Abstract

One distribution that is often used in modeling of survival time is exponential. An example of its application is the problem of the length of time until all the light bulbs go out. In this example, the observed event is the time until all the light bulbs fail to ignite. Thus, the random variable states that the length of time until all the light bulbs is go out. By using an exponential distribution, one assumption that can be made is that the hazard function has a constant hazard rate. This assumption was felt unsatisfactory, so a new model was made. The model is called the piecewise exponential model. The purpose of this study is to build a cumulative hazard model in the form of a non-composite function (one step/piece) with the assumption that the damage rate is constant at each time interval. Thus, the hazard function is a function of time. The model of the hazard function can be in the form of piecewise-exponential constant-linear and constant-quadratic model in the form of a composite function (several steps). The cumulative hazard function in the form of a non-composite (one step) function is obtained from the composite hazard function with the help of an indicator function. The cumulative hazard function in the form of a step function can be seen as a regression function. If data on the length of light bulbs lifespan are available, then the parameters in the cumulative hazard function can be estimated using the least squares method. Chi-square test was used to test the null hypothesis which states that the long life span of a light bulb follows a constant-linear and constant-quadratic piecewise model. The use of Chi-square test requires a frequency distribution table. The table is made with the Sturgess rule to determine the number of interval classes. Based on secondary data, two cumulative hazard models in the form of non-composite functions are produced as a combination of constant-linear and quadratic functions.