Assignment 1 Paper clip (1)

1 | P a g e Assignment 1 Group 11: Tejas Wagh (8862184) Idrish Mansuri (8940612) Mugisha Kagdi (8924498)

2 | P a g e Index Sr no. Title Page no 1. Executive summary 3 2 Data 3 2. Data distribution Analysis 4 3. Survival plot 4. Cumulative plot 5. Hazard plot 6. MTTF 6. Conclusion 7. Reference

4 | P a g e Distribution Id plot: which distribution is the best fit for the data. The above graph shows the probability plot. This Anderson-Darling is a measure used to calculate how good a given distribution fits a set of data. The data shows , the lognormal distribution seems to be the bet fit for the data because it has the smallest Anderson- Darling value. The data show Weibull distribution value is 1.3212 which appears in the middle and below the red line. The Loglogistic distribution value is 1.090 which is close to the smallest and appears near to the redline leaving it as the slightly best fit. But Lognormal having the least value appears to be the best fit.

5 | P a g e Data distribution analysis:

7 | P a g e Survival plot: The below graph shows the survival curve. The chances of paper clip sustaining our MTTF of 3 cycles is almost 95%. The analysis is based on the Weibull distribution with shape= 1.32179 and scale= 10.9165 Cumulative plot: The below graph shows the cumulative plot. We can see the probability of paper clip surviving 5 cycles is only 30%. This analysis is based on Weibull distribution with shape= 1.32179 and scale= 10.9165.

8 | P a g e Hazard plot: The below graph shows the hazard plot (rate of failure to time). The graph indicates an increasing failure rate as the number of cycles increases. We can also notice that rate of failure is rapidly increasing after approximately 15 cycles. This analysis is bases on Weibull distribution with shape=1.32179 and scale=10.9165.

10 | P a g e Mean time to Failure: Mean time to Failure: Table of MTTF Standar d Error 95% Normal CI Distribution Mean Lower Upper Weibull 15.398 8 1.63338 12.5083 18.9572 Lognormal 17.084 6 3.02984 12.0684 24.1857 Exponential 15.500 0 2.82990 10.8374 22.1686 Loglogistic 19.477 9 3.44631 13.7701 27.5518 3-Parameter Weibull 15.518 5 1.56348 12.4541 18.5829 3-Parameter Lognormal 15.500 8 1.58049 12.4031 18.5984 2-Parameter Exponential 15.500 0 2.73861 10.9632 21.9142 3-Parameter Loglogistic 15.533 9 1.71946 12.1638 18.9040 Smallest Extreme Value 15.289 6 1.82587 11.7109 18.8682 Normal 15.500 0 1.58026 12.4027 18.5973 Logistic 15.500 0 1.71856 12.1317 18.8683 The analysis of Mean Time to Failure (MTTF) across various statistical distributions—Weibull, Lognormal, Exponential, Loglogistic, 3-Parameter Weibull, 3-Parameter Lognormal, 2-Parameter Exponential, 3- Parameter Loglogistic, Smallest Extreme Value, Normal, and Logistic—reveals that the mean MTTF estimates are generally consistent, ranging from mid-15s to high-19s. The Weibull and its 3-Parameter counterpart, along with the Normal and Logistic distributions, offer relatively precise MTTF estimates with narrower CIs, suggesting a higher level of confidence in these values. Conclusion According to the study, a Weibull distribution that is derived from the distribution ID plot best fits the dataset. We acquired the statistics based on the Weibull distribution from the probability overview map. The probability that the paperclips would not break was then determined to be 3 cycles from the survival , as inferred from the hazard plot, and the probability that the paperclips would break by 3 cycles was determined to be approximately 16.58% from the cumulative plot. Its reduced Anderson-Darling value, good plot fit, and comparable MTTF estimations between models point to its dependability. The Weibull

11 | P a g e distribution, with an estimated MTTF of about 15.40 cycles, offers helpful insights regarding paperclip dependability, which are crucial for quality control and product design in this experiment.