Statistical Process Control Operations Management Dr. Ron Tibben-Lembke

Designed Size

Natural Variation

Theoretical Basis of Control Charts 95.5% of all  X fall within ± 2  Properties of normal distribution

Theoretical Basis of Control Charts Properties of normal distribution 99.7% of all  X fall within ± 3 

Skewness  Lack of symmetry  Pearson’s coefficient of skewness: Skewness = 0 Negative Skew < 0 Positive Skew > 0

Kurtosis  Amount of peakedness or flatness Kurtosis < 0 Kurtosis > 0 Kurtosis = 0

Design Tolerances  Design tolerance: Determined by users’ needs UTL -- Upper Tolerance Limit LTL -- Lower Tolerance Limit Eg: specified size +/ inches  No connection between tolerance and  completely unrelated to natural variation.

Process Capability and 6   A “capable” process has UTL and LTL 3 or more standard deviations away from the mean, or 3σ.  99.7% (or more) of product is acceptable to customers LTLUTL 33 66 LTLUTL

Process Capability LTLUTL LTL UTL CapableNot Capable LTLUTL LTLUTL

Process Capability  Specs: 1.5 +/  Mean: Std. Dev. =  Are we in trouble?

Process Capability  Specs: 1.5 +/ LTL = 1.5 – 0.01 = 1.49 UTL = = 1.51  Mean: Std. Dev. = LCL = *0.002 = UCL = = Process Specs

Capability Index  Capability Index (C pk ) will tell the position of the control limits relative to the design specifications.  C pk >= 1.0, process is capable  C pk < 1.0, process is not capable

Process Capability, C pk  Tells how well parts produced fit into specs Process Specs 33 33 LTLUTL

Process Capability  Tells how well parts produced fit into specs  For our example:  C pk = min[ 0.015/.006, 0.005/0.006]  C pk = min[2.5,0.833] = < 1 Process not capable

Process Capability: Re-centered  If process were properly centered  Specs: 1.5 +/ LTL = 1.5 – 0.01 = 1.49 UTL = = 1.51  Mean: 1.5 Std. Dev. = LCL = *0.002 = UCL = = Process Specs

If re-centered, it would be Capable Process Specs

Packaged Goods  What are the Tolerance Levels?  What we have to do to measure capability?  What are the sources of variability?

Production Process Make Candy PackagePut in big bags Make Candy Mix Mix % Candy irregularity Wrong wt.

Processes Involved  Candy Manufacturing: Are M&Ms uniform size & weight? Should be easier with plain than peanut Percentage of broken items (probably from printing)  Mixing: Is proper color mix in each bag?  Individual packages: Are same # put in each package? Is same weight put in each package?  Large bags: Are same number of packages put in each bag? Is same weight put in each bag?

Your Job  Write down package # Weigh package and candies, all together, in grams and ounces Write down weights on form  Optional: Open package, count total # candies Count # of each color Write down Eat candies  Turn in form and empty complete wrappers for weighing

Peanut Color Mix website  Brown 17.7%20%  Yellow 8.2%20%  Red 9.5%20%  Blue15.4%20%  Orange26.4%10%  Green22.7%10%

Classwebsite  Brown12.1%30%  Yellow14.7%20%  Red11.4%20%  Blue19.5%10%  Orange21.2%10%  Green21.2%10% Plain Color Mix

So who cares?  Dept. of Commerce  National Institutes of Standards & Technology  NIST Handbook 133  Fair Packaging and Labeling Act

Acceptable?

Package Weight  “Not Labeled for Individual Retail Sale”  If individual is 18g  MAV is 10% = 1.8g  Nothing can be below 18g – 1.8g = 16.2g

Goal of Control Charts  collect and present data visually  allow us to see when trend appears  see when “out of control” point occurs

Process Control Charts  Graph of sample data plotted over time UCL LCL Process Average ± 3  Time X

Process Control Charts  Graph of sample data plotted over time Assignable Cause Variation Natural Variation UCL LCL Time X

Definitions of Out of Control 1. No points outside control limits 2. Same number above & below center line 3. Points seem to fall randomly above and below center line 4. Most are near the center line, only a few are close to control limits 1. 8 Consecutive pts on one side of centerline 2. 2 of 3 points in outer third 3. 4 of 5 in outer two-thirds region

Attributes vs. Variables Attributes:  Good / bad, works / doesn’t  count % bad (P chart)  count # defects / item (C chart) Variables:  measure length, weight, temperature (x-bar chart)  measure variability in length (R chart)

Attribute Control Charts  Tell us whether points in tolerance or not p chart: percentage with given characteristic (usually whether defective or not) np chart: number of units with characteristic c chart: count # of occurrences in a fixed area of opportunity (defects per car) u chart: # of events in a changeable area of opportunity (sq. yards of paper drawn from a machine)

p Chart Control Limits # Defective Items in Sample i Sample i Size

p Chart Control Limits # Defective Items in Sample i Sample i Size z = 2 for 95.5% limits; z = 3 for 99.7% limits # Samples

p Chart Control Limits # Defective Items in Sample i # Samples Sample i Size z = 2 for 95.5% limits; z = 3 for 99.7% limits

p Chart Example You’re manager of a 500- room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control (use z = 3)? © 1995 Corel Corp.

p Chart Hotel Data No.No. Not DayRoomsReady Proportion /200 =

p Chart Control Limits

p Chart Solution

p Chart Solution

p Chart UCL LCL

R Chart  Type of variables control chart Interval or ratio scaled numerical data  Shows sample ranges over time Difference between smallest & largest values in inspection sample  Monitors variability in process  Example: Weigh samples of coffee & compute ranges of samples; Plot

You’re manager of a 500- room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control? Hotel Example

Hotel Data DayDelivery Time

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange Sample Mean =

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange Sample Range = LargestSmallest

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange

R Chart Control Limits Sample Range at Time i # Samples From Exhibit 6.13

Control Chart Limits

R R Chart Control Limits R k i i k      

R Chart Solution From 6.13 (n = 5) R R k UCLDR LCLDR i i k R R        (2.11)(3.894)8232 (0)(3.894) 

R Chart Solution UCL

 X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i

 X Chart Control Limits From Table 6-13

 X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i From 6.13

Exhibit 6.13 Limits

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange

 X Chart Control Limits X X k R R k i i k i i k            

 X Chart Control Limits From 6.13 (n = 5) X X k R R k UCLXAR i i k i i k X            *  

 X Chart Solution From 6.13 (n = 5) X X k R R k UCLXAR LCLXAR i i k i i k X X             (058) 5813(058) (3.894) =   (3.894) = 8.060

 X Chart Solution*  X, Minutes Day UCL LCL

Thinking Challenge You’re manager of a 500- room hotel. The hotel owner tells you that it takes too long to deliver luggage to the room (even if the process may be in control). What do you do? © 1995 Corel Corp. N

 Redesign the luggage delivery process  Use TQM tools Cause & effect diagrams Process flow charts Pareto charts Solution MethodPeople Material Equipment Too Long