managing quality chapter six mcgraw-hill/irwin statistical process control
TRANSCRIPT
Managing Quality
CHAPTER SIX
McGraw-Hill/Irwin
Statistical Process control
Basics of Statistical Process Basics of Statistical Process ControlControl
Basics of Statistical Process Basics of Statistical Process ControlControl
• Statistical Process Control (SPC) developed by
Walter A. Shewhart at Bell Lab in 1920.– 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
UCLUCL
LCLLCL
SPC in TQMSPC in TQMSPC in TQMSPC in TQM
• SPC–tool for identifying problems and make
improvements–contributes to the TQM goal of
continuous improvements
• Real world Example: Honda
Control ChartControl ChartControl ChartControl Chart
• Control Chart
–Purpose: to monitor process output to see if it is random deciding whether the process is in control or not
–A time ordered plot represents sample statistics obtained from an ongoing process (e.g. sample means)
–Upper and lower control limits define the range of acceptable variation
VariabilityVariabilityVariabilityVariability
• Random–common causes–inherent in a process–can be eliminated only
through improvements in the system
• Non-Random–special causes–due to identifiable
factors–can be modified
through operator or management action
Process Control Process Control ChartChart
Process Control Process Control ChartChart
11 22 33 44 55 66 77 88 99 1010Sample numberSample number
UpperUppercontrolcontrol
limitlimit
ProcessProcessaverageaverage
LowerLowercontrolcontrol
limitlimit
Out of controlOut of control
Quality MeasuresQuality MeasuresQuality MeasuresQuality Measures
• Variable–a product characteristic that is continuous and can be
measured–weight - length
• Attribute–a product characteristic that can be evaluated with a
discrete response–good – bad; yes - no
Control ChartsControl ChartsControl ChartsControl Charts
• Types of charts–Variables
•mean (x bar – chart)•range (R-chart)*Note: mean and range charts are used together
–Attributes•p-chart•c-chart
Control Charts for VariablesControl Charts for VariablesControl Charts for VariablesControl Charts for Variables
• Mean control charts
–Used to monitor the central tendency of a process.
–X bar charts
• Range control charts
–Used to monitor the process variability
–R charts
Using x- bar and R-Charts TogetherUsing x- bar and R-Charts TogetherUsing x- bar and R-Charts TogetherUsing x- bar and R-Charts Together
Process average and process variability must be in control
It is possible for samples to have very narrow ranges, but their averages are beyond control limits
It is possible for sample averages to be in control, but ranges might be very large
Mean and Range ChartsMean and Range ChartsMean and Range ChartsMean and Range Charts
UCL
LCL
UCL
LCL
R-chart
x-Chart Detects shift
Does notdetect shift
(process mean is shifting upward)Sampling
Distribution
10-10-1212
x-Chart
UCL
Does notreveal increase
Mean and Range ChartsMean and Range ChartsMean and Range ChartsMean and Range Charts
UCL
LCL
LCL
R-chart Reveals increase
(process variability is increasing)
SamplingDistribution
x-bar Chartx-bar Chartx-bar Chartx-bar Chart
xx = = xx11 + + xx22 + ... + ... xxkk
kk==
UCL = UCL = xx + + AA22RR LCL = LCL = xx - - AA22RR== ==
WhereWhere
xx = average of sample means= average of sample means==
R- ChartR- ChartR- ChartR- Chart
UCL = UCL = DD44RR LCL = LCL = DD33RR
RR = = RRkk
wherewhere
RR = range of each sample= range of each samplekk = number of samples= number of samples
Example Example Example Example
• measuring the weight/packet in grams
• Packet
• Sample 1 2 3 Ri x-bari
• 1 42 40 44
• 2 35 40 45
• 3 44 44 44
• 4 40 40 43
• 5 41 41 38
Total ___ ___
Average ___ ___
Example (cont.)Example (cont.)Example (cont.)Example (cont.)
• # of samples = k =
• Sample size = n =
Example (cont.)Example (cont.)Example (cont.)Example (cont.)
• X-bar chart
Example (cont.)Example (cont.)Example (cont.)Example (cont.)
• R chart
Example (cont.)Example (cont.)Example (cont.)Example (cont.)
R Chart
| | | | |
x-bar Chart
| | | | |
FaFactoctorsrs
FaFactoctorsrs
n A2 D3 D4
SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART
2 1.88 0.00 3.273 1.02 0.00 2.574 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.44 0.18 1.82
10 0.11 0.22 1.7811 0.99 0.26 1.7412 0.77 0.28 1.7213 0.55 0.31 1.6914 0.44 0.33 1.6715 0.22 0.35 1.6516 0.11 0.36 1.6417 0.00 0.38 1.6218 0.99 0.39 1.6119 0.99 0.40 1.6120 0.88 0.41 1.59
Appendix: Determining Control Limits for x-bar and R-Charts
Control Charts for AttributesControl Charts for AttributesControl Charts for AttributesControl Charts for Attributes
p-charts uses portion defective in a sample
c-charts uses number of defects in an item
p-Chartp-Chartp-Chartp-Chart
UCL = p + zp
LCL = p - zp
z = number of standard deviations from process averagep = sample proportion defective; an estimate of process averagep= standard deviation of sample proportion
pp = = pp(1 - (1 - pp))
nn
p-Chart Examplep-Chart Example(assume the sample size of (assume the sample size of
100)100)
p-Chart Examplep-Chart Example(assume the sample size of (assume the sample size of
100)100)
NUMBER OFNUMBER OF PROPORTIONPROPORTIONSAMPLESAMPLE DEFECTIVESDEFECTIVES DEFECTIVEDEFECTIVE
11 1313
22 77
33 2020
44 00
5 105 10
totaltotal
averageaverage
PP-Chart -Chart Example (cont.)Example (cont.) PP-Chart -Chart Example (cont.)Example (cont.)
Step 1: get sigma
Step 2: get UCL and LCL
n
ppp
1
pp pUCL 3
pp pLCL 3
C-ChartC-ChartC-ChartC-Chart
UCL = UCL = cc + + zzcc
LCL = LCL = cc - - zzcc
where
c = number of defects per sample
cc = = cc
C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)
Measuring number of fouls called on a team per gameMeasuring number of fouls called on a team per game
1 371 372 92 93 223 224 254 255 325 32TotalTotalAvg. Avg.
SAMPLESAMPLE
NUMBER OF FOULS
C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)
UCLUCL = = cc + + zzcc
LCLLCL = = cc - - zzcc
Control Chart PatternsControl Chart PatternsControl Chart PatternsControl Chart Patterns
UCLUCL
LCLLCL
Sample observationsSample observationsconsistently above theconsistently above thecenter linecenter line
LCLLCL
UCLUCL
Sample observationsSample observationsconsistently below theconsistently below thecenter linecenter line
Control Chart Patterns (cont.)Control Chart Patterns (cont.)Control Chart Patterns (cont.)Control Chart Patterns (cont.)
LCLLCL
UCLUCL
Sample observationsSample observationsconsistently increasingconsistently increasing
UCLUCL
LCLLCL
Sample observationsSample observationsconsistently decreasingconsistently decreasing
Homework for Ch 6-IIHomework for Ch 6-II
6–6–3030
• Computer upgrade problem
Computer upgrades take 80 minutes. Six samples of five observations each have been taken, and the results are as listed. Determine if the process is in control. You have to use appropriate chart(s)
• 1 2 3 4 5 6• 79.2 80.5 79.6 78.9 80.5 79.7• 78.8 78.7 79.6 79.4 79.6 80.6• 80.0 81.0 80.4 79.7 80.4 80.5• 78.4 80.4 80.3 79.4 80.8 80.0• 81.0 80.1 80.8 80.6 78.8 81.1
Homework for Ch 6-IIHomework for Ch 6-II
6–6–3131
• Wrong account problem• The operations manager of the booking services department of
hometown bank is concerned about the number of wrong customer account numbers recorded by hometown personnel. Each week a random sample of 2,500 deposits is taken, and the number of incorrect account numbers is recorded. The results for the past 12 weeks are shown in the following table. Is the process out of control? Use appropriate control chart and use three sigma control limit, ie. Z=3.
• Sample number 1 2 3 4 5 6 7 8 9 10 11 12
• wrong account 15 12 19 2 19 4 24 7 10 17 15 3