OPSM 501: Operations Management Koç University Graduate School of Business MBA Program OPSM 501: Operations Management Week 7: Quality Zeynep Aksin zaksin@ku.edu.tr

The Ottoman Catapult

Lord of the Rings: Mordor Catapult

Lord of the Rings: Gondor Catapult

Angry Birds Catapult

The OPSM Catapult!

Process Capability 3 3 process width Design tolerance width Cp = (design tolerance width)/(process width) = (max-spec – min-spec)/ /6x Example: Plane is “on time” if it arrives between T – 15min and T + 15min. Design tolerance width is therefore 30 minutes x of arrival time is 12 min Cp = 30/6*12 = 30/72 = 0.42 A “capable” process can still miss target if there is a shift in the mean. Motorola “Six Sigma” is defined as Cp = 2.0 I.e., design tolerance width is +/- 6x or 12 x 3 3 process width Design tolerance width min acceptable max acceptable

There are multiple solutions to most parametric design problems Analytical Expression for Brownie Mix “Chewiness” Chewiness = FactorA + FactorB Where FactorA = 600(1-exp(-7T/600)) + T/10 And FactorB = 10*Time HYPOTHETICAL FactorA FactorB 200F 400F Temperature Time 20 min 26 min Option 1 Option 2 Options 1 and 2 deliver the same value of “chewiness.” Why might you prefer one option over the other?

Taguchi Methods Loss = C(x-T)2 Good Bad Quality Quality Loss Any deviation from the target value is “quality lost.” Good Performance Metric Performance Metric, x Bad Minimum acceptable value Target value Maximum acceptable value Target value

Who is the Better Target Shooter? The mean is important, but the variance is very important as well. Need to look at the distribution. What are the sources of variability? How can obvious sources be eliminated?

Take Aways Products and processes are causal systems Typically have lots of variables Internal variables are set by the manufacturer/provider Target settings and associated variance External variables are set by the environment or the user Target settings and associated variance (variance often much harder to control than with internal variables) Impossible to eliminate all variability GOAL: find target settings for variables such that variability in other values of these variables has minimal effect on output/performance….a “robust design.” Methodology for achieving robust design Causal model, even if not explicitly analytical Early exploratory experimentation Control of variability and increased robustness through design changes Focused experimentation to refine settings

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

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

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

Natural and Assignable Variation

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

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

Process capability 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 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.

Six Sigma Quality

Process Capability Index Cpk Shows how well the parts being produced fit into the range specified by the design specifications Want Cpk larger than one For our example: Cpk 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

Process Capability Index Cp US LS 100 160  = 10 m = 130 Process Interval = 6 Specification interval = US –LS Cp= (US-LS) / 6 99.73% Process Interval = 60 Specification Interval = US – LS = 60 Cp= (US-LS) / 6 = 60 / 60 = 1 Process Interval Specification Interval

Process Capability Index Cp US LS 100 160  = 5 m = 130 99.73% 99.99998% Process Interval = 6 = 30 Specification Interval = US – LS =60 Cp= (US-LS) / 6 =2 3 Process Interval Specification Interval 6 Process Interval

Process Mean Shifted Cpk = min{ (US - )/3, ( - LS)/3 } 100 160  = 10 m = 100 Cpk = min{ (US - )/3, ( - LS)/3 } Cpk = min(2,0)=0 Specification 3 Process 70 130

2. Statistical Process Control: Control Charts Can be used to monitor ongoing production process quality 970 980 990 1000 1010 1020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 LCL UCL

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

Mean and Range Charts (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) UCL LCL R-chart (R-chart detects increase in dispersion) UCL LCL

Process Control and Improvement Out of Control In Control Improved UCL  LCL

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

For upcoming weeks Assignment: Turkish Airlines case-due week 8 (do with your study team) Discuss all, but answer only Question 2 and 6 for your written assignment For question 6 submit excel sheet as well as explanation in writing Littlefield simulation calendar (teams of 3) Register groups by Friday Nov 9 http://lab.responsive.net/lt/koc/start.html Code: operations Screening begins right after all groups are registered: explore interface and first 50 days’ data Start simulation Monday Nov 12 @ 17:00 End simulation Monday Nov 20 @ 17:00 Report due-in class week 9