In this paper we consider an analysis of the categorical data obtained by the accelerating life testing, wherein the stress on an unfailed item is allowed to change at a preassigned time. The damage accumulation law plays a key role in this analysis and is studied from the point of statistical hypothesis testing. Assuming the time scale transformation, we propose an approximate testing method, compare our model with the linear model used in the two-period change-over design, and study the application to the inference of the parameter of the exponential distribution.

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In this paper , the design of a (x, R) simultaneous control chart is proposed. It is derived from the multiple decision theory by applying the same method as the (x, s) simultaneous control chart proposed in the previous paper¹⁵⁾ The probability of the first kind of error and the power of the test using this chart are calculated by the Monte-Carlo method and it is ascertained that the probability of the first kind of error and the power of this (x, R) chart are very similar to those of the (x, s) chart as shown in the previous paper¹⁵⁾ Then it is discussed that this (x, R) chart is practically useful together with x-R charts. Using this (x, R) chart together with x-R charts in practical process control, we can detect the change in the state of process with higher probability than using x-R charts only. This (x, R) chart provides a useful information about the change in the state of a process when the out-of-control point appears in the chart.

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The hazard plotting method using a hazard paper has been widely used to analyze randomly censored lifetime data because of its simplicity and a graphical effectiveness. However, until now small sample properties of the method have not been investigated well. At first, this article explicitly examines biases of the estimators for a cumulative hazard function in case of there being a proportional hazard relationship between failure time and censoring time. Secondly, based on the fact that the method takes account of only the rank of censored time but not fully its length, a modified hazard plotting method will be proposed and its properties are compared with the ordinary one assuming Weibull distributions by Monte Carlo simulation. The results show that a modified method has excellent properties when the shape parameter of a failure time distribution is greater than that of a censoring time distribution.

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