A note on failure rate of the mixture of an exponential distribution and distribution with increasing quadratic failure rate function

• Autorzy: Knopik L.
• Języki publikacji: EN

Abstrakty

EN

We show that a unimodal failure rate function can be obtained as a mixture of two increasing failure rate functions. Specifically, we study the failure rate of the mixture of an exponential distribution and an IFR (increasing failure rate) distribution with increasing quadratic failure rate function. At the end of the paper we show a numerical example of the modified unimodal failure rate function.

Słowa kluczowe

EN

mixture of distributions; quadratic failure rate function; failure rate function

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2017
• Tom: Vol. 46, no. 3
• Strony: 291--297
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Knopik L.

• University of Science and Technology, Faculty of Management, Fordonska 430, 85-890 Bydgoszcz, Poland

Bibliografia

• [1] BARLOW, R. E., MARSHALL, A. W. and PROCHAN, F. (1963) Properties of probability distributions with monotonic hazard rate. Annals of Mathematical Statistics 34(3), 348-350.
• [2] BLOCK, H. W., SAVITS, T. H. and WONMAGEGNEHU, E. T. (2003) Mixtures of distributions with increasing linear failure rates. Journal of Applied Probability, 40 (2003), 485-504.
• [3] CHANG, D. S. (2000) Optimal burn-in decision for product with an unimodal failure rate function. European of Journal of Operational Research, 126, 534-540.
• [4] GUPTA, R. C. and WARREN, R. (2001) Determination of change points of non-monotonic failure rates. Communications of Statistics – Theory and Methods 30, 1903-1920.
• [5] GURLAND, J. and SETHURAMAN, J. (1995) How pooling failure data may reverse increasing failure rates. Journal of the American Statistical Association, 90, 1416-1423.
• [6] JIANG,R. and XIAO, X.(2003) Aging property of unimodal failure rate models. Reliability Engineering and System Safety, 79, 113-116.
• [7] JIANG, R. and MURTHY, D. M. P. (1998) Mixture of Weibull distributions – parametric characterization of failure rate function. Applied Stochastic Models and Data Analysis 14(1), 47-65.
• [8] KLUTKE, G. A., KIESSLER, P. C. and WORTMAN, M. A. (2003) A critical look at bathtub curve. IEEE Transactions of Reliability, 52(1), 125-129.
• [9] LAI, Ch. D. and XIE, M. (2005) Stochastic Ageing and Dependence for Reliability. Springer, Berlin.
• [10] MUDHOLKAR, G. S., SIRVASTAVA D. K. and TREIMER, M. (1995) The exponential Weibull family. A reanalysis of the bus-motor failure data. Technometrics 37(4), 436-445.
• [11] WONDMAGEGNEHU, E. T. (2004) On the behavior and shape of mixture failure rates from family of IFR Weibull distributions. Naval Research Logistic 51, 491-500.
• [12] WONDMAGEGNEHU, E. T., NAVARRO J. and HERNANDEZ P. J. (2005) Bathtub shaped failures rates from mixtures: A practical point of view. IEEE Transactions on Reliability 54(2), 270-275.
• [13] XIE, M., TANG, Y. and GOH, T. N. (2002) A modified Weibull extension with bathtub- shaped failure rate function. Reliability Engineering and System Safety 76, 279-285.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).