JPS63273945A - Check system for adaptation degree of software reliability growth curve - Google Patents
Check system for adaptation degree of software reliability growth curveInfo
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- JPS63273945A JPS63273945A JP62109478A JP10947887A JPS63273945A JP S63273945 A JPS63273945 A JP S63273945A JP 62109478 A JP62109478 A JP 62109478A JP 10947887 A JP10947887 A JP 10947887A JP S63273945 A JPS63273945 A JP S63273945A
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- 239000006185 dispersion Substances 0.000 abstract 1
- 238000000034 method Methods 0.000 description 10
- 230000003111 delayed effect Effects 0.000 description 4
- 238000001514 detection method Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 238000006243 chemical reaction Methods 0.000 description 2
- 230000001186 cumulative effect Effects 0.000 description 2
- 238000005315 distribution function Methods 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
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- 238000012545 processing Methods 0.000 description 2
- 238000003908 quality control method Methods 0.000 description 2
- 230000007704 transition Effects 0.000 description 2
- 238000001134 F-test Methods 0.000 description 1
- 238000001276 Kolmogorov–Smirnov test Methods 0.000 description 1
- 238000007476 Maximum Likelihood Methods 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 238000000876 binomial test Methods 0.000 description 1
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- 238000007796 conventional method Methods 0.000 description 1
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Abstract
Description
【発明の詳細な説明】
笠生分互
本発明は、ソフトウェア信頼度成長曲線の適合度検定方
式に関する。DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a goodness-of-fit test method for software reliability growth curves.
皿米致皇
ソフトウェア信頼度成長曲線の適合度検定に関し、大場
充、第６回ソフトウェア生産における品質管理シンポジ
ウム発表報文集１日本科学技術連盟、 ｐｐ１５？−１
６２（１９８６）には１分散分析に基づく推定誤差の偏
りに関するＦ検定、相関係数による推定値と観測値の合
致度の評価、および信頼度成長曲線の形状の妥当性を評
価するための連の総数にもとづく２項検定の３つの方法
を用いる適合度検定が提案されている。しかし、上記検
定方式は観測データの推定した成長曲線の上側から下側
への遷、移線率を１・／２と仮定しており、バグ・デー
タの順位相関を全く無視している。Regarding the goodness-of-fit test of software reliability growth curve, Mitsuru Ohba, 6th Quality Control Symposium in Software Production Collection of Papers 1, Japan Federation of Science and Technology, pp15? -1
62 (1986) includes the F-test for estimation error bias based on univariance analysis, the evaluation of the degree of agreement between estimated values and observed values using correlation coefficients, and the linkage for evaluating the validity of the shape of the reliability growth curve. A goodness-of-fit test is proposed using three methods: a binomial test based on the total number of . However, the above test method assumes that the observed data's estimated growth curve transitions from the upper side to the lower side, with a transition rate of 1·/2, and completely ignores the rank correlation of bug data.
また、上記以外に ｘｌ検定方式、コルモゴロフΦスミ
ルノフ（にｏｌｍｏｇｏｒｏｖ−Ｓｍｉｒｎｏｖ）検定
方式等が提案されているが、前者のｘｌ検定方式は、得
られたデータにある分布をあてはめる場合、その適合の
可否を調べるノン・パラメトリックな検定法であり、デ
ータ領域を幾つかの区間に分け、各区間での観測期待値
と実際の観測値との一致性を検定するものであるが、一
般に、検出力が弱く、また推定した信頼度成長曲線のパ
ラメータの数だけ自由度が減じ、情報量損失が起きる欠
点がある。また、後者のコルモゴロフ・スミルノフ（Ｋ
ｏｌｍｏｇｏｒｏｖ−Ｓｍｉｒｎｏｖ）検定方式は、前
記ｘ２検定方式同様１分布の適合の可否を調べるノン・
パラメトリックな検定法であり、１ｇ！測された分布の
累積分布関数値と、理論分布（あてはめようとしている
分布）の累積分布関数値との差を求め、その差の絶対値
の最大を評価したものである。而して、この方式は、Ｘ
２検定よりは検出力が強いが、推定した信頼度成長曲線
のパラメータの数だけ自由度が減じ、情報量損失が起き
る欠点がある。In addition, in addition to the above, the XL test method, the Kolmogorov Φ Smirnov test method, etc. have been proposed, but the former XL test method is used to evaluate the suitability of the distribution when applying a certain distribution to the obtained data. This is a non-parametric test method that examines the data, dividing the data region into several intervals, and testing the agreement between the expected observed value and the actual observed value in each interval, but it generally has low power. Moreover, the degree of freedom is reduced by the number of parameters of the estimated confidence growth curve, resulting in a loss of information. Also, the latter Kolmogorov Smirnov (K
The olmogorov-Smirnov) test method is a non-standard method that checks whether a single distribution fits, similar to the x2 test method described above.
It is a parametric test method, and 1g! The difference between the cumulative distribution function value of the measured distribution and the cumulative distribution function value of the theoretical distribution (the distribution to be fitted) is calculated, and the maximum absolute value of the difference is evaluated. Therefore, this method is
Although the detection power is stronger than the 2-test, the disadvantage is that the degree of freedom is reduced by the number of parameters in the estimated reliability growth curve, resulting in a loss of information.
且−一煎
本発明は、上述のごとき実情に鑑みてなされたもので、
特に、ソフトウェア信頼度成長曲線に関して、バグ・デ
ータが順序統計量、かつ、打ち切りデータ（ｃａｎｓｏ
ｒｉｎｇ ｄａｔａ）であるといった信頼度データのも
つ本質的な性質を考慮した適合度検定法が提案されてい
ない点に注目し、規準化した２重指数分布の順序統計量
の各確率密度分布が正規分布に十分近似できることを示
し、この性質を用いて順位による誤差分散を考慮した各
種ソフトウェア信頼度成長曲線の適合度検定方式を提案
することを目的としてなされたものである。The present invention was made in view of the above-mentioned circumstances.
In particular, with respect to software reliability growth curves, bug data is ordered statistics and censored data (canso
Note that no goodness-of-fit testing method has been proposed that takes into account the essential properties of reliability data, such as ring data). The purpose of this study was to show that the distribution can be sufficiently approximated, and to use this property to propose a goodness-of-fit test method for various software reliability growth curves that takes into account error variance due to ranks.
諺−一一皮
本発明は、上記目的を達成するために、ソフトウェア信
頼度成長曲線を規準化２重指数分布に置換し、規準化２
重指数分布に従うｎ個中ｉ番目の確率密度分布がｎとｉ
をどのように変えても正規分布に近似できることを用い
ることにより、正規分布の適合度検定に帰着させる。順
位による誤差分散を考慮したことを特徴としたものであ
る。以下、本発明の実施例に基づいて説明する。In order to achieve the above object, the present invention replaces the software reliability growth curve with a normalized double exponential distribution.
The probability density distribution of the i-th out of n according to the multiple exponential distribution is n and i
By using the fact that it can be approximated to a normal distribution no matter how you change it, it results in a goodness-of-fit test for the normal distribution. This method is characterized by taking into account error variance due to ranking. Hereinafter, the present invention will be explained based on examples.
本発明は、ソフトウェアの信頼性を評価するために、い
くつかの信頼度成長曲線の中から最も適当なモデルを選
択し、そのモデルの妥当性を評価する方式である。従来
法ではソフトウェアのバグ出現の順位による相関関係や
、バラツキの大きさを考慮していなかったために、検定
結果に信頼がおけなかった。特に、検出力が弱いために
選択したモデルが実際の観測データに適合していないこ
とを検出することができないという欠点をもっている。The present invention is a method of selecting the most appropriate model from several reliability growth curves and evaluating the validity of the model in order to evaluate the reliability of software. Conventional methods do not take into account the correlation between the rankings of software bugs or the size of variation, making the test results unreliable. In particular, it has the disadvantage of being unable to detect that the selected model does not fit the actual observed data due to its weak detection power.
そこで、本発明は、バグ出現を順序統計量に基づき、順
位によるバラツキを考慮して、選択したモデルの妥当性
を評価することを可能にしたものである。Accordingly, the present invention makes it possible to evaluate the validity of a selected model based on the order statistics of bug occurrence and taking into account variations in ranking.
第１図は、本発明の一実施例を説明するための処理概念
図、第２図は１本発明の実施例として遅延Ｓ字型モデル
をあてはめ、線型変換した信頼度成長曲線とその回帰直
線を示す図である。Fig. 1 is a processing conceptual diagram for explaining one embodiment of the present invention, and Fig. 2 is a reliability growth curve linearly transformed by applying a delayed S-shaped model as an embodiment of the present invention and its regression line. FIG.
以下１本発明による適合度検定手順について説明する。Below, a goodness-of-fit test procedure according to the present invention will be explained.
■最適モデルのＶ
あてはまるべき信頼度成長曲線のモデルを表１に示す０
表１は、ソフトウェア信頼度成長曲線と、規準化２重指
数分布への変換式を示し、表中ｔは時刻、Ｎはソフトウ
ェアに潜在する総エラー数、Φは単位時間当たりのエラ
ー発見率、ｒはエラー発見率の増加率である０表１に示
すモデルの中からにｕｌｌｂａｃｋ−Ｌｅｉｂｌｅｒの
情報量、あるいはＡＩＣ（＾ｋａｉｋａ’ｓ Ｉｎｆｏ
ｒ＋ｗａｔｉｏｎ Ｃｒ１ｔｅｒｉｏｎ：赤池の情報量
規準）に基づいて、最適モデルを選択する。■V of the optimal model The reliability growth curve model that should be applied is shown in Table 1.
Table 1 shows the software reliability growth curve and the conversion formula to the normalized double exponential distribution, where t is time, N is the total number of errors latent in the software, Φ is the error discovery rate per unit time, r is the rate of increase in the error discovery rate. Among the models shown in Table 1, the information amount of Ullback-Leibler or AIC (^kaika's Info
The optimal model is selected based on r+wation crterion (Akaike's information criterion).
次に１選択したモデルを実際のｍ副データにあてはめて
、モデル式の母数を推定する。Next, one selected model is applied to the actual m sub-data to estimate the parameters of the model equation.
■バグ データ標準正 布データへの前記■の手順
で得た最適モデル式を、その母数推定値を用いて表１の
変換式を施すことにより。■Bug Data Standard Cloth By applying the conversion formula in Table 1 to the optimal model formula obtained in the procedure in (■) above using the estimated parameter value.
基準化２重指数分布に置換する。基準化２重指数分布に
従う順序統計量の確率密度分布の平均、および分散が分
かっているので、これらを用いて観測データを標準正規
分布に従うデータに変換する。Replace with the normalized double exponential distribution. Since the mean and variance of the probability density distribution of the order statistics that follow the scaled double exponential distribution are known, these are used to convert the observed data into data that follows the standard normal distribution.
■正月ＪＪ口１姐
前記■、■の手順で得たデータ列が標準正規分布に従う
か否かの検定を行うａ Ｎｅｙｍａｎのスムーズ・テス
ト、あるいはＳｈａｐｉｒｏ−ｗｉｌｋの検定を利用す
る。■ New Year's JJ 口 1 8 Test whether or not the data string obtained by the procedures of (1) and (2) above follows a standard normal distribution.a Neyman's smooth test or Shapiro-Wilk's test is used.
■墾ｎ界ＩＬ匿
Ｎｅｙｍａｎのスムーズ・テスト、あるいは５ｈａｐｉ
ｒ。■Kenkai IL Hidden Neyman's smooth test or 5hapi
r.
−ｖｉｌｋの検定の結果、正規性の仮説が棄却されない
ならば、任意の観測時刻におけるバグ推定値の信頼限界
を求める。If the normality hypothesis is not rejected as a result of the −vilk test, then the confidence limit of the bug estimate at any observation time is determined.
実施例
表２は、遅延Ｓ型モデルをあてはめたバグ・データの一
例を示す図で、実際に、表２に示すバグ・データが観測
された。ここで時刻ｔ１はバグの発見された正確な時間
ではなく１時間区間［Ｏｍ ｔ Ｊ ］までにバグが発
見されたことを示す時間の区切りであることに留意する
。Example Table 2 is a diagram showing an example of bug data to which the delayed S-type model was applied, and the bug data shown in Table 2 was actually observed. Note that the time t1 is not the exact time when the bug was discovered, but is a time interval indicating that the bug was discovered within a one-hour period [Om t J ].
時刻はテスト開始からの日数である。したがって表２．
左の３欄は、１日目のデバッグ終了時点での２個のバグ
が発見されたことを、また２日目のデバッグ終了時点で
の６個のバグが発見されたことを示す。The time is the number of days from the start of the test. Therefore, Table 2.
The three columns on the left show that two bugs were discovered at the end of debugging on the first day, and six bugs were found at the end of debugging on the second day.
表２
■：表２に示すバグ・データを、ＡＩＣ（Ａｋａｉｋｅ
’ｓＩｎｆｏｒｍａｔｉｏｎ Ｃｒ１ｔｅｒｉｏｎ：赤
池の情報量規準）を用いて評価し、適合するモデルとし
て遅延Ｓ字型モデルを選択する。非定常ポアソン過程（
Ｎｏｎ−＋１ｏｓＩｅｇａｎｓｏｕｓ Ｐｏ１ｓｓｏｎ
Ｐｒｏｃｅｓｓ）に基づき最尤法で母数を推定すると
、
Ｎ＝３１．２． ｃＢ＝ｏ、ｓｏ４
どなる。Table 2 ■: The bug data shown in Table 2 is
'sInformation Criterion: Akaike's Information Criterion) is used to select the delayed S-shaped model as a suitable model. Unsteady Poisson process (
Non-+1osIegansous Po1sson
Estimating the parameter using the maximum likelihood method based on N = 31.2. cB=o, so4 yell.
■：Ｎは発見されうる総バグ数であるので、整数値でな
くてはならない、推定した総バグ数よりも多くのバグが
発見されると危険を無くすために小数部を切り上げ、Ｎ
＝３２とする。■: Since N is the total number of bugs that can be discovered, it must be an integer value.If more bugs are discovered than the estimated total number of bugs, the decimal part is rounded up to eliminate the risk.
=32.
ここで、ｊ＝１の場合に注目すると１時刻ｔ１までに発
見されたバグは２個であるから、［ｔ、＝０．ｔユニ１
］で発見されたバグは、ｎ＝３２個中２番目にバグが発
見されたときのＩｎ１ｎ（１／ｅｘｐ［−ｅｘｐ（ｘ）
］）の期待値（平均）、および分散はそれぞれ
μｍ＝−３，０２７゜
σ□”＝ ０．６４５０ ＝（０，８０３１）”トナル
、一方、 Ｉｔ ’ｔＪＡ （ｉｉ ｙ 、 Ｉｔ、ｙ
、Ｊｎｌｎ（１／（１÷Φｔ□）ｅｘｐ［−Φｔ１コ）
＝ＩｎＩｎ（１／（１＋０．５０４）ｅｘｐ［−０，５
０４コ）＝ −２，３４６
となる、よって、標準正規分布に従うデータＺｌ ：（
Ｖｘ−μ３２９２）／σ、２．ア＝０．８４８を得る。Here, if we pay attention to the case where j=1, the number of bugs discovered by one time t1 is two, so [t,=0. t uni 1
] is In1n(1/exp[-exp(x)
]) and the variance are respectively μm = -3,027°σ
, Jnln(1/(1÷Φt□)exp[-Φt1ko)
=InIn(1/(1+0.504)exp[-0,5
04 ko) = -2,346 Therefore, data Zl following the standard normal distribution: (
Vx-μ3292)/σ, 2. We obtain a = 0.848.
ｊ＝２の場合も同様に、３２個中６番目にバグが発見さ
れたとみなすことにより、ｚ２が算出できる。このよう
にして１点列（２工、ｚ２．・・・、ｚｌ。）を得る（
表２）。Similarly, when j=2, z2 can be calculated by assuming that the 6th bug out of 32 was discovered. In this way, we obtain a 1-point sequence (2 steps, z2..., zl.) (
Table 2).
■二点列（ＺｉｌＺ２１”’１ＺｌＯ）を用いてＮｅｙ
ｓ＋ａｎのスムーズ・テスト、および５ｈａｐｉｒｏ−
Ｗｉｌｋの検定を行うと、正規性の仮説は危険率５％で
棄却された。■ Ney using a two-point sequence (ZilZ21”'1ZlO)
s+an smooth test, and 5hapiro-
When Wilk's test was performed, the hypothesis of normality was rejected with a significance level of 5%.
すなわち、正規分布に適合しないことがわかった。In other words, it was found that it does not fit a normal distribution.
■： Ｎｅｙｍａｎのスムーズ・テストあるいは５ｈａ
ｐｉｒｏ−Ｖｉｌｋの検定の結果、正規性の仮説が棄却
されたので、ソフトウェアの残存バグの信頼限界（バグ
の推定値の存在範囲）を算出せずに終了する。■: Neyman's smooth test or 5ha
As a result of the Piro-Vilk test, the hypothesis of normality was rejected, so the process ends without calculating the confidence limit of the remaining software bug (existence range of the estimated value of the bug).
％−−米
以上の説明から明らかなように、本発明によると、種々
提案されてきたソフトウェア信頼度成長曲線の適合度を
、順位による誤差分散を考慮して検定することができる
。標本をそのまま用いるため、コルモゴロフ・スミルノ
フ（Ｋｏｌｍｏｇｏｒｏｖ−８■１ｒｎｏｖ）検定方式
やＸ２検定のような情報量損失がなく高い検出力を得る
ことができる。また、バグ推定値の信頼限界も容易に求
めることができる。%--As is clear from the above description, according to the present invention, the goodness of fit of various software reliability growth curves that have been proposed can be tested in consideration of error variance based on rank. Since the sample is used as it is, high detection power can be obtained without loss of information as in the Kolmogorov-Smirnov test method or the X2 test. Moreover, the confidence limit of the bug estimate value can also be easily determined.
これにより開発・生産中のソフトウェアのバグの出現を
予測することができるので、生産物としてのソフトウェ
アの品質管理、生産管理、および原価管理に役立そるこ
とができる利点がある。This makes it possible to predict the appearance of bugs in software during development and production, which has the advantage of being useful for quality control, production control, and cost control of software products.
第１図は４本発明の一実施例を説明するための処理概念
図、第２図は、本発明の実施例として遅延Ｓ字型モデル
をあてはめ、線型変換した信頼度成長曲線とその回帰直
線を示す図である。Fig. 1 is a processing conceptual diagram for explaining one embodiment of the present invention, and Fig. 2 is a reliability growth curve and its regression line after linear transformation by applying a delayed S-shaped model as an embodiment of the present invention. FIG.
Claims (1)
換し、規準化２重指数分布に従うｎ個中ｉ番目の確率密
度分布がｎとｉをどのように変えても正規分布に近似で
きることを用いることにより、正規分布の適合度検定に
帰着させる、順位による誤差分散を考慮したソフトウェ
ア信頼度成長曲線の適合度検定方式。Replace the software reliability growth curve with a normalized double exponential distribution and use the fact that the i-th probability density distribution among n that follows the normalized double exponential distribution can be approximated to a normal distribution no matter how n and i are changed. A goodness-of-fit test method for software reliability growth curves that takes into account rank-based error variance, resulting in a goodness-of-fit test for a normal distribution.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP62109478A JP2693435B2 (en) | 1987-05-01 | 1987-05-01 | Software reliability growth curve fitness test method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP62109478A JP2693435B2 (en) | 1987-05-01 | 1987-05-01 | Software reliability growth curve fitness test method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS63273945A true JPS63273945A (en) | 1988-11-11 |
| JP2693435B2 JP2693435B2 (en) | 1997-12-24 |
Family
ID=14511258
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP62109478A Expired - Fee Related JP2693435B2 (en) | 1987-05-01 | 1987-05-01 | Software reliability growth curve fitness test method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2693435B2 (en) |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110348123A (en) * | 2019-07-11 | 2019-10-18 | 浙江树人学院（浙江树人大学） | A kind of oil-gas pipeline compressional deformation estimation method based on AIC-RBF |
| CN112612719A (en) * | 2020-12-31 | 2021-04-06 | 山西大学 | Method for optimizing and selecting software reliability model through weighting standardization |
| CN113762981A (en) * | 2021-03-30 | 2021-12-07 | 中国人民解放军国防科技大学 | Product credibility calculation method based on exponential distribution |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP4349216B2 (en) | 2004-06-21 | 2009-10-21 | 富士ゼロックス株式会社 | Distribution suitability test device, consumable supply timing judgment device, image forming device, distribution suitability test method and program |
-
1987
- 1987-05-01 JP JP62109478A patent/JP2693435B2/en not_active Expired - Fee Related
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110348123A (en) * | 2019-07-11 | 2019-10-18 | 浙江树人学院（浙江树人大学） | A kind of oil-gas pipeline compressional deformation estimation method based on AIC-RBF |
| CN110348123B (en) * | 2019-07-11 | 2022-12-02 | 浙江树人学院（浙江树人大学） | AIC-RBF-based oil and gas pipeline extrusion deformation estimation method |
| CN112612719A (en) * | 2020-12-31 | 2021-04-06 | 山西大学 | Method for optimizing and selecting software reliability model through weighting standardization |
| CN112612719B (en) * | 2020-12-31 | 2023-09-22 | 山西大学 | Weighted standardized optimization selection software reliability model method |
| CN113762981A (en) * | 2021-03-30 | 2021-12-07 | 中国人民解放军国防科技大学 | Product credibility calculation method based on exponential distribution |
| CN113762981B (en) * | 2021-03-30 | 2023-11-28 | 中国人民解放军国防科技大学 | Product credibility calculation method based on index distribution |
Also Published As
| Publication number | Publication date |
|---|---|
| JP2693435B2 (en) | 1997-12-24 |
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