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Publications : Microbiological Sampling Plans
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> Microbiological sampling plans Microbiological sampling plans: a tool to explore ICMSF recommendations (some explanation) Two-class sampling plans (2class) The sheet has several components containing graphs, input/output fields, and calculation results. For the normal user only the graphs and input/output fields shown in lines 1 to 32 and columns A to X should be of interest. Input fields are shown in yellow. In the following text information that can be entered in such fields is written in italics. Graphs for two-class sampling plans (from left to right): Plot 1 – Common type of operating characteristic (OC) curve relating probability of accepting a lot to the proportion defective it contains. Acceptance probabilities are calculated for given number of sampling units that are examined, n, given microbiological limit specified by the sampling plan, m, and given maximum number of sampling units that are allowed to exceed the limit, c. Plot 2 – Normal frequency distribution assumed for Log-transformed colony count numbers per gram to be found in sampling units drawn randomly from a lot characterized by given mean Log count per gram and given standard deviation sigma. The red vertical line indicates the microbiological limit, m, specified in the sampling plan. Right to m the area under the curve corresponds to the proportion defective the lot contains. Plot 3 – Proportion defective contained in lots in relation to varying mean Log counts per gram (orange) and proportions acceptable accordingly (green). These proportions are derived from Normal frequency distributions with given standard deviation sigma and limit m as shown in Plot 2. Using these proportions defective and the given sampling plan specifications for n and c corresponding probabilities of lot acceptance are calculated. Results are plotted (black) to show the OC curve in relation to mean Log counts per gram. Plot 4 – Combines the OC curve shown in Plot 3 with the frequency distribution in Plot 2. The brown vertical line indicates that mean Log count per gram that is accepted with a given probability of P(accept). [Point for discussion: This mean Log count is called ‚FSO' or ‚performance criterion' (for P(accept)=0.05) or ‚alternate performance criterion' (for alternate P(accept)) in the spreadsheet. I don't think this is a lucky choice.] Input fields for two-class sampling plans (from left to right): Yellow fields on the left –
To change any of these values go to that field, type in a new value, and press Enter. Calculation results, like P(accept), and graphs will be changed accordingly.
P(accept) can be changed to 0.05 by clicking the upper grey box. Alternatively, different values (between 0 and 1) can be entered in the yellow field below and set to P(accept) by clicking the lower grey box. In both cases the mean Log count per gram accepted with this new probability P(accept) is calculated and graphs are changed accordingly. Yellow field in the middle – To calculate the acceptance probability P(accept) for a specific proportion defective type in this proportion as Pd and press Enter. The result will be shown in the next field to the right. For this calculation only the given values for n and c are needed (see Plot 1). Yellow fields on the right – Only sampling plan specifications can be manipulated here, lot characteristics remain unchanged. When new values for n and/or c are entered the corresponding acceptance probability P(accept) is calculated using the microbiological limit m as given. When the grey box on the right side is clicked a new value for m is derived that yields the same combination of mean Log count per gram and lot acceptance probability P(accept) that is achieved by the sampling plan described on the left. Three-class sampling plans (3class) The sheet has several components containing graphs, input/output fields, and calculation results as well. For the normal user only the graphs and input/output fields shown in lines 1 to 32 and columns A to U should be of interest. Input fields are shown in yellow. In the following text information that can be entered in such fields is written in italics. Graphs for three-class sampling plans (from left to right): Plot 1 – Operating characteristic (OC) surface showing probabilities of accepting a lot depending on two proportions: the proportion defective in the lot exceeding the microbiological limit M, named Pd, and the proportion marginally defective between the two microbiological limits m and M, named Pm. Acceptance probabilities are calculated for given number of sampling units that are examined, n, given microbiological limits m and M, and given maximum number of sampling units that are allowed to be marginally defective, c, i.e. that are allowed to exceed the limit m but not M. The number of sampling units that are allowed to exceed M is assumed to be zero. Plot 2 – Normal frequency distribution assumed for Log-transformed colony count numbers per gram to be found in sampling units drawn randomly from a lot characterized by given mean Log count per gram and given standard deviation sigma. The red vertical line indicates the microbiological limit M specified in the sampling plan. Right to M the area under the curve corresponds to the proportion defective the lot contains, Pd. The yellow vertical line indicates the microbiological limit m specified in the sampling plan. The area under the curve between m and M corresponds to the proportion marginally defective in the lot, Pm. Plot 3 – Proportions defective contained in lots in relation to varying mean Log counts per gram (orange), proportions marginally defective (yellow), and proportions acceptable accordingly (green). These proportions are derived from Normal frequency distributions with given standard deviation sigma and microbiological limits m and M as shown in Plot 2. Using these proportions defective, these proportions marginally defective, and the given sampling plan specifications for n and c corresponding probabilities of lot acceptance are calculated. Results are plotted (black) to show the OC curve in relation to mean Log counts per gram. Input fields for two-class sampling plans (from left to right): Yellow fields on the left –
To change any of these values go to that field, type in a new value, and press Enter. Calculation results, like P(accept), and graphs will be changed accordingly. The acceptance probability for a lot with mean Log count per gram as given in the yellow field on the left and as shown in Plot 2: P(accept). P(accept) can be changed to 0.05 by clicking the upper grey box. Alternatively, different values (between 0 and 1) can be entered in the yellow field below and set to P(accept) by clicking the lower grey box. In both cases the mean Log count per gram accepted with this new probability P(accept) is calculated and graphs are changed accordingly. Yellow field in the middle – To calculate the acceptance probability P(accept) for a specific combination of proportion defective, i.e. exceeding M, and proportion marginally defective, i.e. between m and M, type in these proportion as Pd and Pm, respectively, and press Enter. The result will be shown in the next field to the right. For this calculation only the given values for n and c are needed (see Plot 1). Yellow fields on the right – Only sampling plan specifications can be manipulated here, lot characteristics remain unchanged. When new values for n and/or i are entered the corresponding acceptance probability P(accept) is calculated using the microbiological limits m and M as given. When the grey box on the right side is clicked a new value for m is derived that yields the same combination of mean Log count per gram and lot acceptance probability P(accept) that is achieved by the sampling plan described on the left. The microbiological limit M is left unchanged.
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