OPTIMAL DESIGNING OF QUICK SWITCHING SAMPLING SYSTEM UNDER
WEIBULL DISTRIBUTION BASED ON TRUNCATED LIFE TEST
S. BALAMURALI* 1 , P. JEYADURGA 2 AND M. USHA 3
Department of Mathematics
Kalasalingam University
Krishnan Koil 626 126, TN, India.
* 1 sbmurali@rediffmail.com
, 2 jeyadurga2810@yahoo.com
, 3 umahalingam@rediffmail.com
ABSTRACT
Statistical quality control (SQC) is classified as process control, product control and life testing. Acceptance sampling falls under product control. Acceptance sampling is an inspection process that involves taking random samples from lots of products and examining (inspecting) them for specified requirements. Acceptance sampling makes acceptance or non-acceptance decision of the submitted lot based on the results of random samples. Typically, acceptance sampling is applied for providing quality assurance of incoming products. Acceptance sampling plan prescribes the acceptance criteria for lot disposition.
Attribute acceptance sampling is a well-known concept in acceptance sampling.
Attributes acceptance sampling can be used to just classify the products whether good or bad for some specific quality characteristic. The main advantage of attributes acceptance sampling is that it may be applied for testing more than one characteristic at a time, but in case of variables sampling only one characteristic can be considered at a time.
Importance of attributes sampling plans has been discussed by some authors and also such sampling plans have been developed for various situations. In the literature, single acceptance sampling plan is referred to as basic for all the plans. The extensions of this plan are double sampling plan and multiple sampling plan and those plans are implemented under lot-bylot inspection only. Later, new type of sampling plans were introduced for inspecting the lots when the lots are coming serially in the order of production and often such type of sampling plans are called as special purpose sampling plans. Some of the special purpose plans are chain sampling plan, multiple dependent (deferred) state sampling plan, skip-lot plan etc. Dodge
(1955) introduced the concept of chain sampling inspection for attribute characteristics.
Balamurali and Palaniswamy (2012) have determined the minimum variance outgoing quality limit (VOQL) chain sampling plan for compliance testing. Calvin (1977) developed attributes tightened-normal-tightened (TNT) sampling scheme. Soundararajan and Vijayaraghavan (1990) investigated the TNT scheme of type TNT-( n
1
, n
2
; c ). Most of those attributes sampling plans just inspect the products whether defective or non-defective according to specified requirements.
But we attempt to classify the product whether defective or non-defective according to life time.

When life time is considered as a quality characteristic of the product, Weibull distribution is preferred as an appropriate life time model for determining the life time of a product. This distribution is widely used in acceptance sampling due to its character of flexibleness. In acceptance sampling, some studies are available related with Weibull distribution. Jun et al. (2006) proposed variables single and double sampling plans under Weibull distribution based on sudden death testing. In particular, Weibull distribution is used in acceptance sampling under the basis of truncated life test. Aslam et al. (2012) have designed the repetitive acceptance sampling plans for assuring percentile life under Weibull distribution.
Any sampling inspection consists of more than one sampling plan for making decision on the disposition of the lot is known as sampling system. If only normal and tightened inspection involved in any sampling system, such system is referred to as two-plan system. Dodge (1967) introduced one of the two-plan systems for attributes application which is called as quick switching system (QSS). Romboski (1969) has investigated the quick switching system of type
QSS-1 by using single sampling plan as the reference plan. Balamurali and Usha (2013) have proposed the QSS under the Weibull life time model for variables inspection.
This paper proposes the designing of quick switching sampling system when truncated life test is performed to ensure the median life of the product under the Weibull life time distribution. The median life is considered as quality of the product and also the ratio of original median life with specified one is taken as measurement of the quality. Tables are constructed for selecting the optimal parameters of the quick switching system are determined when both of the producer’s and consumer’s risks are satisfied simultaneously at various combinations of acceptable quality level and limiting quality level with different shape parameters. The proposed plan is compared with existing plan.
Keywords: Statistical quality control, Acceptance sampling plan, Quick switching sampling
system, Weibull distribution, Truncated life test, Median life ratio, Producer’s risk,
Consumer’s risk.