Food Protection Trends - July/August 2017 - 285
APPENDIX B. DEVELOPMENT OF SAMPLE SIZES FOR MEDIAN AND RANGE/d2 BY MINITAB
SIMULATION
Sample Size Calculations
* Goal: determine the core temperature sample size for a variable sampling plan with a lower specification limit (LSL) and
the following specifications:
* RQL = 1% and β = 0.05. Based on these values, we can be 95% confident that at least 99% of the population is good when
we accept the lot.
* Core temperature follows a normal distribution.
* Instead of estimating μ with the sample mean, it is estimated with the sample median.
* Instead of estimating σ with the sample standard deviation, it is estimated with range/d2.
* The k factor equals 3. In other words, the decision rule has the form
Accept the lot if median -3 range > LSL
d2
Simulation Steps
1. Simulate 10,000 samples of size n from a normal distribution with a mean 2.32635 μ above the LSL. This results in
exactly 1% of the population out-of-spec. When the true defect rate is equal to the RQL (1%) and β = 0.05, we should
accept the lot 5% of the time and reject the lot 95% of the time.
2. Store the median and range for each of the 10,000 samples.
3. Estimate σ by dividing the range by d2.
4. Calculate the percent of times the simulation accepts the lot and repeat steps 1-4 for different sample sizes (n) until the
range
percent of times the lot is accepted (median -3
d2 > LSL) equals 5%. In other words, when the true defect rate is
equal to the RQL, as is the case here, we want to find the n so that we accept the lot 100 β% of the time and reject the
lot 100 (1-β)% of the time.
To do this for an RQL = 5% and β = 0.05, replace step 1 with:
Simulate 10,000 samples of size n from a normal distribution with a mean 1.64485σ above the LSL. This results in exactly
5% of the population out-of-spec. When the true defect rate is equal to the RQL (5%) and β = 0.05, we should accept the lot
5% of the time and reject the lot 95% of the time.
Comparison of n = 15 to n = 60 for Variables Plan RQL = 1% and Beta = 0.05
Median - 3*Range/d2
Example of Simulation
The graph below shows a histogram of the simulated median-3
range
values for n = 15 and n = 60. The distribution for
d2
core temperatures in the simulation had a defect rate of 1%. When n = 60, the lot is accepted approximately 5% of the time and
rejected approximately 95% of the time. Therefore, 60 is the correct sample size for an RQL = 1% and β = 0.05. When n = 15,
the lot is incorrectly accepted much more than 5% of the time. This high β (or Type II error) indicates that a sample size of 15
is too small.
July/August Food Protection Trends
285
Table of Contents for the Digital Edition of Food Protection Trends - July/August 2017
Contents
Food Protection Trends - July/August 2017 - Cover1
Food Protection Trends - July/August 2017 - Cover2
Food Protection Trends - July/August 2017 - Contents
Food Protection Trends - July/August 2017 - 234
Food Protection Trends - July/August 2017 - 235
Food Protection Trends - July/August 2017 - 236
Food Protection Trends - July/August 2017 - 237
Food Protection Trends - July/August 2017 - 238
Food Protection Trends - July/August 2017 - 239
Food Protection Trends - July/August 2017 - 240
Food Protection Trends - July/August 2017 - 241
Food Protection Trends - July/August 2017 - 242
Food Protection Trends - July/August 2017 - 243
Food Protection Trends - July/August 2017 - 244
Food Protection Trends - July/August 2017 - 245
Food Protection Trends - July/August 2017 - 246
Food Protection Trends - July/August 2017 - 247
Food Protection Trends - July/August 2017 - 248
Food Protection Trends - July/August 2017 - 249
Food Protection Trends - July/August 2017 - 250
Food Protection Trends - July/August 2017 - 251
Food Protection Trends - July/August 2017 - 252
Food Protection Trends - July/August 2017 - 253
Food Protection Trends - July/August 2017 - 254
Food Protection Trends - July/August 2017 - 255
Food Protection Trends - July/August 2017 - 256
Food Protection Trends - July/August 2017 - 257
Food Protection Trends - July/August 2017 - 258
Food Protection Trends - July/August 2017 - 259
Food Protection Trends - July/August 2017 - 260
Food Protection Trends - July/August 2017 - 261
Food Protection Trends - July/August 2017 - 262
Food Protection Trends - July/August 2017 - 263
Food Protection Trends - July/August 2017 - 264
Food Protection Trends - July/August 2017 - 265
Food Protection Trends - July/August 2017 - 266
Food Protection Trends - July/August 2017 - 267
Food Protection Trends - July/August 2017 - 268
Food Protection Trends - July/August 2017 - 269
Food Protection Trends - July/August 2017 - 270
Food Protection Trends - July/August 2017 - 271
Food Protection Trends - July/August 2017 - 272
Food Protection Trends - July/August 2017 - 273
Food Protection Trends - July/August 2017 - 274
Food Protection Trends - July/August 2017 - 275
Food Protection Trends - July/August 2017 - 276
Food Protection Trends - July/August 2017 - 277
Food Protection Trends - July/August 2017 - 278
Food Protection Trends - July/August 2017 - 279
Food Protection Trends - July/August 2017 - 280
Food Protection Trends - July/August 2017 - 281
Food Protection Trends - July/August 2017 - 282
Food Protection Trends - July/August 2017 - 283
Food Protection Trends - July/August 2017 - 284
Food Protection Trends - July/August 2017 - 285
Food Protection Trends - July/August 2017 - 286
Food Protection Trends - July/August 2017 - 287
Food Protection Trends - July/August 2017 - 288
Food Protection Trends - July/August 2017 - 289
Food Protection Trends - July/August 2017 - 290
Food Protection Trends - July/August 2017 - 291
Food Protection Trends - July/August 2017 - 292
Food Protection Trends - July/August 2017 - 293
Food Protection Trends - July/August 2017 - 294
Food Protection Trends - July/August 2017 - 295
Food Protection Trends - July/August 2017 - 296
Food Protection Trends - July/August 2017 - 297
Food Protection Trends - July/August 2017 - 298
Food Protection Trends - July/August 2017 - 299
Food Protection Trends - July/August 2017 - 300
Food Protection Trends - July/August 2017 - 301
Food Protection Trends - July/August 2017 - 302
Food Protection Trends - July/August 2017 - 303
Food Protection Trends - July/August 2017 - 304
Food Protection Trends - July/August 2017 - 305
Food Protection Trends - July/August 2017 - 306
Food Protection Trends - July/August 2017 - 307
Food Protection Trends - July/August 2017 - 308
Food Protection Trends - July/August 2017 - Cover3
Food Protection Trends - July/August 2017 - Cover4
https://www.nxtbook.com/nxtbooks/trilix/fpt_20240910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20240708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20240506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20240304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20240102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20231112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20230910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20230708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20230506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20230304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20230102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20221112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20220910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20220708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20220506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20220304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20220102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20211112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20210910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20210708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20210506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20210304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20210102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20201112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20200910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20200708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20200506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20200304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20200102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20191112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20190910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20190708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20190506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20190304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20190102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20181112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20180910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20180708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20180506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20180304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20180102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20171112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20170910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20170708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20170506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20170304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20170102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20161112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20160910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20160708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20160506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20160304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20160102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20151112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20150910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20150708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20150506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20150304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20150102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20141112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20140910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20140708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20140506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20140304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20140102
https://www.nxtbook.com/nxtbooks/trilix/fpt_20131112
https://www.nxtbook.com/nxtbooks/trilix/fpt_20130910
https://www.nxtbook.com/nxtbooks/trilix/fpt_20130708
https://www.nxtbook.com/nxtbooks/trilix/fpt_20130506
https://www.nxtbook.com/nxtbooks/trilix/fpt_20130304
https://www.nxtbook.com/nxtbooks/trilix/fpt_20130102
https://www.nxtbook.com/nxtbooks/trilix/fpt_201212
https://www.nxtbook.com/nxtbooks/trilix/fpt_201211
https://www.nxtbook.com/nxtbooks/trilix/fpt_201210
https://www.nxtbook.com/nxtbooks/trilix/fpt_201209
https://www.nxtbook.com/nxtbooks/trilix/fpt_201208
https://www.nxtbook.com/nxtbooks/trilix/fpt_201207
https://www.nxtbook.com/nxtbooks/trilix/fpt_201206
https://www.nxtbook.com/nxtbooks/trilix/fpt_201205
https://www.nxtbook.com/nxtbooks/trilix/fpt_201204
https://www.nxtbook.com/nxtbooks/trilix/fpt_201203
https://www.nxtbook.com/nxtbooks/trilix/fpt_201202
https://www.nxtbook.com/nxtbooks/trilix/fpt_201201
https://www.nxtbook.com/nxtbooks/trilix/fpt_201112
https://www.nxtbook.com/nxtbooks/trilix/fpt_201111
https://www.nxtbook.com/nxtbooks/trilix/fpt_201110
https://www.nxtbook.com/nxtbooks/trilix/fpt_201109
https://www.nxtbook.com/nxtbooks/trilix/fpt_201108
https://www.nxtbook.com/nxtbooks/trilix/fpt_201107
https://www.nxtbook.com/nxtbooks/trilix/fpt_201106
https://www.nxtbook.com/nxtbooks/trilix/fpt_201105
https://www.nxtbook.com/nxtbooks/trilix/fpt_201104
https://www.nxtbook.com/nxtbooks/trilix/fpt_201103
https://www.nxtbook.com/nxtbooks/trilix/fpt_201102
https://www.nxtbook.com/nxtbooks/trilix/fpt_201101
https://www.nxtbook.com/nxtbooks/trilix/fpt_201012
https://www.nxtbook.com/nxtbooks/trilix/fpt_201011
https://www.nxtbook.com/nxtbooks/trilix/fpt_201010
https://www.nxtbook.com/nxtbooks/trilix/fpt_201009
https://www.nxtbook.com/nxtbooks/trilix/fpt_201008
https://www.nxtbook.com/nxtbooks/trilix/fpt_201007
https://www.nxtbook.com/nxtbooks/trilix/fpt_201006
https://www.nxtbook.com/nxtbooks/trilix/fpt_201005
https://www.nxtbook.com/nxtbooks/trilix/fpt_201004
https://www.nxtbook.com/nxtbooks/trilix/fpt_201003
https://www.nxtbook.com/nxtbooks/trilix/fpt_201002
https://www.nxtbook.com/nxtbooks/trilix/fpt_201001
https://www.nxtbook.com/nxtbooks/trilix/fpt_200912
https://www.nxtbook.com/nxtbooks/trilix/fpt_200911
https://www.nxtbook.com/nxtbooks/trilix/fpt_200910
https://www.nxtbook.com/nxtbooks/trilix/fpt_200909
https://www.nxtbook.com/nxtbooks/trilix/fpt_200908
https://www.nxtbook.com/nxtbooks/trilix/fpt_200907
https://www.nxtbook.com/nxtbooks/trilix/fpt_200906
https://www.nxtbook.com/nxtbooks/trilix/fpt_200905
https://www.nxtbook.com/nxtbooks/trilix/fpt_200904
https://www.nxtbook.com/nxtbooks/trilix/fpt_200903
https://www.nxtbook.com/nxtbooks/trilix/fpt_200902
https://www.nxtbook.com/nxtbooks/trilix/fpt_200901
https://www.nxtbook.com/nxtbooks/trilix/fpt_200812
https://www.nxtbook.com/nxtbooks/trilix/fpt_200811
https://www.nxtbook.com/nxtbooks/trilix/fpt_200810
https://www.nxtbook.com/nxtbooks/trilix/fpt_200809
https://www.nxtbook.com/nxtbooks/trilix/fpt_200808
https://www.nxtbook.com/nxtbooks/trilix/fpt_200807
https://www.nxtbookmedia.com