Description
The PPT explaining on Z chart and loss function chart complete.
Z-Chart & Loss Function
F(Z) is the probability that a variable from a standard normal distribution will be less than or equal to Z, or alternately, the service level for a quantity ordered with a z-value of Z. L(Z) is the standard loss function, i.e. the expected number of lost sales as a fraction of the standard deviation. Hence, the lost sales = L(Z) x sDEMAND
Z
-3.00 -2.96 -2.92 -2.88 -2.84 -2.80 -2.76 -2.72 -2.68 -2.64 -2.60 -2.56 -2.52 -2.48 -2.44 -2.40 -2.36 -2.32 -2.28 -2.24 -2.20 -2.16 -2.12 -2.08 -2.04 -2.00 -1.96 -1.92 -1.88 -1.84 -1.80 -1.76 -1.72 -1.68 -1.64 -1.60 -1.56 -1.52
F(Z)
0.0013 0.0015 0.0018 0.0020 0.0023 0.0026 0.0029 0.0033 0.0037 0.0041 0.0047 0.0052 0.0059 0.0066 0.0073 0.0082 0.0091 0.0102 0.0113 0.0125 0.0139 0.0154 0.0170 0.0188 0.0207 0.0228 0.0250 0.0274 0.0301 0.0329 0.0359 0.0392 0.0427 0.0465 0.0505 0.0548 0.0594 0.0643
L(Z)
3.000 2.960 2.921 2.881 2.841 2.801 2.761 2.721 2.681 2.641 2.601 2.562 2.522 2.482 2.442 2.403 2.363 2.323 2.284 2.244 2.205 2.165 2.126 2.087 2.048 2.008 1.969 1.930 1.892 1.853 1.814 1.776 1.737 1.699 1.661 1.623 1.586 1.548
Z
-1.48 -1.44 -1.40 -1.36 -1.32 -1.28 -1.24 -1.20 -1.16 -1.12 -1.08 -1.04 -1.00 -0.96 -0.92 -0.88 -0.84 -0.80 -0.76 -0.72 -0.68 -0.64 -0.60 -0.56 -0.52 -0.48 -0.44 -0.40 -0.36 -0.32 -0.28 -0.24 -0.20 -0.16 -0.12 -0.08 -0.04 0.00
F(Z)
0.0694 0.0749 0.0808 0.0869 0.0934 0.1003 0.1075 0.1151 0.1230 0.1314 0.1401 0.1492 0.1587 0.1685 0.1788 0.1894 0.2005 0.2119 0.2236 0.2358 0.2483 0.2611 0.2743 0.2877 0.3015 0.3156 0.3300 0.3446 0.3594 0.3745 0.3897 0.4052 0.4207 0.4364 0.4522 0.4681 0.4840 0.5000
L(Z)
1.511 1.474 1.437 1.400 1.364 1.327 1.292 1.256 1.221 1.186 1.151 1.117 1.083 1.050 1.017 0.984 0.952 0.920 0.889 0.858 0.828 0.798 0.769 0.740 0.712 0.684 0.657 0.630 0.605 0.579 0.554 0.530 0.507 0.484 0.462 0.440 0.419 0.399
Z
0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20 1.24 1.28 1.32 1.36 1.40 1.44 1.48 1.52
F(Z)
0.5160 0.5319 0.5478 0.5636 0.5793 0.5948 0.6103 0.6255 0.6406 0.6554 0.6700 0.6844 0.6985 0.7123 0.7257 0.7389 0.7517 0.7642 0.7764 0.7881 0.7995 0.8106 0.8212 0.8315 0.8413 0.8508 0.8599 0.8686 0.8770 0.8849 0.8925 0.8997 0.9066 0.9131 0.9192 0.9251 0.9306 0.9357
L(Z)
0.379 0.360 0.342 0.324 0.307 0.290 0.274 0.259 0.245 0.230 0.217 0.204 0.192 0.180 0.169 0.158 0.148 0.138 0.129 0.120 0.112 0.104 0.097 0.090 0.083 0.077 0.071 0.066 0.061 0.056 0.052 0.047 0.044 0.040 0.037 0.034 0.031 0.028
Z
1.56 1.60 1.64 1.68 1.72 1.76 1.80 1.84 1.88 1.92 1.96 2.00 2.04 2.08 2.12 2.16 2.20 2.24 2.28 2.32 2.36 2.40 2.44 2.48 2.52 2.56 2.60 2.64 2.68 2.72 2.76 2.80 2.84 2.88 2.92 2.96 3.00
F(Z)
0.9406 0.9452 0.9495 0.9535 0.9573 0.9608 0.9641 0.9671 0.9699 0.9726 0.9750 0.9772 0.9793 0.9812 0.9830 0.9846 0.9861 0.9875 0.9887 0.9898 0.9909 0.9918 0.9927 0.9934 0.9941 0.9948 0.9953 0.9959 0.9963 0.9967 0.9971 0.9974 0.9977 0.9980 0.9982 0.9985 0.9987
L(Z)
0.026 0.023 0.021 0.019 0.017 0.016 0.014 0.013 0.012 0.010 0.009 0.008 0.008 0.007 0.006 0.005 0.005 0.004 0.004 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.000
Z & L(z) for special service levels
Service Level F(z) 75% 90% 95% 99% z 0.67 1.28 1.64 2.33 L(z) 0.150 0.047 0.021 0.003
F(Z) = Service Level
0
Z
z
z-scale
doc_354605177.ppt
The PPT explaining on Z chart and loss function chart complete.
Z-Chart & Loss Function
F(Z) is the probability that a variable from a standard normal distribution will be less than or equal to Z, or alternately, the service level for a quantity ordered with a z-value of Z. L(Z) is the standard loss function, i.e. the expected number of lost sales as a fraction of the standard deviation. Hence, the lost sales = L(Z) x sDEMAND
Z
-3.00 -2.96 -2.92 -2.88 -2.84 -2.80 -2.76 -2.72 -2.68 -2.64 -2.60 -2.56 -2.52 -2.48 -2.44 -2.40 -2.36 -2.32 -2.28 -2.24 -2.20 -2.16 -2.12 -2.08 -2.04 -2.00 -1.96 -1.92 -1.88 -1.84 -1.80 -1.76 -1.72 -1.68 -1.64 -1.60 -1.56 -1.52
F(Z)
0.0013 0.0015 0.0018 0.0020 0.0023 0.0026 0.0029 0.0033 0.0037 0.0041 0.0047 0.0052 0.0059 0.0066 0.0073 0.0082 0.0091 0.0102 0.0113 0.0125 0.0139 0.0154 0.0170 0.0188 0.0207 0.0228 0.0250 0.0274 0.0301 0.0329 0.0359 0.0392 0.0427 0.0465 0.0505 0.0548 0.0594 0.0643
L(Z)
3.000 2.960 2.921 2.881 2.841 2.801 2.761 2.721 2.681 2.641 2.601 2.562 2.522 2.482 2.442 2.403 2.363 2.323 2.284 2.244 2.205 2.165 2.126 2.087 2.048 2.008 1.969 1.930 1.892 1.853 1.814 1.776 1.737 1.699 1.661 1.623 1.586 1.548
Z
-1.48 -1.44 -1.40 -1.36 -1.32 -1.28 -1.24 -1.20 -1.16 -1.12 -1.08 -1.04 -1.00 -0.96 -0.92 -0.88 -0.84 -0.80 -0.76 -0.72 -0.68 -0.64 -0.60 -0.56 -0.52 -0.48 -0.44 -0.40 -0.36 -0.32 -0.28 -0.24 -0.20 -0.16 -0.12 -0.08 -0.04 0.00
F(Z)
0.0694 0.0749 0.0808 0.0869 0.0934 0.1003 0.1075 0.1151 0.1230 0.1314 0.1401 0.1492 0.1587 0.1685 0.1788 0.1894 0.2005 0.2119 0.2236 0.2358 0.2483 0.2611 0.2743 0.2877 0.3015 0.3156 0.3300 0.3446 0.3594 0.3745 0.3897 0.4052 0.4207 0.4364 0.4522 0.4681 0.4840 0.5000
L(Z)
1.511 1.474 1.437 1.400 1.364 1.327 1.292 1.256 1.221 1.186 1.151 1.117 1.083 1.050 1.017 0.984 0.952 0.920 0.889 0.858 0.828 0.798 0.769 0.740 0.712 0.684 0.657 0.630 0.605 0.579 0.554 0.530 0.507 0.484 0.462 0.440 0.419 0.399
Z
0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20 1.24 1.28 1.32 1.36 1.40 1.44 1.48 1.52
F(Z)
0.5160 0.5319 0.5478 0.5636 0.5793 0.5948 0.6103 0.6255 0.6406 0.6554 0.6700 0.6844 0.6985 0.7123 0.7257 0.7389 0.7517 0.7642 0.7764 0.7881 0.7995 0.8106 0.8212 0.8315 0.8413 0.8508 0.8599 0.8686 0.8770 0.8849 0.8925 0.8997 0.9066 0.9131 0.9192 0.9251 0.9306 0.9357
L(Z)
0.379 0.360 0.342 0.324 0.307 0.290 0.274 0.259 0.245 0.230 0.217 0.204 0.192 0.180 0.169 0.158 0.148 0.138 0.129 0.120 0.112 0.104 0.097 0.090 0.083 0.077 0.071 0.066 0.061 0.056 0.052 0.047 0.044 0.040 0.037 0.034 0.031 0.028
Z
1.56 1.60 1.64 1.68 1.72 1.76 1.80 1.84 1.88 1.92 1.96 2.00 2.04 2.08 2.12 2.16 2.20 2.24 2.28 2.32 2.36 2.40 2.44 2.48 2.52 2.56 2.60 2.64 2.68 2.72 2.76 2.80 2.84 2.88 2.92 2.96 3.00
F(Z)
0.9406 0.9452 0.9495 0.9535 0.9573 0.9608 0.9641 0.9671 0.9699 0.9726 0.9750 0.9772 0.9793 0.9812 0.9830 0.9846 0.9861 0.9875 0.9887 0.9898 0.9909 0.9918 0.9927 0.9934 0.9941 0.9948 0.9953 0.9959 0.9963 0.9967 0.9971 0.9974 0.9977 0.9980 0.9982 0.9985 0.9987
L(Z)
0.026 0.023 0.021 0.019 0.017 0.016 0.014 0.013 0.012 0.010 0.009 0.008 0.008 0.007 0.006 0.005 0.005 0.004 0.004 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.000
Z & L(z) for special service levels
Service Level F(z) 75% 90% 95% 99% z 0.67 1.28 1.64 2.33 L(z) 0.150 0.047 0.021 0.003
F(Z) = Service Level
0
Z
z
z-scale
doc_354605177.ppt