total quality management control charts for variables and attributes
DESCRIPTION
Continuous Variables: Take on a continuum of values. Ex.: length, diameter, thickness Modeled by the Normal Distribution Attribute Variables: Take on discrete values Ex.: present/absent, conforming/non-conformingTRANSCRIPT
TOTAL QUALITY MANAGEMENT
CONTROL CHARTS FOR VARIABLES AND ATTRIBUTES
Continuous Variables:
Take on a continuum of values. Ex.: length, diameter, thickness
Modeled by the Normal Distribution
Attribute Variables:
Take on discrete valuesEx.: present/absent, conforming/non-conforming
Discrete Variables Classes• Defectives
– The presence of a non-conformity ruins the entire unit – the unit is defective
• Example – fuses with disconnects
• Defects– The presence of one or more non-conformities may lower the value of
the unit, but does not render the entire unit defective• Example – paneling with scratches
• Factor for x-Chart
• A2 • D3 • D4
• 2 • 1.88 • 0.00 • 3.27
• 3 • 1.02 • 0.00 • 2.57
• 4 • 0.73 • 0.00 • 2.28
• 5 • 0.58 • 0.00 • 2.11
• 6 • 0.48 • 0.00 • 2.00
• 7 • 0.42 • 0.08 • 1.92
• 8 • 0.37 • 0.14 • 1.86
• 9 • 0.34 • 0.18 • 1.82
• 10 • 0.31 • 0.22 • 1.78
• 11 • 0.29 • 0.26 • 1.74
• 12 • 0.27 • 0.28 • 1.72
• 13 • 0.25 • 0.31 • 1.69
• 14 • 0.24 • 0.33 • 1.67
• 15 • 0.22 • 0.35 • 1.65
• Factors for R-Chart• Sample Size• (n)
X- BAR AND R CHART
Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 51 10.68 10.689 10.776 10.798 10.7142 10.79 10.86 10.601 10.746 10.7793 10.78 10.667 10.838 10.785 10.7234 10.59 10.727 10.812 10.775 10.735 10.69 10.708 10.79 10.758 10.6716 10.75 10.714 10.738 10.719 10.6067 10.79 10.713 10.689 10.877 10.6038 10.74 10.779 10.11 10.737 10.759 10.77 10.773 10.641 10.644 10.72510 10.72 10.671 10.708 10.85 10.71211 10.79 10.821 10.764 10.658 10.70812 10.62 10.802 10.818 10.872 10.72713 10.66 10.822 10.893 10.544 10.7514 10.81 10.749 10.859 10.801 10.70115 10.66 10.681 10.644 10.747 10.728
Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges.Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Avg Range
1 10.68 10.689 10.776 10.798 10.714 10.732 0.1162 10.79 10.86 10.601 10.746 10.779 10.755 0.2593 10.78 10.667 10.838 10.785 10.723 10.759 0.1714 10.59 10.727 10.812 10.775 10.73 10.727 0.2215 10.69 10.708 10.79 10.758 10.671 10.724 0.1196 10.75 10.714 10.738 10.719 10.606 10.705 0.1437 10.79 10.713 10.689 10.877 10.603 10.735 0.2748 10.74 10.779 10.11 10.737 10.75 10.624 0.6699 10.77 10.773 10.641 10.644 10.725 10.710 0.13210 10.72 10.671 10.708 10.85 10.712 10.732 0.17911 10.79 10.821 10.764 10.658 10.708 10.748 0.16312 10.62 10.802 10.818 10.872 10.727 10.768 0.25013 10.66 10.822 10.893 10.544 10.75 10.733 0.34914 10.81 10.749 10.859 10.801 10.701 10.783 0.15815 10.66 10.681 10.644 10.747 10.728 10.692 0.103
Averages 10.728 0.220400
Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values
x Chart Control Limits
UCL = x + A R
LCL = x - A R2
2
R Chart Control Limits
UCL = D R
LCL = D R4
3
n A2 D3 D42 1.88 0 3.273 1.02 0 2.574 0.73 0 2.285 0.58 0 2.116 0.48 0 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.82
10 0.31 0.22 1.7811 0.29 0.26 1.74
Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values
60110220405872810
85610220405872810
2
2
.)=.(-..R - AxLCL =
.)=.(..R + AxUCL =
10.550
10.600
10.650
10.700
10.750
10.800
10.850
10.900
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Sample
Mea
ns SamplemeanUCL
LCL
grandmean of x
Example of x-bar and R charts: Steps 5&6: Calculate R-chart and Plot Values
0
0.46504
)2204.0)(0(R D= LCL
)2204.0)(11.2(R D= UCL
3
4
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample
RRangeUCLLCLR-bar
© Wiley 2010 11
P-Chart Example: A production manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires. Calculate the control limits.
Sample
Number of
Defective Tires
Number of Tires in each
Sample
Proportion
Defective
1 3 20 .152 2 20 .103 1 20 .054 2 20 .105 2 20 .05
Total 9 100 .09
Solution:
0.1023(.064).09σzpLCL
.2823(.064).09σzpUCL
0.6420
(.09)(.91)n
)p(1pσ
.09100
9Inspected Total
Defectives#pCL
p
p
p
npppLCL
pCLnpppUCL
)1(3
)1(3
© Wiley 2010 12
P- Control Chart
)1(3
)1(3
ppnpnLCL
pnCL
ppnpnUCL
ANSWER:
Upper Control Limit = 20.22Lower Control Limit = 1.54
© Wiley 2010 16
C-Chart Example: The number of weekly customer complaints are monitored in a large hotel using a c-chart. Develop three sigma control limits using the data table below.
Week Number of Complaints
1 32 23 34 15 36 37 28 19 310 1
Total 22
Solution:
02.252.232.2ccLCL
6.652.232.2ccUCL
2.21022
samples of #complaints#CL
c
c
z
z
negativeisLCLif0orc3cLCL
cCL
c3cUCL
© Wiley 2010 17
C- Control Chart
For ‘u’ chart refer KV web portal.
THANK YOU…!!!