# A continuous manufacturing processes to manage the outgoing quality

- Abstract
- Procedure of a single level continuous sampling plan
- Single sampling plan by attributes
- A two Markhov chain model in CSP and assumptions
- The AOQ formula for CSP
- The EOQ expressions
- Suggestions to quality assurance practitioner
- References

When the production is continuous and the process is not under statistical control (i.e., p is the probability of a defective unit is constant) and at the same time it does not follow a scheme of total control, it is remarked that a dependent process will be more realistic than the existing Bernoulli model. Further, it is remarked that when one carries out the data analysis to assess the validity of a two-state Markov chain (MC) model, the estimate of the serial correlation coefficient would be automatically available. If the parameters are unknown and no reliable estimates are available, the two step empirical Bayes' rule may still likely to achieve considerable gain over the empirical independence rule if _ the dependence parameter of the MC is near 0 or 2 and is not likely to lose much if _ is near 1 (the Bernoulli Process). A sampling inspection plan for continuous production exhibiting the Markovian character has been proposed in this paper. The procedure of Continuous Sampling Plan (CSP) is given in Section - 1. A two-state MC Model in CSP with two assumptions has been proposed in Section - 2. The expected outgoing Quality (EOQ) formula for any CSP is given in Section - 3. Numerical comparisons are made and remarks are made. In Section -6 some suggestions have been made to the quality assurance practitioner to manage the dependent process to enhance the performance of the production process.

[...] However, the distribution of U is common to all the Dodge - Type plans SINGLE SAMPLING PLAN (SSP) BY ATTRIBUTES: It would only be practicable, if a lot of large number of manufactured items could be accepted (or rejected) on the basis of the testing of a reasonably small number of samples randomly drawn from the population of every such lot of large number of manufactured items. That is, with every lot of, say N number of items, a random sample of size n(n < is drawn and a decision in respect of the acceptance of the lot of size N is thereby made only on the basis of inspection of n number of item. [...]

[...] i.e., max - 1 / ? < p < min / ? , SUGGESTIONS TO THE QUALITY ASSURANCE PRACTITIONER: As mentioned in Remark - 1 it is suggested that the quality assurance practitioner should use SSP in each lot of cycle - j (finite) and decide whether to accept the jth lot (i.e., E(Vj) = Nj the size of the jth lot in cycle Since, each cycle - j = of a CSP or MLP - T - 2 or for any CSP under MMP lot Nj are received in the outgoing quality, one may use Skip lot Sampling Plan ( SkSP )to decide whether to accept the lot of size Nj in the jth cycle instead of SSP. [...]

[...] Assumption - The sequence n follows a 0-1 valued time-homogeneous MC with initial distribution given by P[X 0 = = ? ? 0 Assumption - The zeroth unit is assumed to be always a defective unit. That is, ? 0 = 1. We set ? 0 = 1 as the success run (See the Definition- 1.2 .19) in an implementation is going to follow a defective unit in the immediately preceding cycle. This assumption, viz., ? 0 = P[X 0 = = 1 together with the strong Markov property (See Breiman (1968)) of the MC n essentially implies that completion of an implementation of a plan is a recurrent event (See Feller (1975)). [...]