4-b Process Capability
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TQM - Capability Analysis - Histogram
Normality and Customer specifications
Process Capability Analysis (Histogram)
• We have studied that the data should be normally distributed. • Lets place supplier specification limits on normally distributed histogram. • Next chart shows Histogram of soft drink filled in 250 ml bottles. It is a normally distribution.
Irfan Rashid Farooqui
Irfan Rashid Farooqui
Summary for Soft drink filled (ml) A nderson-Darling Normality Test
246
248
250
252
A -Squared P-V alue <
9.66 0.005
Mean StDev V ariance Skewness Kurtosis N
250.00 2.44 5.97 -0.00000 -1.07147 690
Minimum 1st Q uartile Median 3rd Q uartile Maximum
254
246.00 248.00 250.00 252.00 254.00
95% C onfidence Interv al for Mean 249.82
250.18
95% C onfidence Interv al for Median 250.00 2.32
Mean
• Suppose the supplier requirements were 250 + & - 2 ml • Putting limits on histogram shows liquid in some bottles is out of specification limits.
250.00
95% C onfidence Interv al for StDev
95% Confidence Intervals
Control Limits
2.58
• We calculate weather a process is capable of meeting customer specifications or not?
Median 249.8
249.9
250.0
250.1
Irfan Rashid Farooqui
Irfan Rashid Farooqui
250.2
Irfan Rashid Farooqui
1
TQM - Capability Analysis - Histogram
Summary for Soft drink filled (ml)
PROCESS CAPABILITY
A nderson-Darling Normality Test
246
248
250
252
A -Squared P-V alue <
9.66 0.005
Mean StDev V ariance Skewness Kurtosis N
250.00 2.44 5.97 -0.00000 -1.07147 690
Minimum 1st Q uartile Median 3rd Q uartile Maximum
254
246.00 248.00 250.00 252.00 254.00
Cp
=
USL - LSL
Standard = Deviation
6 =
=
52 - 48 6 X 2.44
=
2.44
95% C onfidence Interv al for Mean 249.82
250.18
95% C onfidence Interv al for Median 250.00
250.00
95% C onfidence Interv al for StDev
95% Confidence Intervals
2.32
4.00 14.64
2.58
Mean
0.27
Median 249.8
249.9
250.0
250.1
250.2
Irfan Rashid Farooqui
Irfan Rashid Farooqui
Process Capability Index USL - X Cpk =
X - LSL OR
3
=
Measure capability
3
• If Cp or Cpk < 1, process not capable. =
252 - 250 3 X 3.11
=
2 9.33
=
250-248 3 X 8.23
=
2 9.33
=
0.21
• If Cp or Cpk = 1, process tightly capable. • If Cp or Cpk > 1.33 process is capable.
0.21
=
Best if Cp or Cpk = 2
Smaller of the two values Irfan Rashid Farooqui
Irfan Rashid Farooqui
Irfan Rashid Farooqui
2
TQM - Capability Analysis - Histogram
Sigma value and defects count
3 Sigma and 6 Sigma
Irfan Rashid Farooqui
Sigma
Centered ppm
Off centered ppm
1
317,310.000
697,700.000
2
45,500.000
308,777.000
3
2,700.000
66,811.000
4
63.000
6,210.000
5
0.570
233.000
6
0.002
3.400
Irfan Rashid Farooqui
But If your process is capable to 3 sigma, result will be 2,700,000 errors per one billion of opportunities
Irfan Rashid Farooqui
Irfan Rashid Farooqui
If your process is capable to 6 sigma, result will be only 2 errors per one billion of opportunities Irfan Rashid Farooqui
3
Normality and Customer specifications
Process Capability Analysis (Histogram)
• We have studied that the data should be normally distributed. • Lets place supplier specification limits on normally distributed histogram. • Next chart shows Histogram of soft drink filled in 250 ml bottles. It is a normally distribution.
Irfan Rashid Farooqui
Irfan Rashid Farooqui
Summary for Soft drink filled (ml) A nderson-Darling Normality Test
246
248
250
252
A -Squared P-V alue <
9.66 0.005
Mean StDev V ariance Skewness Kurtosis N
250.00 2.44 5.97 -0.00000 -1.07147 690
Minimum 1st Q uartile Median 3rd Q uartile Maximum
254
246.00 248.00 250.00 252.00 254.00
95% C onfidence Interv al for Mean 249.82
250.18
95% C onfidence Interv al for Median 250.00 2.32
Mean
• Suppose the supplier requirements were 250 + & - 2 ml • Putting limits on histogram shows liquid in some bottles is out of specification limits.
250.00
95% C onfidence Interv al for StDev
95% Confidence Intervals
Control Limits
2.58
• We calculate weather a process is capable of meeting customer specifications or not?
Median 249.8
249.9
250.0
250.1
Irfan Rashid Farooqui
Irfan Rashid Farooqui
250.2
Irfan Rashid Farooqui
1
TQM - Capability Analysis - Histogram
Summary for Soft drink filled (ml)
PROCESS CAPABILITY
A nderson-Darling Normality Test
246
248
250
252
A -Squared P-V alue <
9.66 0.005
Mean StDev V ariance Skewness Kurtosis N
250.00 2.44 5.97 -0.00000 -1.07147 690
Minimum 1st Q uartile Median 3rd Q uartile Maximum
254
246.00 248.00 250.00 252.00 254.00
Cp
=
USL - LSL
Standard = Deviation
6 =
=
52 - 48 6 X 2.44
=
2.44
95% C onfidence Interv al for Mean 249.82
250.18
95% C onfidence Interv al for Median 250.00
250.00
95% C onfidence Interv al for StDev
95% Confidence Intervals
2.32
4.00 14.64
2.58
Mean
0.27
Median 249.8
249.9
250.0
250.1
250.2
Irfan Rashid Farooqui
Irfan Rashid Farooqui
Process Capability Index USL - X Cpk =
X - LSL OR
3
=
Measure capability
3
• If Cp or Cpk < 1, process not capable. =
252 - 250 3 X 3.11
=
2 9.33
=
250-248 3 X 8.23
=
2 9.33
=
0.21
• If Cp or Cpk = 1, process tightly capable. • If Cp or Cpk > 1.33 process is capable.
0.21
=
Best if Cp or Cpk = 2
Smaller of the two values Irfan Rashid Farooqui
Irfan Rashid Farooqui
Irfan Rashid Farooqui
2
TQM - Capability Analysis - Histogram
Sigma value and defects count
3 Sigma and 6 Sigma
Irfan Rashid Farooqui
Sigma
Centered ppm
Off centered ppm
1
317,310.000
697,700.000
2
45,500.000
308,777.000
3
2,700.000
66,811.000
4
63.000
6,210.000
5
0.570
233.000
6
0.002
3.400
Irfan Rashid Farooqui
But If your process is capable to 3 sigma, result will be 2,700,000 errors per one billion of opportunities
Irfan Rashid Farooqui
Irfan Rashid Farooqui
If your process is capable to 6 sigma, result will be only 2 errors per one billion of opportunities Irfan Rashid Farooqui
3
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