Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A HYPOTHESIS TESTING PROCEDURE OF ASSESSMENT FOR THE LIFETIME PERFORMANCE INDEX UNDER A GENERAL CLASS OF INVERSE EXPONENTIATED DISTRIBUTIONS WITH PROGRESSIVE TYPE I INTERVAL CENSORING

  • KAYAL, TANMAY (Department of Mathematics, Indian Institute of Technology Patna) ;
  • TRIPATHI, YOGESH MANI (Department of Mathematics, Indian Institute of Technology Patna) ;
  • WU, SHU-FEI (Department of Statistics, Tamkang University)
  • Received : 2017.11.09
  • Accepted : 2018.08.23
  • Published : 2019.01.30
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Abstract

One of the main objective of manufacturing industries is to assess the capability performance of different processes. In this paper, we use the lifetime performance index $C_L$ as a criterion to measure larger-the-better type quality characteristic for evaluating the product performance. The lifetimes of products are assumed to follow a general class of inverted exponentiated distributions. We use maximum likelihood estimator to estimate the lifetime performance index under the assumption that data are progressive type I interval censored. We also obtain asymptotic distribution of this estimator. Based on this estimator, a new hypothesis testing procedure is developed with respect to a given lower specification limit. Finally, two numerical examples are discussed in support of the proposed testing procedure.

Keywords

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FIGURE 1. Power function test at γ = 0:1 under m = 7, p = 0:05 for n = 70, 85, 100.

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FIGURE 2. Power function test at γ = 0:1 under n = 70, p = 0:05 for m = 7, 8, 9, 10.

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FIGURE 4. Power function test at γ = 0:1 under n = 70, m = 7 for p = 0:05, 0:075, 0:1.

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FIGURE 5. Power function test under n = 70, m = 7, p = 0:05 for γ = 0:01, 0:05, 0:1.

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FIGURE 3. Power function test at γ = 0:1 under n = 70, m = 7 for p = 0:05, 0:075, 0:1.

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FIGURE 6. β vs p-value for the real data set.

TABLE 1. The lifetime performance index CL and its corre-sponding conforming rates Pr

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TABLE 2. The values of h(d1) at γ = 0:01 for d1 = 0:7, 0:75(0:025)0:95, m = 7(1)10, n = 70(15)100 and p = 0:05(0:025)0:1 under L = 0:05, T = 0:1 and d0 = 0:825

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TABLE 3. The values of h(d1) at γ = 0:05 for d1 = 0:7, 0:75(0:025)0:95, m = 7(1)10, n = 70(15)100 and p = 0:05(0:025)0:1 under L = 0:05, T = 0:1 and d0 = 0:825

E1MCA9_2019_v37n1_2_105_t0003.png 이미지

TABLE 4. The values of h(d1) at γ = 0:1 for d1 = 0:7, 0:75(0:025)0:95, m = 7(1)10, n = 70(15)100 and p = 0:05(0:025)0:1 under L = 0:05, T = 0:1 and d0 = 0:825

E1MCA9_2019_v37n1_2_105_t0004.png 이미지

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