1.25 inch ±0.005 inch Specification Limits Lower specification Limit:LSL=1.25-0.005=1.245 Upper Specification Limit:USL=1.25+0.005=1.255 Example:Producing bearings for a rotating shaft

7. Relating Specs to Process Limits Process performance (Diameter of the products produced=D): Average 1.25 inch Std. Dev: 0.002 inch Frequency Diameter 1.25 Question:What is the probability That a bearing does not meet specifications? (i.e. diameter is outside (1.245,1.255) ) P(defect)=0.006+0.006=0.012 or 1.2% This is not good enough!!

8. Process capability  What can we do to improve capability of our process? What should  be to have Six-Sigma quality?  We want to have: (1.245-1.25)/  = 6   =0.00083 inch  We need to reduce variability of the process. We cannot change specifications easily, since they are given by customers or design requirements. If P(defect)>0.0027 then the process is not capable of producing according to specifications. To have this quality level (3 sigma quality), we need to have: Lower Spec: mean-3  Upper Spec:mean+3  If we want to have P(defect)  0, we aim for 6 sigma quality, then, we need: Lower Spec: mean-6  Upper Spec:mean+6 

9. Six Sigma Quality

10. Process Capability Index C pk  Shows how well the parts being produced fit into the range specified by the design specifications  Want C pk larger than one For our example: C pk tells how many standard deviations can fit between the mean and the specification limits. Ideally we want to fit more, so that probability of defect is smaller

11. Process Capability Index C p Process Interval = 6  Specification interval = US –LS C p = (US-LS) / 6  Process Interval = 60 Specification Interval = US – LS = 60 C p = (US-LS) / 6  = 60 / 60 = 1 Process Interval Specification Interval 99.73% USUSLSLS 100160  = 10 

12. Process Capability Index C p Process Interval = 6  = 30 Specification Interval = US – LS =60 C p = (US-LS) / 6  =2 Specification Interval 6  Process Interval 3  Process Interval USLS 100160  = 5  99.73% 99.99998%

13. Process Mean Shifted US LS 100160  = 10  130 C pk = min{ (US -  )/3 , (  - LS)/3  } C pk = min(2,0)=0 Specification 3  Process 70

14. 2. Statistical Process Control: Control Charts Can be used to monitor ongoing production process quality 970 980 990 1000 1010 1020 0123456789101112131415 LCL UCL

15. Setting Chart Limits For x-Charts when we know  Upper control limit (UCL) = x + z  x Lower control limit (LCL) = x - z  x wherex=mean of the sample means or a target value set for the process z=number of normal standard deviations (=3)  x =standard deviation of the sample means =  / n  =population standard deviation n=sample size

16. Setting Control Limits Hour 1 sample itemWeight of NumberOat Flakes 117 213 316 418 517 616 715 817 916 Mean16.1  =1 HourMeanHourMean 116.1715.2 216.8816.4 315.5916.3 416.51014.8 516.51114.2 616.41217.3 n = 9 For 99.73% control limits, z = 3 Sample size

17. Setting Control Limits Hour 1 SampleWeight of NumberOat Flakes 117 213 316 418 517 616 715 817 916 Mean16.1  =1 HourMeanHourMean 116.1715.2 216.8816.4 315.5916.3 416.51014.8 516.51114.2 616.41217.3 n = 9 For 99.73% control limits, z = 3 UCL x = x + z  x = 16 + 3(1/3) = 17 LCL x = x - z  x = 16 - 3(1/3) = 15

18. 17 = UCL 15 = LCL 16 = Mean Setting Control Limits Control Chart for sample of 9 boxes Sample number |||||||||||| 123456789101112 Variation due to assignable causes Variation due to natural causes Out of control

19. R – Chart  Type of variables control chart  Shows sample ranges over time  Difference between smallest and largest values in sample  Monitors process variability  Independent from process mean

20. Setting Chart Limits For R-Charts Lower control limit (LCL R ) = D 3 R Upper control limit (UCL R ) = D 4 R where R=average range of the samples D 3 and D 4 =control chart factors

21. Setting Control Limits UCL R = D 4 R = (2.115)(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 D 4 = 2.115, D 3 = 0 UCL = 11.2 Mean = 5.3 LCL = 0

22. Mean and Range Charts (a) These sampling distributions result in the charts below (Sampling mean is shifting upward but range is consistent) R-chart (R-chart does not detect change in mean) UCLLCL x-chart (x-chart detects shift in central tendency) UCLLCL

23. Mean and Range Charts R-chart (R-chart detects increase in dispersion) UCLLCL (b) These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) x-chart (x-chart does not detect the increase in dispersion) UCLLCL

24. Process Control and Improvement LCL  UCL Out of ControlIn ControlImproved

25. Six Sigma Quality

26. Six Sigma  a vision;  a philosophy;  a symbol;  a metric;  a goal;  a methodology  All of the Above

27. Six Sigma : Organizational Structure  Champion –Executive Sponsor  Master Black Belts –Process Improvement Specialist –Promotes Org / Culture Change  Black Belts –Full Time –Detect and Eliminate Defects –Project Leader  Green Belts –Part-time involvement

28. Six Sigma Quality: DMAIC Cycle (Continued) 5. Control (C) Customers and their priorities Process and its performance Causes of defects Remove causes of defects Maintain quality 1. Define (D) 2. Measure (M) 3. Analyze (A) 4. Improve (I)

29. Process Control and Capability: Review  Every process displays variability: normal or abnormal  Do not tamper with process “in control” with normal variability Correct “out of control” process with abnormal variability  Control charts monitor process to identify abnormal variability  Control charts may cause false alarms (or missed signals) by mistaking normal (abnormal) for abnormal (normal) variability  Local control yields early detection and correction of abnormal  Process “in control” indicates only its internal stability  Process capability is its ability to meet external customer needs  Improving process capability involves changing the mean and reducing normal variability, requiring a long term investment  Robust, simple, standard, and mistake - proof design improves process capability  Joint, early involvement in design improves quality, speed, cost