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 / δ < p < min / δ , 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. [...]
[...] Use of simple random sampling is mathematically intractable under Markovian Manufacturing Processes for any CSP REMARK Observe that, an explicit relationship between g and EOQL can be obtained for such a relationship cannot obtained even if we assume that the dependence parameter δ or the serial correlation coefficient of the MC is known apriori. Table - 1 compares the OC values in CSP - 1 for Bernoulli Process and CSPp - 1 for MMP. For the fixed EOQ level (i.e., one out of every 100 units produced will be defective at the maximum) and g = 20 when the serial correlation coefficient is known apriori. [...]
[...] That is to consider a model “intermediate” between independent and identically distributed and unrestricted model in which quality fluctuates according to a two-state time homogeneous MC model. Preston (1971) while discussing a two - state MC model of production process pointed out that long strings of non-defective and defective units are more likely if the serial correlation coefficient of the MC is positive and alternative sequences of non-defective units are more likely if the serial correlation coefficient is negative. It may be remarked here that often in the production process, the quality of items is serially dependent and one may propose Wald's sequential inspection plan for Markov - dependent production processes. [...]
[...] First of all, it must be noted that a CSP is a MC and in general, a continuous sampling scheme can be thought of as a Markov Process with various inspection levels being the states of the process. Also, it may be noted that in CSP - 1 transition takes place between screening state to fractional sampling state and vice versa by forming a Birth and Death representation of a CSP. We assume that the quality of an item is an attribute which can be classified as defective or non-defective with the Markov dependence structure as follows. [...]
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