ASSIGNMENT III Question 1 Consider the ChSP-1 plan and obtain the relative slope at the unity Indifference Quality Level (IQL, np0) using the definition h dlogPa dlogp 2dPa 0 dnp p p0 p np0       . Obtain the parameters of the 'matching' single sampling plans using the empirical relationship 2 h 20  = n sp0 + 0.06 = Ac + 0.73 where n s is the sample size of the matching single sampling plan with fractional acceptance number. Provide a comparison of single and chain sampling plans using the unity sample sizes np0 and n sp0. Question 2 Zero acceptance number single sampling plans require the minimum sample size for a given one point on the operating characteristic curve when compared to single (Ac  1), double and multiple sampling plans. This question requires you to employ it as a 'reference sampling plan' in the Skip-lot sampling plan SkSP-2 of Perry (1973a; reproduced in the Book of Readings). Explore the advantages of using zero acceptance number plan as a reference plan in a SkSP-2 system. Draw few OC curves of the SkSP-2 scheme assuming any reasonable plan parametric values. That is, consider two or three combinations of i, f and n and draw the OC curves of the zero acceptance number and SkSP-2 plans. What advantages are seen in employing the zero acceptance number plan as a reference sampling plan? Based on the observations made on the behaviour of the SkSP-2 OC function, develop a procedure for designing a SkSP-2 plan with a zero acceptance number reference plan for given values of p1, p2,  and . In your answer, you may provide a Table of unity values or simply indicate how a search procedure based on the properties of the OC function can be developed. What are the limitations of a SkSP-2 plan having a zero acceptance number reference plan? Discuss.Question 3 CSP-1 continuous sampling plan requires 100% inspection to be performed when required and hence the AOQL is the suitable index for designing. Explain how you may proceed to find the AOQL of a given CSP-1 plan. Your answer may be deriving an expression for AOQL in terms the parameters i and f or writing a suitable computer program to compute the AOQL for given i and f. You should include a numerical example to illustrate the computation of AOQL. Question 4 Given AQL = 0.5% and LQL = 2%. Assume that these quality levels are not associated with any given values of  and  but it is desired that the risks are kept as small as possible. For administrative reasons, the sample size is fixed as 200. Derive a formula for the acceptance number of the single sampling plan which minimises the sum of producer's and consumer's risks namely 1-P a(p1)+ Pa(p2) assuming binomial distribution for OC curve. Verify your result numerically. What are the advantages with this designing approach? + + + + + +