Single and double sampling

1. SINGLE AND DOUBLE SAMPLING By SHIVANI GARG

2. WHAT IS SAMPLING? Sampling is the act, process, or technique of selecting a suitable sample, or a representative part of a population for the purpose of determining parameters or characteristics of the whole population.

3. SINGLE SAMPLING DOUBLE SAMPLING

4. SINGLE SAMPLING

5. Definition of a Single-Sampling Plan A single sampling plan is defined by sample size, n, and the acceptance number c. Say there are N total items in a lot. Choose n of the items at random. If at least c of the items are unacceptable, reject the lot. N = lot size n = sample size c = acceptance number d = observed number of defectives.

6. The acceptance or rejection of the lot is based on the results from a single sample - thus a single-sampling plan.

7. Conditions of Single-Sampling Plan:- Acceptance or rejection decision is made after drawing only one sample from the lot. If the number of defectives, d, does not exceed the acceptance criteria, c, the lot is accepted.

8. Single-Sampling Plan Lot of N Items Random Sample of n Items N - n Items Inspect n Items d > c d < c Replace Defectives n Nondefectives d Defectives Found in Sample Reject Lot Accept Lot

9. DOUBLE SAMPLING

10. Definition of a Double-Sampling Plan Defined by four parameters: n 1 = sample size for the first sample c 1 = acceptance number of the first sample n 2 = sample size for the second sample c 2 = acceptance number of the second sample

11. Conditions of Double-Sampling Plan:- One small sample is drawn initially. If the number of defectives is less than or equal to some lower limit, the lot is accepted. If the number of defectives is greater than some upper limit, the lot is rejected. If the number of defectives is neither, a second larger sample is drawn. Lot is either accepted or rejected on the basis of the information from both of the samples.

12. Double-Sampling Plan Lot of N Items Random Sample of n 1 Items N – n 1 Items Inspect n 1 Items d 1 > c 2 d 1 < c 1 Replace Defectives n 1 Nondefectives d 1 Defectives Found in Sample Reject Lot Accept Lot Continue c 1 < d 1 < c 2 (to next slide)

13. (d 1 + d 2 ) > c 2 Double-Sampling Plan N – n 1 Items Random Sample of n 2 Items N – (n 1 + n 2 ) Items Inspect n 2 Items Replace Defectives n 2 Nondefectives d 2 Defectives Found in Sample Reject Lot Accept Lot Continue (d 1 + d 2 ) < c 2 (from previous slide)

14. Double sampling plans Advantages Can reduce the total amount of inspection Allows the vendor a second chance Disadvantages Can lose the economical advantage More record keeping is needed