Downloaded from https://www.everyspec.com Homogeneity of lot and randumness of sample wrong decision, that is, accepting a bad lot or are closely related, If a lot of units is thor- rejecting a good lot, may be reduced by increas- oughly mixed, that is, homogeneous, each unit ing the sample size. However, in so doing, the has an equal chance of being located in a cer- costs of inspection are increased. tain part of the lot. By randomness of sample 5-5. Operating Characteristic Curve. Four im- is meant the selection of sample units In such a manner that each unit of the lot has an equal sampling chance of being selected.
It follows, therefore, plan operates with respect to lots that are de- that any sample drawn from a homogeneous lot fective in various percentages. Of these, the is equivalent to a random sample drawn from a operating characteristic (OC) curve is the most heterogeneous lot. important because it gives an adequate picture of the plan's severity anddiscriminatory power. The purpose of restricting lot sire in the specd- It pictures the probability of acceptance Pa for cTheuronise of asurecting h ogty ore uniformity - lots of various qualities, p' percent defective.
ftcation is to assure homogeneity or uniformity The exact probability of finding d defectives .in by controlling the material which goes into the T eacpr i of f deces dN product, and the conditions under which the pro- a sample of n pieces drawn from a lot of N duct is produced. However, if all variables pieces containing D defects is determined by which may make for some degree of nonuni- the hypergeometric distribution, and is given formity are strictly controlled, the resulting by the formula lot may be so small that the cost of inspection, N.DCn-d - DCd subsequent handling, and use is disproportion- Pd N NCn ately high.
It follows, then, that only the major sources of variation, with respectto the specific The first factor of the numerator is the number product requirements, ought to be controlled. of ways in which (n - d) good pieces may be In practice, it is often difficult, if not impos- drawn trom (N - D) good pieces in the lot, and sible, to select perfectly random samples. For the second factor is the number of ways in which example, if a lot of e0,000 components is of- d defectives may be drawn from D defectives in feted for inspection on trays containing 100 the lot.
The denominator is the number of ways fere fo Insecton o trys cntaning100 in which n pieces in the sample may be drawn components in each tray, for practical reasons fro it may be necessary to treat eachtrayas a sub- m N pieces in the lot. lot, and select one sample unit drawn at ran- The use of this hypergeometric formula is t3- dora from each tray. Thus, the lackof complete dious.
For example, in a sampling plan where assurance of homogeneity (a result of control- ling only major sources of variation) is n d 150, and c (the acceptance number) a 4 counterbalanced by partial randomness of efectives, applied to a lot of N = 3,000 pieces sampuling, of p' 1 percent defective, gives a probability ' of acceptance 5-4. Sampling Risks. In any form of accept- ance sampling, there is the inherent risk that a 2= 9 7 0 C 15 0 2 9 7 0 C 1 4 9 " 30C1 lot of acceptable quality will be rejected, while 3 0 0 C 1 5 0 a lot of rejectable quality will be accepted.
Fundamentally, there are three criteria by 2 9 70 C 1 4 6 " 30C4 (1) which a sampling plan should be judged to en- + 300OC150 sure that the plan selected is the correct one to use. These criteria are: Where n 5 0.IN, the binomial approximation to a. How the plan will operate with respect the hypergeometric distribution may be used. to lots of acceptable quality; Thus, fer the above plan b. How it will operate on lots which should be rejected; Pa = 1 5 0 C 0 (0.99) 1 5 0 + 15 0 C 1 (0.99) 14 9 (0.01) + c. How it will affect the cost of inspection.
The first two criteria may be determined by + 1 5 0 C 4 (0"99) 14 6 (0.01) 4 (2) calculations involving the probabilities of ac- However, this is still a somewhat complicated ceptance. In general, the risks of making a calculation, unless a set of "Tables of the Bi- 5-2