The design of acceptance sampling plans is developed under truncated life testing based on the percentiles of half normal distribution. The minimum sample size necessary to ensure the specified life percentile is obtained under a given consumer’s risk. The operating characteristic values of the sampling plans as well as the producer’s risk are presented. The results are illustrated by examples.
Acceptance sampling is concerned with inspection and decision making regarding lots of products and constitutes one of the oldest techniques in quality control. If the lifetime of the product represents the quality characteristics of interest, the acceptance sampling is as follows: a company receives a shipment of product from a vendor. This product is often a component or raw material used in the company’s manufacturing process. A sample is taken from the lot and the relevant quality characteristic of the units in the sample is inspected. On the basis of the information in the sample, a decision is made regarding lot disposition. Traditionally, when the life test indicates that the mean life of products exceeds the specified one, the lot of products is accepted, otherwise it is rejected. Accepted lots are put into production, while rejected lots may be returned to the vendor or may be subjected to some other lot disposition actions. For the purpose of reducing the test time and cost, a truncated life test may be conducted to determine the sample size to ensure a certain mean life of products when the life test is terminated at a time
A common practice in life testing is to terminate the life test by a predetermined time
Studies regarding truncated life tests can be found in Epstein [
Normal distribution is the most preferred distribution in statistical studies. But for life test models it is not suitable distribution because of its domain
In this paper, acceptance sampling plans are developed for percentiles of half normal distribution life test and are given in Section
The probability density function (pdf) of a half normal distribution is given by
Its cumulative distribution function (cdf) is
Given
Substituting
We consider large sized lots so that the binomial distribution can be applied. The problem is to determine for given values of
Minimum sample sizes necessary to assert the median life of a product.
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0.1 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | ||
0.75 | 0 | 26 | 13 | 6 | 4 | 3 | 3 | 2 | 2 | 2 | 1 |
0.75 | 1 | 50 | 25 | 12 | 8 | 6 | 5 | 3 | 3 | 2 | 2 |
0.75 | 2 | 72 | 36 | 18 | 12 | 9 | 7 | 5 | 4 | 4 | 3 |
0.75 | 3 | 94 | 47 | 23 | 16 | 12 | 10 | 7 | 5 | 5 | 4 |
0.75 | 4 | 116 | 58 | 29 | 19 | 15 | 12 | 8 | 7 | 6 | 5 |
0.75 | 5 | 137 | 68 | 34 | 23 | 17 | 14 | 10 | 8 | 7 | 6 |
0.75 | 6 | 158 | 79 | 39 | 26 | 20 | 16 | 11 | 9 | 8 | 8 |
0.75 | 7 | 179 | 89 | 45 | 30 | 23 | 18 | 13 | 11 | 9 | 9 |
0.75 | 8 | 200 | 100 | 50 | 33 | 25 | 21 | 14 | 12 | 10 | 10 |
0.75 | 9 | 220 | 110 | 55 | 37 | 28 | 23 | 16 | 13 | 12 | 11 |
0.75 | 10 | 241 | 120 | 60 | 40 | 31 | 25 | 18 | 14 | 13 | 12 |
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0.90 | 0 | 42 | 21 | 10 | 7 | 5 | 4 | 2 | 2 | 2 | 2 |
0.90 | 1 | 71 | 35 | 17 | 11 | 8 | 7 | 4 | 3 | 3 | 2 |
0.90 | 2 | 98 | 48 | 24 | 16 | 12 | 9 | 6 | 5 | 4 | 4 |
0.90 | 3 | 123 | 61 | 30 | 20 | 15 | 12 | 8 | 6 | 5 | 5 |
0.90 | 4 | 147 | 73 | 36 | 24 | 18 | 14 | 10 | 8 | 6 | 6 |
0.90 | 5 | 171 | 85 | 42 | 28 | 21 | 17 | 11 | 9 | 8 | 7 |
0.90 | 6 | 194 | 96 | 48 | 32 | 24 | 19 | 13 | 10 | 9 | 8 |
0.90 | 7 | 217 | 108 | 53 | 35 | 27 | 21 | 15 | 12 | 10 | 9 |
0.90 | 8 | 240 | 119 | 59 | 39 | 29 | 24 | 16 | 13 | 11 | 10 |
0.90 | 9 | 262 | 130 | 65 | 43 | 32 | 26 | 18 | 14 | 12 | 11 |
0.90 | 10 | 284 | 141 | 70 | 47 | 35 | 28 | 20 | 16 | 14 | 12 |
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0.95 | 0 | 55 | 27 | 13 | 8 | 6 | 5 | 3 | 2 | 2 | 2 |
0.95 | 1 | 87 | 43 | 21 | 14 | 10 | 8 | 5 | 4 | 3 | 3 |
0.95 | 2 | 115 | 57 | 28 | 18 | 13 | 11 | 7 | 5 | 4 | 4 |
0.95 | 3 | 142 | 70 | 34 | 23 | 17 | 13 | 9 | 7 | 6 | 5 |
0.95 | 4 | 168 | 83 | 41 | 27 | 20 | 16 | 11 | 8 | 7 | 6 |
0.95 | 5 | 193 | 96 | 47 | 31 | 23 | 18 | 12 | 10 | 8 | 7 |
0.95 | 6 | 218 | 108 | 53 | 35 | 26 | 21 | 14 | 11 | 9 | 8 |
0.95 | 7 | 242 | 120 | 59 | 39 | 29 | 23 | 16 | 12 | 11 | 10 |
0.95 | 8 | 266 | 132 | 65 | 43 | 32 | 26 | 18 | 14 | 12 | 11 |
0.95 | 9 | 289 | 143 | 71 | 47 | 35 | 28 | 19 | 15 | 13 | 12 |
0.95 | 10 | 312 | 155 | 77 | 51 | 38 | 30 | 21 | 16 | 14 | 13 |
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0.99 | 0 | 84 | 41 | 20 | 13 | 9 | 7 | 4 | 3 | 2 | 2 |
0.99 | 1 | 121 | 59 | 29 | 19 | 14 | 11 | 7 | 5 | 4 | 3 |
0.99 | 2 | 154 | 76 | 37 | 24 | 17 | 14 | 9 | 7 | 5 | 5 |
0.99 | 3 | 184 | 91 | 44 | 29 | 21 | 17 | 11 | 8 | 7 | 6 |
0.99 | 4 | 212 | 105 | 51 | 33 | 25 | 19 | 13 | 10 | 8 | 7 |
0.99 | 5 | 240 | 119 | 58 | 38 | 28 | 22 | 15 | 11 | 9 | 8 |
0.99 | 6 | 267 | 132 | 65 | 42 | 31 | 25 | 16 | 13 | 10 | 9 |
0.99 | 7 | 293 | 145 | 71 | 47 | 35 | 27 | 18 | 14 | 12 | 10 |
0.99 | 8 | 319 | 158 | 77 | 51 | 38 | 30 | 20 | 15 | 13 | 12 |
0.99 | 9 | 345 | 171 | 84 | 55 | 41 | 33 | 22 | 17 | 14 | 13 |
0.99 | 10 | 370 | 183 | 90 | 59 | 44 | 35 | 24 | 18 | 15 | 14 |
The operating characteristic (OC) function
OC values of sampling plans.
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1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 |
0.75 | 50 | 0.1 | 0.2420 | 0.4605 | 0.6093 | 0.7075 | 0.7741 | 0.8207 | 0.8545 | 0.8796 | 0.8989 |
25 | 0.2 | 0.2345 | 0.4576 | 0.6090 | 0.7084 | 0.7754 | 0.8221 | 0.8559 | 0.8810 | 0.9001 | |
12 | 0.4 | 0.2408 | 0.4764 | 0.6301 | 0.7281 | 0.7928 | 0.8373 | 0.8690 | 0.8924 | 0.9101 | |
8 | 0.6 | 0.2283 | 0.4759 | 0.6347 | 0.7342 | 0.7989 | 0.8430 | 0.8742 | 0.8970 | 0.9142 | |
6 | 0.8 | 0.2173 | 0.4788 | 0.6425 | 0.7427 | 0.8070 | 0.8502 | 0.8805 | 0.9026 | 0.9191 | |
5 | 1.0 | 0.1875 | 0.4609 | 0.6328 | 0.7373 | 0.8038 | 0.8482 | 0.8793 | 0.9018 | 0.9185 | |
3 | 1.5 | 0.2309 | 0.5616 | 0.7262 | 0.8143 | 0.8662 | 0.8992 | 0.9214 | 0.9370 | 0.9484 | |
3 | 2.0 | 0.0832 | 0.4276 | 0.6317 | 0.7464 | 0.8157 | 0.8602 | 0.8905 | 0.9120 | 0.9272 | |
2 | 2.5 | 0.1752 | 0.6334 | 0.7938 | 0.8680 | 0.9084 | 0.9327 | 0.9484 | 0.9593 | 0.9670 | |
2 | 3.0 | 0.0843 | 0.5920 | 0.7711 | 0.8535 | 0.8983 | 0.9253 | 0.9428 | 0.9548 | 0.9634 | |
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0.90 | 71 | 0.1 | 0.0993 | 0.2723 | 0.4274 | 0.5466 | 0.6354 | 0.7019 | 0.7524 | 0.7915 | 0.8221 |
35 | 0.2 | 0.0980 | 0.2752 | 0.4332 | 0.5534 | 0.6424 | 0.7085 | 0.7586 | 0.7971 | 0.8272 | |
17 | 0.4 | 0.0961 | 0.2833 | 0.4473 | 0.5695 | 0.6583 | 0.7235 | 0.7723 | 0.8095 | 0.8384 | |
11 | 0.6 | 0.0953 | 0.2950 | 0.4654 | 0.5891 | 0.6772 | 0.7409 | 0.7879 | 0.8235 | 0.8509 | |
8 | 0.8 | 0.0958 | 0.3109 | 0.4880 | 0.6124 | 0.6989 | 0.7604 | 0.8053 | 0.8388 | 0.8645 | |
7 | 1.0 | 0.0625 | 0.2634 | 0.4449 | 0.5767 | 0.6698 | 0.7365 | 0.7854 | 0.8221 | 0.8503 | |
4 | 1.5 | 0.0928 | 0.3766 | 0.5734 | 0.6949 | 0.7725 | 0.8243 | 0.8605 | 0.8866 | 0.9061 | |
3 | 2.0 | 0.0832 | 0.4276 | 0.6317 | 0.7464 | 0.8157 | 0.8602 | 0.8905 | 0.9120 | 0.9277 | |
3 | 2.5 | 0.0237 | 0.3441 | 0.5687 | 0.7000 | 0.7805 | 0.8329 | 0.8688 | 0.8942 | 0.9130 | |
2 | 3.0 | 0.0843 | 0.5930 | 0.7711 | 0.8535 | 0.8983 | 0.9253 | 0.9428 | 0.9548 | 0.9364 | |
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0.95 | 87 | 0.1 | 0.0484 | 0.1766 | 0.3176 | 0.4390 | 0.5362 | 0.6127 | 0.6730 | 0.7209 | 0.7594 |
43 | 0.2 | 0.0468 | 0.1773 | 0.3210 | 0.4440 | 0.5420 | 0.6186 | 0.6788 | 0.7264 | 0.7645 | |
21 | 0.4 | 0.0441 | 0.1804 | 0.3302 | 0.4566 | 0.5558 | 0.6325 | 0.6920 | 0.7388 | 0.7760 | |
14 | 0.6 | 0.0377 | 0.1753 | 0.3298 | 0.4595 | 0.5605 | 0.6380 | 0.6978 | 0.7445 | 0.7815 | |
10 | 0.8 | 0.0404 | 0.1948 | 0.3602 | 0.4932 | 0.5935 | 0.6688 | 0.7259 | 0.7699 | 0.8043 | |
8 | 1.0 | 0.0352 | 0.1951 | 0.3671 | 0.5033 | 0.6047 | 0.6798 | 0.7363 | 0.7795 | 0.8131 | |
5 | 1.5 | 0.0354 | 0.2431 | 0.4397 | 0.5795 | 0.6761 | 0.7441 | 0.7933 | 0.8297 | 0.8575 | |
4 | 2.0 | 0.0194 | 0.2436 | 0.4558 | 0.6002 | 0.6969 | 0.7633 | 0.8105 | 0.8450 | 0.8710 | |
3 | 2.5 | 0.0237 | 0.3441 | 0.5687 | 0.7000 | 0.7805 | 0.8329 | 0.8688 | 0.8942 | 0.9130 | |
3 | 3.0 | 0.0054 | 0.2983 | 0.5323 | 0.6726 | 0.7597 | 0.8166 | 0.8557 | 0.8836 | 0.9041 | |
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0.99 | 121 | 0.1 | 0.0098 | 0.0662 | 0.1603 | 0.2633 | 0.3593 | 0.4433 | 0.5148 | 0.5749 | 0.6256 |
59 | 0.2 | 0.0100 | 0.0695 | 0.1679 | 0.2740 | 0.3718 | 0.4565 | 0.5280 | 0.5878 | 0.6378 | |
29 | 0.4 | 0.0086 | 0.0688 | 0.1709 | 0.2807 | 0.3811 | 0.4672 | 0.5392 | 0.5991 | 0.6489 | |
19 | 0.6 | 0.0075 | 0.0694 | 0.1766 | 0.2908 | 0.3938 | 0.4812 | 0.5536 | 0.6133 | 0.6626 | |
14 | 0.8 | 0.0066 | 0.0714 | 0.1851 | 0.3044 | 0.4103 | 0.4987 | 0.5712 | 0.6303 | 0.6788 | |
11 | 1.0 | 0.0059 | 0.0751 | 0.1971 | 0.3221 | 0.4307 | 0.5199 | 0.5919 | 0.6501 | 0.6974 | |
7 | 1.5 | 0.0047 | 0.0942 | 0.2439 | 0.3841 | 0.4975 | 0.5859 | 0.6446 | 0.7083 | 0.7509 | |
5 | 2.0 | 0.0042 | 0.1328 | 0.3177 | 0.4694 | 0.5819 | 0.6644 | 0.7257 | 0.7721 | 0.8079 | |
4 | 2.5 | 0.0029 | 0.1730 | 0.3843 | 0.5395 | 0.6469 | 0.7222 | 0.7764 | 0.8164 | 0.8467 | |
3 | 3.0 | 0.0054 | 0.2983 | 0.5323 | 0.6726 | 0.7597 | 0.8166 | 0.8557 | 0.8836 | 0.9041 |
OC values of sampling plans.
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1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 |
0.75 | 137 | 0.1 | 0.2484 | 0.6314 | 0.8348 | 0.9234 | 0.9623 | 0.9802 | 0.9891 | 0.9936 | 0.9961 |
68 | 0.2 | 0.2493 | 0.6407 | 0.8427 | 0.9284 | 0.9652 | 0.9820 | 0.9901 | 0.9943 | 0.9966 | |
34 | 0.4 | 0.2408 | 0.6506 | 0.8533 | 0.9354 | 0.9694 | 0.9845 | 0.9916 | 0.9952 | 0.9972 | |
23 | 0.6 | 0.2228 | 0.6527 | 0.8596 | 0.9400 | 0.9723 | 0.9862 | 0.9926 | 0.9959 | 0.9976 | |
17 | 0.8 | 0.2359 | 0.6888 | 0.8833 | 0.9527 | 0.9790 | 0.9898 | 0.9947 | 0.9971 | 0.9983 | |
14 | 1.0 | 0.2120 | 0.6898 | 0.8883 | 0.9561 | 0.9809 | 0.9909 | 0.9953 | 0.9974 | 0.9985 | |
10 | 1.5 | 0.1711 | 0.7193 | 0.9118 | 0.9685 | 0.9871 | 0.9942 | 0.9971 | 0.9985 | 0.9991 | |
8 | 2.0 | 0.1556 | 0.7826 | 0.9428 | 0.9816 | 0.9930 | 0.9970 | 0.9986 | 0.9993 | 0.9996 | |
7 | 2.5 | 0.1297 | 0.8341 | 0.9625 | 0.9889 | 0.9960 | 0.9983 | 0.9992 | 0.9996 | 0.9998 | |
6 | 3.0 | 0.2323 | 0.9326 | 0.9880 | 0.9969 | 0.9989 | 0.9996 | 0.9998 | 0.9999 | 1.0000 | |
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0.90 | 171 | 0.1 | 0.0008 | 0.0143 | 0.0541 | 0.1154 | 0.1868 | 0.2595 | 0.3288 | 0.3925 | 0.4497 |
85 | 0.2 | 0.0007 | 0.0137 | 0.0536 | 0.1156 | 0.1879 | 0.2615 | 0.3314 | 0.3955 | 0.4531 | |
42 | 0.4 | 0.0005 | 0.0129 | 0.0534 | 0.1173 | 0.1918 | 0.2673 | 0.3387 | 0.4038 | 0.4619 | |
28 | 0.6 | 0.0004 | 0.0117 | 0.0519 | 0.1169 | 0.1930 | 0.2701 | 0.3428 | 0.4087 | 0.4675 | |
21 | 0.8 | 0.0002 | 0.0108 | 0.0516 | 0.1185 | 0.1970 | 0.2760 | 0.3501 | 0.4170 | 0.4763 | |
17 | 1.0 | 0.0001 | 0.0096 | 0.0501 | 0.1182 | 0.1983 | 0.2789 | 0.3542 | 0.4219 | 0.4818 | |
11 | 1.5 | 0.0001 | 0.0120 | 0.0654 | 0.1499 | 0.2431 | 0.3321 | 0.4117 | 0.4810 | 0.5404 | |
9 | 2.0 | 0.0000 | 0.0093 | 0.0619 | 0.1492 | 0.2459 | 0.3377 | 0.4193 | 0.4898 | 0.5499 | |
8 | 2.5 | 0.0000 | 0.0078 | 0.0604 | 0.1503 | 0.2499 | 0.3439 | 0.4268 | 0.4980 | 0.5584 | |
7 | 3.0 | 0.0000 | 0.0109 | 0.0779 | 0.1823 | 0.2907 | 0.3885 | 0.4722 | 0.5422 | 0.6006 | |
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0.95 | 193 | 0.1 | 0.0003 | 0.0071 | 0.0328 | 0.0787 | 0.1376 | 0.2019 | 0.2661 | 0.3273 | 0.3841 |
96 | 0.2 | 0.0002 | 0.0068 | 0.0324 | 0.0787 | 0.1382 | 0.2031 | 0.2680 | 0.3298 | 0.3869 | |
47 | 0.4 | 0.0002 | 0.0067 | 0.0335 | 0.0824 | 0.1449 | 0.2124 | 0.2793 | 0.3425 | 0.4006 | |
31 | 0.6 | 0.0001 | 0.0063 | 0.0339 | 0.0849 | 0.1499 | 0.2197 | 0.2884 | 0.3529 | 0.4117 | |
23 | 0.8 | 0.0001 | 0.0062 | 0.0352 | 0.0892 | 0.1575 | 0.2301 | 0.3008 | 0.3666 | 0.4262 | |
18 | 1.0 | 0.0001 | 0.0068 | 0.0395 | 0.0991 | 0.1728 | 0.2495 | 0.3228 | 0.3901 | 0.4503 | |
12 | 1.5 | 0.0000 | 0.0070 | 0.0462 | 0.1166 | 0.2004 | 0.2845 | 0.3624 | 0.4320 | 0.4930 | |
10 | 2.0 | 0.0000 | 0.0046 | 0.0399 | 0.1092 | 0.1938 | 0.2794 | 0.3590 | 0.4299 | 0.4920 | |
8 | 2.5 | 0.0000 | 0.0078 | 0.0604 | 0.1503 | 0.2499 | 0.3439 | 0.4268 | 0.4980 | 0.5584 | |
7 | 3.0 | 0.0000 | 0.0109 | 0.0779 | 0.1823 | 0.2907 | 0.3885 | 0.4722 | 0.5422 | 0.6006 | |
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0.99 | 240 | 0.1 | 0.0000 | 0.0015 | 0.0110 | 0.0339 | 0.0700 | 0.1153 | 0.1657 | 0.2177 | 0.2691 |
119 | 0.2 | 0.0000 | 0.0015 | 0.0109 | 0.0343 | 0.0710 | 0.1172 | 0.1683 | 0.2211 | 0.2731 | |
58 | 0.4 | 0.0000 | 0.0015 | 0.0117 | 0.0369 | 0.0764 | 0.1254 | 0.1792 | 0.2341 | 0.2877 | |
38 | 0.6 | 0.0000 | 0.0015 | 0.0122 | 0.0393 | 0.0813 | 0.1331 | 0.0189 | 0.0246 | 0.3012 | |
28 | 0.8 | 0.0000 | 0.0015 | 0.0132 | 0.0428 | 0.0883 | 0.1435 | 0.2026 | 0.2617 | 0.3183 | |
22 | 1.0 | 0.0000 | 0.0016 | 0.0149 | 0.0480 | 0.0978 | 0.1571 | 0.2195 | 0.2810 | 0.3392 | |
15 | 1.5 | 0.0000 | 0.0014 | 0.0159 | 0.0535 | 0.1096 | 0.1750 | 0.2424 | 0.3075 | 0.3681 | |
11 | 2.0 | 0.0000 | 0.0023 | 0.0256 | 0.0793 | 0.1518 | 0.2299 | 0.3057 | 0.3756 | 0.4383 | |
9 | 2.5 | 0.0000 | 0.0034 | 0.0365 | 0.1055 | 0.1912 | 0.2781 | 0.3588 | 0.4307 | 0.4937 | |
8 | 3.0 | 0.0000 | 0.0045 | 0.0457 | 0.1256 | 0.2197 | 0.3115 | 0.3945 | 0.4668 | 0.5289 |
The producer’s risk is defined as the probability of rejecting the lot when
Minimum ratio for the acceptability of a lot with producer’s risk 0.05.
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0.1 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 |
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0.75 | 0 | 27.2995 | 27.3264 | 25.2820 | 25.3354 | 25.3887 | 31.7358 | 31.8683 | 42.4911 | 53.1138 | 32.2612 |
0.75 | 1 | 7.5211 | 7.4707 | 7.0638 | 6.9551 | 6.8415 | 7.0279 | 5.9340 | 7.9120 | 5.9356 | 7.1227 |
0.75 | 2 | 4.6982 | 4.6579 | 4.5740 | 4.4857 | 4.3925 | 4.1606 | 4.2240 | 4.2572 | 5.3215 | 4.2191 |
0.75 | 3 | 3.6690 | 3.6354 | 3.4860 | 3.5693 | 3.4898 | 3.5650 | 3.5335 | 3.0410 | 3.8013 | 3.1989 |
0.75 | 4 | 3.1398 | 3.1106 | 3.0490 | 2.9280 | 3.0224 | 2.9465 | 2.7276 | 3.0537 | 3.0610 | 2.6281 |
0.75 | 5 | 2.7959 | 2.7492 | 2.6938 | 2.6752 | 2.5684 | 2.5816 | 2.5929 | 2.5693 | 2.6240 | 2.3656 |
0.75 | 6 | 2.5649 | 2.5411 | 2.4575 | 2.4019 | 2.4074 | 2.3411 | 2.2305 | 2.2542 | 2.3369 | 2.8043 |
0.75 | 7 | 2.3985 | 2.3630 | 2.3429 | 2.2910 | 2.2887 | 2.1705 | 2.1968 | 2.3400 | 2.1320 | 2.5584 |
0.75 | 8 | 2.2725 | 2.2520 | 2.2076 | 2.1353 | 2.1038 | 2.1610 | 1.9808 | 2.1336 | 1.9782 | 2.3739 |
0.75 | 9 | 2.1635 | 2.1442 | 2.1022 | 2.0753 | 2.0432 | 2.0464 | 1.9775 | 1.9748 | 2.1740 | 2.2298 |
0.75 | 10 | 2.0847 | 2.0577 | 2.0176 | 1.9725 | 1.9931 | 1.9550 | 1.9712 | 1.8485 | 2.0464 | 2.1137 |
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0.90 | 0 | 44.0826 | 44.1095 | 42.0653 | 44.2167 | 42.1723 | 42.2257 | 31.8683 | 42.4911 | 53.1138 | 63.7366 |
0.90 | 1 | 10.7007 | 10.4994 | 10.0945 | 9.6860 | 9.2735 | 10.0728 | 8.2474 | 7.9120 | 9.8900 | 7.1227 |
0.90 | 2 | 6.4092 | 6.2376 | 6.1553 | 6.0698 | 5.9809 | 5.4907 | 5.2368 | 5.6320 | 5.3215 | 6.3857 |
0.90 | 3 | 4.8111 | 4.7384 | 4.5906 | 4.5183 | 4.4422 | 4.3623 | 4.1426 | 3.8877 | 3.8013 | 4.5615 |
0.90 | 4 | 3.9865 | 3.9303 | 3.8153 | 3.7515 | 3.6839 | 3.5015 | 3.5805 | 3.6368 | 3.0610 | 3.6731 |
0.90 | 5 | 3.4961 | 3.4497 | 3.3544 | 3.2966 | 3.2348 | 3.2105 | 2.9167 | 3.0187 | 3.2117 | 3.1488 |
0.90 | 6 | 3.1546 | 3.0983 | 3.0488 | 2.9954 | 2.9380 | 2.8428 | 2.7494 | 2.6193 | 2.8177 | 2.8043 |
0.90 | 7 | 2.9122 | 2.8770 | 2.7767 | 2.6995 | 2.7270 | 2.5857 | 2.6252 | 2.6377 | 2.5401 | 2.5584 |
0.90 | 8 | 2.7309 | 2.6877 | 2.6215 | 2.5512 | 2.4762 | 2.5130 | 2.3481 | 2.3904 | 2.3338 | 2.3739 |
0.90 | 9 | 2.5801 | 2.5413 | 2.5003 | 2.4353 | 2.3657 | 2.3516 | 2.2950 | 2.2008 | 2.1740 | 2.2298 |
0.90 | 10 | 2.4598 | 2.4243 | 2.3678 | 2.3422 | 2.2768 | 2.2240 | 2.2503 | 2.2469 | 2.3107 | 2.1137 |
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0.95 | 0 | 57.7180 | 56.6969 | 54.6527 | 50.5105 | 50.5640 | 52.7154 | 47.6037 | 42.4911 | 53.1138 | 63.7366 |
0.95 | 1 | 13.1233 | 12.9222 | 12.5182 | 12.4144 | 11.7015 | 11.5919 | 10.5419 | 10.9966 | 9.8900 | 11.8680 |
0.95 | 2 | 7.5278 | 7.4222 | 7.2090 | 6.8610 | 6.5094 | 6.8151 | 6.2408 | 5.6320 | 5.3215 | 6.3857 |
0.95 | 3 | 5.5593 | 5.4474 | 5.2215 | 5.2290 | 5.0756 | 4.7596 | 4.7466 | 4.7113 | 4.8596 | 4.5615 |
0.95 | 4 | 4.5600 | 4.4766 | 4.3623 | 4.2449 | 4.1238 | 4.0540 | 4.0012 | 3.6368 | 3.8171 | 3.6731 |
0.95 | 5 | 3.9491 | 3.9029 | 3.7669 | 3.6688 | 3.5670 | 3.4192 | 3.2373 | 3.4572 | 3.2117 | 3.1488 |
0.95 | 6 | 3.5477 | 3.4916 | 3.3770 | 3.2917 | 3.2025 | 3.1754 | 3.0050 | 2.9739 | 2.8177 | 2.8043 |
0.95 | 7 | 3.2501 | 3.2015 | 3.1018 | 3.0256 | 2.9455 | 2.8609 | 2.8366 | 2.6377 | 2.9250 | 3.0482 |
0.95 | 8 | 3.0289 | 2.9859 | 2.8972 | 2.8279 | 2.7544 | 2.7464 | 2.7084 | 2.6410 | 2.6670 | 2.8005 |
0.95 | 9 | 2.8479 | 2.7993 | 2.7389 | 2.6749 | 2.6067 | 2.5540 | 2.4517 | 2.4208 | 2.4685 | 2.6088 |
0.95 | 10 | 2.7041 | 2.6687 | 2.6127 | 2.5529 | 2.4889 | 2.4024 | 2.3882 | 2.2469 | 2.3107 | 2.4557 |
| |||||||||||
0.99 | 0 | 88.1383 | 86.0673 | 84.0232 | 81.9790 | 75.7389 | 73.6945 | 63.3385 | 63.4716 | 53.1138 | 63.7366 |
0.99 | 1 | 18.2712 | 17.7675 | 17.3645 | 16.9596 | 16.5526 | 16.1433 | 15.1091 | 14.0558 | 13.7457 | 11.8680 |
0.99 | 2 | 10.0941 | 9.9229 | 9.5790 | 9.2329 | 8.6206 | 8.7969 | 8.2360 | 8.3211 | 7.0400 | 8.4480 |
0.99 | 3 | 7.2133 | 7.1017 | 6.7979 | 6.6493 | 6.3403 | 6.3445 | 5.9462 | 5.5234 | 5.8892 | 5.8316 |
0.99 | 4 | 5.7617 | 5.6786 | 5.4559 | 5.2305 | 5.2214 | 4.8799 | 4.8365 | 4.7740 | 4.5460 | 4.5805 |
0.99 | 5 | 4.9170 | 4.8504 | 4.6741 | 4.5363 | 4.3954 | 4.2512 | 4.1877 | 3.8890 | 3.7734 | 3.8540 |
0.99 | 6 | 4.3502 | 4.2779 | 4.16472 | 3.9820 | 3.8621 | 3.8379 | 3.5116 | 3.6659 | 3.2741 | 3.3812 |
0.99 | 7 | 3.9395 | 3.8776 | 3.7517 | 3.6770 | 3.5993 | 3.4087 | 3.2557 | 3.2162 | 3.2971 | 3.0482 |
0.99 | 8 | 3.6363 | 3.5820 | 3.4483 | 3.3804 | 3.3092 | 3.2113 | 3.0646 | 2.8874 | 2.9880 | 3.2004 |
0.99 | 9 | 3.4034 | 3.3549 | 3.2557 | 3.1533 | 3.0872 | 3.0576 | 2.9161 | 2.8494 | 2.7510 | 2.9622 |
0.99 | 10 | 3.2100 | 3.1574 | 3.0673 | 2.9738 | 2.9118 | 2.8460 | 2.7972 | 2.6279 | 2.5624 | 2.7713 |
OC values of sampling plans for
|
1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 |
---|---|---|---|---|---|---|---|---|---|
OC | 0.0832 | 0.4276 | 0.6317 | 0.7464 | 0.8157 | 0.8602 | 0.8905 | 0.9120 | 0.9272 |
In this section, we consider two examples with real data sets to illustrate the proposed acceptance sampling plans.
The first data refers to software reliability presented by Wood [
Suppose that the experimenter would like to establish the unknown 50th percentile life time for the software mentioned above to be at least 300 h and the life test would be ended at 600 h which should have led to the ratio
The OC values for acceptance sampling plan in (
The producer’s risk is almost equal to
From Table
The second data refers to the data obtained from Aarset [
Suppose that we would like to establish the unknown 50th percentile life time for the devices to be at least 10 hours and the life test would be ended at 15 hrs which should have led to the ratio of
This paper provides the minimum sample size required to decide upon accepting/rejecting a lot based on its specified 50th percentile (median) when the data follows half normal distribution. Assuming that the size of the given sample is minimum, we can use the tables in this paper to pick up acceptance number
The authors thank the editor and the reviewers for their helpful suggestions, comments, and encouragement, which helped in improving the final version of the paper.