One of the possible advantages in the double or sequential sampling procedures is that, if a lot is very bad or if it is very good, it can be either rejected or accepted with small initial sample/samples. Any lot which cannot be decided easily can be examined further by means of additional sample/samples. Therefore, in some cases, the multiple sampling procedures provide short cuts to the decision without jeopardizing the incoming/outgoing quality of material. In such cases, obviously, the inspection load is reduced as compared to the single sampling procedure. But this may not always be true. If the process average of defectives in the lot supplied by the vendor varies considerably, the inspection load under the multiple sampling procedures might also vary appreciably. In such a case, the advantage claimed above for the multiple sampling procedures may no longer be valid, unless there is some other way of utilizing the inspection manpower when the workload on inspection is low. There is one psychological advantage with the double or sequential sampling procedures – people may feel more secure with the idea of providing a second or third chance to the lot of material before it is rejected. Otherwise, for the incoming lots with percent defectives level close to the acceptance quality level, the single sampling procedures may be more economical than double or sequential sampling.
Dodge and Romig have also come up with sampling tables for Double sampling. These tables are of two categories: (1) providing protection in terms of AOQL, and (2) LYPD with certain consumer’s risk.
Dodge –Romig Tables for Double sampling:
In order to use the former (AOQL) table, one needs to know (a) the lot size supplied by the vendor, (b) the process average percentage of the defectives in the lots supplied by the vendor and (c) the AOQL protection desired by the company for that material. Once these are known, the values of the recommended first and second sample size and the two different cut-off points as well as the corresponding LTPD protection under the plan can all be read off from the tables. For instance, if the maximum risk in terms of the AOQL is taken as 2%, the lot size is 1,500 items, and the process average of defectives is 1.5% then the table recommends the following sampling plan:
n1= 80, c1=1, n2 = 160, (n1 + n2) = 240 and c2=8
The value of LTPD corresponding to 10% consumer’s risk can also be read off as 5.8.
The latter category of Dodge-Romig table can be used if one knows (1) LTPD with corresponding desired consumer’s risk. (2) the process average per cent defectives, and (3) the lot size as supplied by the vendor. An example of such a Dodge-Romig table for Double Sampling is also furnished in the Appendix. Let us have LTPD = 5% and corresponding consumer’s risk = 10%. Let us lot size and process average be 1,500 and 1.5% respectively. The table gives the following sampling plan:
n1=90, c1=1, n2=185, n1+n2= 275 and c2= 8
The corresponding AOQL protection available under the plan is 1.7%. The reader may check the similarity of values in the sampling plans for AOQL protection and LTPD protection as found in these paragraphs.
In addition to the Dodge-Romig tables other useful tables for acceptance sampling, such as MII –STD -105 and Sequential Sampling Tables are available. These tables have simplified the working of acceptance sapling procedures.
So far, we have implicitly assumed that, other than a few exceptional cases, acceptance sampling procedures are a must. It is advisable to make some comparisons of costs of inspection and costs of reworking when the defective parts are incorporated into the finished or semi-finished product These comparisons can be utilized to decide whether we should go in for a 100% inspection, or a sampling inspection.
The earlier discussion focused on the use of statistical methods to control quality. Although statistical quality control is an important aspect of quality management, it is only a part of the comprehensive quality management function. It is one of the tools/ techniques useful for quality management. Comprehensive quality management has to deal with organization, costs, motivation, communication, planning and monitoring aspects of the management function as well. Unless these various aspects of the quality management effort are properly attended to, the tools of statistical methods will have a limited effect on the functioning of the quality management process.