|Construction of single sampling plan indexed through limiting quality level. |
Ponnuraja, C.; Santhi, S.
IOSR Journal of Mathematics; 2014; 10; 42-47.
Abstract: Acceptance sampling procedures are the practical tools for quality assurance applications involving product control. Acceptance sampling systems are advocated when small sample size are necessary or desirable towards costlier testing for product quality.
Dodge – Romig plans can be single or double plans. There are two sets of plans. One is based on satisfying a given limiting quality level (LQL) based on a consumers risk ß, the target value of which is 0.10 (Dodge and Romig, 1959). The other based on meeting a certain value of the average outgoing limit. For both sets of plans, the objective is to minimize the average total inspection.
If the parameters of the plan under consideration (eg., lot size and process average) are within certain range, the Dodge – Romig tables allow us to determine feasible plans very readily. Determining these plans from basic principles would take much more time. The trade-off is that the Dodge-Romig tables provide a sampling plan for a range at lot sizes and process averages. In this juncture there is a considerable procedure to deal with this problem using Poisson distribution which is often used as a standard probability model for dealing with this kind of single sampling plan. However many data sets in general are not well fitted by a Poisson model, because they consists of more zero counts than are compatible with the Poisson model. Zero inflated models are used to model count data for which proportion of zero counts is greater than expected. For these situations, a zero inflated Poisson (ZIP) model is generally proposed.
It is very logical and encouraging that zero inflated Poisson (ZIP) Distribution provided better fit as compared to Poisson distribution in the data sets because of more number of zeros.
In this paper the procedure for the construction of Single Sampling Plan indexed through Limiting quality Level (LQL) using Zero Inflated Poisson (ZIP) distribution as the base line distribution is presented and a table is also presented using Excel packages for the easy selection of the plans.
Keywords: Limiting quality level; Zero inflated poisson (ZIP) distribution; Single sampling plan; Operating characteristic curve
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