JPH06119370A - Weibull analyzing method marked survival rate of product taken into consideration - Google Patents

Abstract

PURPOSE:To provide a Weibull analyzing method capable of executing automatically prediction in which the survival rate of a product is taken into consideration and the number of the cases of the occurrence of a claim is universal when only observed data is inputted. CONSTITUTION:In order to execute the long-term prediction of the number of the cases of the occurrence of the claim by Weibull distribution from the remaining number of products data NOi and the number of the abandoned products NGi of every arbitrary using period ti and number of cases of claim data ni due to a fault etc., a significant level period Ki is calculated by standardizing the using period ti, and probability to satisfy the significant level period Ki in the whole using period (t) is calculated as the survival rate Pi by probability distribution, and corrected number of cases of claim data ni not taking abandonment into consideration is calculated from the number of cases of claim data ni, and a cumulative failure rate F(i) in each using period ti is calculated from this data, and an approximate value F(i)' is calculated from the value of this failure rate in each time ti by a prescribed approximating method, and the number of cases of claim ni' in the using period DELTAti is calculated, and the numb of cases of claim ni''' in the using period DELTAti to take the survival rate into consideration is calculated by using the survival rate Pi.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a Weibull analysis method for calculating a future cumulative failure rate which is a measure for judging the reliability of products used for a long period of time.

[0002]

2. Description of the Related Art In the field of quality control, for example, a statistical analysis method based on failure life has been often used as an index of product reliability.

Generally, not only reliability but also products manufactured in the same lot having the same properties are observed for their characteristics and lifespans, and probabilistic information is obtained from their distributions or decisions are made. ing. In this case, assuming a population with the same quality, even if there are only a few products,
It is necessary to extract a limited sample from the sample, observe reliability characteristic values such as reliability and failure life and quality characteristics of this sample, and estimate the characteristics of the original population. Therefore, naturally, when the number of samples is small, the characteristic value obtained from the sample stochastically differs from the characteristic value of the population.

In particular, when trying to estimate the reliability of the product from the number of complaints due to product failure, the number of complaints usually follows the Weibull distribution, but the number of samples is much larger than the number of products (population). This is a small value, and the number of future complaints has been predicted using the approximation of probabilistic data by visual observation using Weibull probability paper. For the estimation method using Weibull analysis paper, please refer to Nikkan Giren Reliability Engineering Series Vol. 4 "How to Use Probability Paper in Reliability" published by the second printing on March 4, 1988 Hiroshi Shiomi, Mihashi Takeshi, Motoo Saito, and Akihiko Masuda co-authored by Nikka Giren Publishing Co., Ltd.

[0005]

The approximation of the probabilistic data by visual observation using the Weibull probability paper as described above is as follows.
There is a drawback in that there is no reproducibility because there are individual differences in the method of plotting data and how to draw a straight line for approximation depending on the person who visually observes it.

Further, since each product has a life span and some are discarded before a complaint occurs, the number of population changes when estimating the number of complaints over a long period of time, so that an accurate complaint is generated. There was a problem that the number of cases could not be estimated.

The present invention has been made in view of the problems of the related art. When the observation data is input, the number of complaints can be automatically predicted in consideration of the product residual rate, and the prediction can be made. The purpose is to provide a universal Weibull analysis method.

[0008]

The present invention SUMMARY OF] The remaining number data N _Oi for each arbitrary period of use t _i, from waste number N _Gi and a failure such as a product of the number marked with the claim by the number of complaints data n _i when performing long-term prediction of the claim incidence according to the product with the Weibull distribution, the use period t _i

[0009]

[Equation 6]

The significance level period K _i is calculated by standardization according to the above, and the probability of satisfying the significance level period K _i in all usage periods t is calculated as the residual rate P _i by a predetermined probability distribution, and the claim count data n _i is calculated. From

[0011]

[Equation 7]

Further, the amended complaint number data n _i ′ which does not consider disposal is calculated, and the amended complaint number data n
using _i '

[0013]

[Equation 8]

The cumulative failure rate F (i) in each usage period t _i is calculated by the following, and each time t of the cumulative failure rate F (i) is calculated.
_The approximate value F (i) ′ is calculated by linearly approximating the value in _i by a predetermined approximation method, and the number of complaints n _i ″ in a predetermined use period Δt is calculated.

[0015]

[Equation 9]

The number of complaints n calculated in accordance with the above, and using the remaining rate P _i in consideration of the remaining rate in the usage period Δt _i
i '''

[0017]

[Equation 10]

It is calculated by

[0019]

According to the above configuration, even if the product is discarded during the prediction period, the number of complaints can be predicted for a long time taking this into consideration, and the value is reproducible and highly reliable. Will be things.

[0020]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the Weibull analysis method of the present invention will be described in detail below with reference to the drawings.

FIGS. 1 and 2 show an algorithm for long-term prediction of the number of complaints.

First, the production number N observed in step S1
_P (N_P = N_Oi+ N_Gi, But N_OiIs the period of use t_i To
Number of remaining cars, N_GiIs also the number of discarded units)
Interval t _i , Number of complaints n_i , Average usage period x, standard
Enter the deviation s and the period Δt you want to predict.
It Here, the average usage period x and standard deviation s depend on the product.
Pre-calculated data and interpolation of this data
Fixed value in the algorithm using the data obtained by
(For example, x = 6 [year], s = 2.5 [year]).

The observed production number N _P is 100
[Table], and the extracted data of the usage period t _i and the number of complaint occurrences n _i are as shown in Table 1 below.

[0024]

[Table 1]

This input is the number of i (for example, in Table 1, i =
Only 5) is performed, and when input is completed, the process proceeds to step S2.

Step S2 is a part for calculating the significance level K _i by normalizing the use period t _i for fitting to the Weibull distribution to be used later. This is calculated using the following equation 11, and when the calculation is completed for one i, step S3
Go to.

[0027]

[Equation 11]

Step S3 is a part for calculating the probability P _i of the product remaining at the significance level K _i obtained in step S2. The calculation method at this time may be performed using various probability distributions, but the probability P _i here follows a normal distribution, and the residual rate P _i is calculated for each i. When the calculation of one P _i is completed, the process proceeds to step S4.

In step S4, the residual rate P _i is used to correct the number of complaints in consideration of the residual rate n _i '
Is calculated by the following equation 12.

[0030]

[Equation 12]

When the number of complaint occurrences n _i 'corrected for all _i is calculated in steps S2 to S4 in this way, the process proceeds to step S5.

In step S5, the cumulative failure rate F in the usage period t _i is calculated from the corrected number of complaint occurrences n _i ′.
This is a part for calculating (i) by the following equation 13.

[0033]

[Equation 13]

The cumulative failure rate F (i) obtained here is ideally a value according to the Weibull distribution. Therefore, the process proceeds to step S6, and the value deviating from the Weibull distribution is approximated to a value that follows the Weibull distribution. As a calculation method for this purpose, for example, an approximation method based on the method of least squares may be used. The operation of step S6 corresponds to a conventional operation of plotting data on a Weibull probability sheet and visually drawing a straight line.

When the approximate cumulative failure rate F (i) 'according to the Weibull distribution is calculated in this way, the process proceeds to step S7 and the number of complaint occurrences n _i "at the prediction time Δt (= t _i -t _i-1 )". Is the approximate cumulative failure rate F before and after the prediction time
(I) 'and F (i-1)' are used to calculate by Equation 14.

[0036]

[Equation 14]

The number of complaint occurrences n _i ″ calculated here
Is the number of complaints when all the manufactured products remain, the process proceeds to the next step S8, and the number of complaints n _i 'considering the remaining rate by the following equation 15 using the remaining rate P _i. '' Is calculated.

[0038]

[Equation 15]

This is the target expected number of complaints. If necessary, the predicted number of complaints n _i ′ ″ is plotted on the Weibull analysis paper on the display prepared in advance or output on the table.

Table 2 shows the values when the predicted number of complaints is calculated without considering the residual rate, and Table 3 shows the values when the predicted number of complaints is calculated considering the residual rate. Further, FIG. 3 shows a chart when the values are plotted on the Weibull analysis paper in consideration of the residual rate, and FIG. 4 shows a chart when the residual rate is not considered using the same observation data.

[0041]

[Table 2]

[0042]

[Table 3]

As is clear from the comparison between Tables 2 and 3, if the residual rate is not taken into consideration, the number of complaints will increase as the prediction period goes far into the future, while the residual rate is taken into consideration. And t _i are saturated at 11 or more,
After that, complaints will not occur, and for regular products, the products will not remain in the market after a certain period of time,
It makes more sense to consider the survival rate.

Even if the same observation data is used, as is apparent from comparison between FIG. 3 and FIG. 4, it is noticed that the increase rate (gradient in the figure) of the number of predicted complaints obtained greatly differs between the two. Ah In this way, the conventional method that does not consider the residual rate would have calculated the number of predicted complaints with extremely low reliability, and the fact that this example makes highly accurate predictions greatly contributes to product manufacturing planning. Can be expected.

[0045]

As described above, according to the present invention, it is possible to automatically calculate the predicted number of complaints by the Weibull analysis in consideration of the product residual rate in the market by inputting the observation data as in the conventional case. The value is uniquely determined if the conditions are the same, and it will be highly reliable in accordance with the current situation.
It is expected that the data will be useful data such as product manufacturing plans and parts storage management plans.

[Brief description of drawings]

FIG. 1 is a first half of a flowchart showing an algorithm for calculating a predicted number of complaints generated according to the present invention.

FIG. 2 is the latter half of the flowchart following the algorithm of FIG.

FIG. 3 is a chart showing an output situation of a predicted number of complaints generated on Weibull probability paper when the residual rate is not taken into consideration.

FIG. 4 is a chart showing an output situation of predicted number of complaint occurrences on Weibull probability paper according to the present invention in consideration of remaining rate.

Claims (1)

[Claims] 1. The number of remaining data N _{Oi for} each arbitrary use period t _i , the number N _{Gi of} discarded products, and the number n _{i of} complaint products, which is the number of products with complaints due to breakdown, etc., are assigned to the product using a Weibull distribution. When making a long-term prediction of the number of such complaints, the use period t _i is calculated as follows: And normalized to calculate the significance level period K _i by the probability of meeting the significance level period K _i in the whole use period t is calculated as a residual ratio P _i by a predetermined probability distribution, Equation from the number of complaints data n _i 2] The corrected complaint number data n _i ′ that does not consider discarding is calculated, and the corrected complaint number data n _i ′ is used to calculate Then, the cumulative failure rate F (i) in each usage period t _i is calculated, and the approximate value F (i) ′ is linearly approximated from the value of the cumulative failure rate F (i) at each time t _i by a predetermined approximation method. Is calculated, and the number of complaints n _i ”in a predetermined use period Δt is calculated as follows: And the number of complaints n _i ′ ″ in consideration of the remaining rate in the usage period Δt _i is calculated by using the above remaining rate P _i. A Weibull analysis method that considers the market survival rate of the product, which is calculated by