Statistical Process Control 1 Chapter 3

Lecture Outline Basics of Statistical Process Control Control Charts Control Charts for Attributes Control Charts for Variables Control Chart Patterns SPC with Excel and OM Tools Process Capability Copyright 2011 John Wiley & Sons, Inc.3-2

Statistical Process Control (SPC) Statistical Process Control monitoring production process to detect and prevent poor quality Sample subset of items produced to use for inspection Control Charts process is within statistical control limits Copyright 2011 John Wiley & Sons, Inc.3-3 UCL LCL

Process Variability Random inherent in a process depends on equipment and machinery, engineering, operator, and system of measurement natural occurrences Non-Random special causes identifiable and correctable include equipment out of adjustment, defective materials, changes in parts or materials, broken machinery or equipment, operator fatigue or poor work methods, or errors due to lack of training Copyright 2011 John Wiley & Sons, Inc.3-4

SPC in Quality Management SPC uses Is the process in control? Identify problems in order to make improvements Contribute to the TQM goal of continuous improvement Copyright 2011 John Wiley & Sons, Inc.3-5

Quality Measures: Attributes and Variables Attribute A characteristic which is evaluated with a discrete response good/bad; yes/no; correct/incorrect Variable measure A characteristic that is continuous and can be measured Weight, length, voltage, volume Copyright 2011 John Wiley & Sons, Inc.3-6

SPC Applied to Services Nature of defects is different in services Service defect is a failure to meet customer requirements Monitor time and customer satisfaction Copyright 2011 John Wiley & Sons, Inc.3-7

SPC Applied to Services Hospitals timeliness & quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance & checkouts Grocery stores waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors Airlines flight delays, lost luggage & luggage handling, waiting time at ticket counters & check-in, agent & flight attendant courtesy, accurate flight information, cabin cleanliness & maintenance Copyright 2011 John Wiley & Sons, Inc.3-8

SPC Applied to Services Fast-food restaurants waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy Catalogue-order companies order accuracy, operator knowledge & courtesy, packaging, delivery time, phone order waiting time Insurance companies billing accuracy, timeliness of claims processing, agent availability & response time Copyright 2011 John Wiley & Sons, Inc.3-9

Where to Use Control Charts Process Has a tendency to go out of control Is particularly harmful and costly if it goes out of control Examples At beginning of process because of waste to begin production process with bad supplies Before a costly or irreversible point, after which product is difficult to rework or correct Before and after assembly or painting operations that might cover defects Before the outgoing final product or service is delivered Copyright 2011 John Wiley & Sons, Inc.3-10

Control Charts A graph that monitors process quality Control limits upper and lower bands of a control chart Attributes chart p-chart c-chart Variables chart mean (x bar – chart) range (R-chart) Copyright 2011 John Wiley & Sons, Inc.3-11

Process Control Chart Copyright 2011 John Wiley & Sons, Inc Sample number Upper control limit Process average Lower control limit Out of control

Normal Distribution Probabilities for Z= 2.00 and Z = 3.00 Copyright 2011 John Wiley & Sons, Inc.3-13  =011 22 33 -1  -2  -3  95% 99.74%

A Process Is in Control If … Copyright 2011 John Wiley & Sons, Inc … no sample points outside limits 2.… most points near process average 3.… about equal number of points above and below centerline 4.… points appear randomly distributed

Control Charts for Attributes p-chart uses portion defective in a sample c-chart uses number of defects (non-conformities) in a sample Copyright 2011 John Wiley & Sons, Inc.3-15

p-Chart Copyright 2011 John Wiley & Sons, Inc.3-16 UCL = p + z  p LCL = p - z  p z=number of standard deviations from process average p=sample proportion defective; estimates process mean  p = standard deviation of sample proportion  p = p(1 - p)n

Construction of p-Chart Copyright 2011 John Wiley & Sons, Inc samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLE #DEFECTIVESDEFECTIVE :::

Construction of p-Chart Copyright 2011 John Wiley & Sons, Inc.3-18 UCL = p + z = p(1 - p) n 0.10( ) 100 UCL = LCL = LCL = p - z = p(1 - p) n 0.10( ) 100 = 200 / 20(100) = 0.10 total defectives total sample observations p =

Construction of p-Chart Copyright 2011 John Wiley & Sons, Inc Proportion defective Sample number UCL = LCL = p = 0.10

p-Chart in Excel Copyright 2011 John Wiley & Sons, Inc.3-20 Click on “Insert” then “Charts” to construct control chart I4 + 3*SQRT(I4*(1-I4)/100) I4 - 3*SQRT(I4*(1-I4)/100) Column values copied from I5 and I6

c-Chart Copyright 2011 John Wiley & Sons, Inc.3-21 UCL = c + z  c LCL = c - z  c where c = number of defects per sample  c = c

c-Chart Copyright 2011 John Wiley & Sons, Inc.3-22 Number of defects in 15 sample rooms : SAMPLE c = = UCL= c + z  c = = LCL= c - z  c = = 1.99 NUMBER OF DEFECTS

c-Chart Copyright 2011 John Wiley & Sons, Inc Number of defects Sample number UCL = LCL = 1.99 c = 12.67

Control Charts for Variables Copyright 2011 John Wiley & Sons, Inc.3-24  Range chart ( R-Chart )  Plot sample range (variability)  Mean chart ( x -Chart )  Plot sample averages

3-25 x-bar Chart:  Known UCL = x + z  x LCL = x - z  x - - = = Where  = process standard deviation  x = standard deviation of sample means =  / k = number of samples (subgroups) n = sample size (number of observations) x 1 + x x k k X = = --- n Copyright 2011 John Wiley & Sons, Inc.

Observations(Slip-Ring Diameter, cm) n Sample k x-bar Chart Example:  Known Copyright 2011 John Wiley & Sons, Inc x We know σ =.08

x-bar Chart Example:  Known Copyright 2011 John Wiley & Sons, Inc = (.08 / ) 10 = 4.93 _____ = 5.01X = = LCL = x - z  x = - UCL = x + z  x = - = (.08 / ) 10 = 5.09

x-bar Chart Example:  Unknown Copyright 2011 John Wiley & Sons, Inc _ UCL = x + A 2 RLCL = x - A 2 R == _ where x = average of the sample means R = average range value = _

Copyright 2011 John Wiley & Sons, Inc.3-29 Control Chart Factors n A2D3D Factors for R-chart Sample Size Factor for X-chart

x-bar Chart Example:  Unknown Copyright 2011 John Wiley & Sons, Inc.3-30 OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 12345xR Totals

x-bar Chart Example:  Unknown Copyright 2011 John Wiley & Sons, Inc.3-31 ∑ R k R == = _ ____ _ UCL = x + A 2 R = = _____ x = = = 5.01 cm xkxk ___ = (0.58)(0.115) = 5.08 _ LCL = x - A 2 R = = (0.58)(0.115) = 4.94

x- bar Chart Example Copyright 2011 John Wiley & Sons, Inc.3-32 UCL = 5.08 LCL = 4.94 Mean Sample number |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | – 5.08 – 5.06 – 5.04 – 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – x = 5.01 =

R- Chart Copyright 2011 John Wiley & Sons, Inc.3-33 UCL = D 4 RLCL = D 3 R R = RkRk Where R = range of each sample k = number of samples (sub groups)

R-Chart Example Copyright 2011 John Wiley & Sons, Inc.3-34 OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 12345xR Totals

R-Chart Example Copyright 2011 John Wiley & Sons, Inc.3-35 Retrieve chart factors D 3 and D 4 UCL = D 4 R = 2.11(0.115) = LCL = D 3 R = 0(0.115) = 0 _ _

R-Chart Example Copyright 2011 John Wiley & Sons, Inc.3-36 UCL = LCL = 0 Range Sample number R = |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | – 0.24 – 0.20 – 0.16 – 0.12 – 0.08 – 0.04 – 0 –

X-bar and R charts – Excel & OM Tools Copyright 2011 John Wiley & Sons, Inc.3-37

Using x- bar and R-Charts Together Process average and process variability must be in control Samples can have very narrow ranges, but sample averages might be beyond control limits Or, sample averages may be in control, but ranges might be out of control An R-chart might show a distinct downward trend, suggesting some nonrandom cause is reducing variation Copyright 2011 John Wiley & Sons, Inc.3-38

Control Chart Patterns Run sequence of sample values that display same characteristic Pattern test determines if observations within limits of a control chart display a nonrandom pattern Copyright 2011 John Wiley & Sons, Inc.3-39

Control Chart Patterns To identify a pattern look for: 8 consecutive points on one side of the center line 8 consecutive points up or down 14 points alternating up or down 2 out of 3 consecutive points in zone A (on one side of center line) 4 out of 5 consecutive points in zone A or B (on one side of center line) Copyright 2011 John Wiley & Sons, Inc.3-40

Control Chart Patterns Copyright 2011 John Wiley & Sons, Inc.3-41 UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line

Control Chart Patterns Copyright 2011 John Wiley & Sons, Inc.3-42 LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

Zones for Pattern Tests 3-43 UCL LCL Zone A Zone B Zone C Zone B Zone A Process average 3 sigma = x + A 2 R = 3 sigma = x - A 2 R = 2 sigma = x + (A 2 R) = sigma = x - (A 2 R) = sigma = x + (A 2 R) = sigma = x - (A 2 R) = 1313 x = Sample number |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | 10 | 11 | 12 | 13 Copyright 2011 John Wiley & Sons, Inc.

Performing a Pattern Test Copyright 2011 John Wiley & Sons, Inc B—B 25.00BUC 34.95BDA 44.96BDA 54.99BUC 65.01—UC 75.02AUC 85.05AUB 95.08AUA ADB SAMPLExABOVE/BELOWUP/DOWNZONE

Sample Size Determination Attribute charts require larger sample sizes 50 to 100 parts in a sample Variable charts require smaller samples 2 to 10 parts in a sample Copyright 2011 John Wiley & Sons, Inc.3-45

Process Capability Compare natural variability to design variability Natural variability What we measure with control charts Process mean = 8.80 oz, Std dev. = 0.12 oz Tolerances Design specifications reflecting product requirements Net weight = 9.0 oz  0.5 oz Tolerances are  0.5 oz Copyright 2011 John Wiley & Sons, Inc.3-46

Process Capability Copyright 2011 John Wiley & Sons, Inc.3-47 (b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time. Design Specifications Process (a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time. Design Specifications Process

Process Capability Copyright 2011 John Wiley & Sons, Inc.3-48 (c) Design specifications greater than natural variation; process is capable of always conforming to specifications. Design Specifications Process (d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification. Design Specifications Process

Process Capability Ratio Copyright 2011 John Wiley & Sons, Inc.3-49 Cp=Cp= tolerance range process range upper spec limit - lower spec limit 6  =

Computing C p Copyright 2011 John Wiley & Sons, Inc.3-50 Net weight specification = 9.0 oz  0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz C p = = = 1.39 upper specification limit - lower specification limit 6  (0.12)

Process Capability Index Copyright 2011 John Wiley & Sons, Inc.3-51 C pk = minimum x - lower specification limit 3  = upper specification limit - x 3  =,

Computing C pk Copyright 2011 John Wiley & Sons, Inc.3-52 Net weight specification = 9.0 oz  0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz C pk = minimum = minimum, = 0.83 x - lower specification limit 3  = upper specification limit - x 3  =, (0.12) (0.12)

Process Capability With Excel Copyright 2011 John Wiley & Sons, Inc.3-53 =(D6-D7)/(6*D8) See formula bar

Process Capability With OM Tools Copyright 2011 John Wiley & Sons, Inc.3-54

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