Developing a sampling plan by variables inspection for controlling lot fraction of defectives

Construction of closed interval for process capability indicesCpu,Cpl, andSpkbased on Boole’s inequality and de Morgan’s laws

“…Note that, when T = M (symmetric case), S pk attains its maximum at μ = T. For fixed σ , the value of S pk decreases as μ shifts away from T. Clearly, S pk is more suitable to evaluating quality characteristics with symmetrical bilateral specifications. [16,[21][22][23] For a normally distributed process, the quality yield, yield%, can be calculated as yield% = [(USL − μ)/σ ] − [(μ − LSL)/σ ]. According to Equations (3) and (4), the quality yield of the smaller-the-best and larger-the-best C pu and C pl can be expressed as yield% = (3C pu ) and yield% = (3C pl ), respectively.…”

A Novel Lot Sentencing Method by Variables Inspection Considering Multiple Dependent State

“…Recently, several new types of variables acceptance sampling plans have been developed by considering process capability indices. Examples include Pearn and Wu, Negrin et al , Wu, Wu et al , Aslam et al , Pearn et al , Liu et al , Wu and Liu …”

“…Examples include Pearn and Wu, 13 Negrin et al, 14 Wu, 15 Wu et al, 16 Aslam et al, 17 Pearn et al, 18 Liu et al, 19 Wu and Liu. 20 The concept of multiple dependent (or deferred) state (MDS) sampling was first introduced by Wortham and Baker. 21 Similarly, the MDS-1 p1an was introduced by Vaerst 22 as an extension of the chain sampling plan of type ChSP-l, which was proposed by Dodge.…”

Sampling Schemes by Variables Inspection for the First-Order Autoregressive Model between Linear Profiles

“…That is, in order to reflect the actual lot quality, the sample size must be very large. In such circumstances, various authors [7][8][9][10] found variables 2 Mathematical Problems in Engineering sampling plans based on capability indices to be the most efficient methods of lot sentencing. In addition, variables sampling plans, based on the exponentially weighted moving average (EWMA) statistic, resubmitted sampling, repetitive group sampling (RGS), and multiple dependent state (MDS) sampling are proved to guarantee a reduction in sample size [11].…”

“…It must be remembered, however, that the superiority of the variables plan rests on the assumption of the underlying distribution of the measurements [6]. Whether the performance measure is single quality characteristic [7][8][9][10]15] or profile data [16,21] sampling schemes in the literature share two basic assumptions: the quality characteristic follows a normal distribution and data is independent. However, in some manufacturing processes, data is correlated or self-dependent.…”